Instructor’s Manualfor Price Theory and Applications by Steven E. Landsburg Ninth Edition Chapter One: Supply, Demand, and Equilibrium General Discussion Even after a course in principles, many students are confused about the fundamentals of supply and demand. The most frequent sources of difficulty are: 1) The distinction between demand and quantity demanded. The text places consid- erable emphasis on this. I always tell my students that a failure to grasp this distinction results in the ability to make arguments that sound very logical but are in fact incorrect; problem 5 at the end of the chapter provides a good example. I have occasionally made it a semester-long assignment to collect examples of such fallacies from the popular press; students with subscriptions to the New York Times or the Wall Street Journal have ample raw material to work from. 2) A failure to understand that the equilibrating process does not affect the supply and demand curves. The story that we tell about price adjustment following a tempo- rary disequilibrium does not involve any changes in the quantities that people desire to exchange. 3) A failure to understand the role of price adjustment from a point of disequilibrium in the supply and demand model. It is important for students to understand that in this simple model we always assume that all markets are in equilibrium. We do tell stories about what we think would happen out of equilibrium (demanders bidding up prices that are too low or suppliers bidding down prices that are too high), but the purpose of these stories is only to motivate the assumption that disequilibrium does not occur. Students sometimes come away with the false impression that the details of price adjustment are an integral part of the model and that the model attempts to describe the path to equilibrium. It is important to be on guard against this. 4) An incorrect approach to comparative statics. Ask students what will happen to the price of bread following a rise in the price of butter. Some will respond that bread is now less desirable, so that people want less of it, which causes the price to be bid down. Others may respond that in that case, less bread will be produced, and this fall in quantity will lead to a higher price. This in turn calls more bread into the market, which causes the price to be bid down, which causes... It is distressingly common for students to begin reasoning in such a circle, stop at an arbitrary point, and think that they have reached a correct conclusion. I stress to my students that when you are asked how the price of bread will react in a given circumstance, it is never correct to begin by thinking about the price of bread. One must begin by thinking about the effects on supply and demand (in this case, demand is down and supply is unchanged) and only then infer the effect on price (in this case, price is down). Many students are bothered by two aspects of this analysis. First, it will seem to them (correctly) that each step in the earlier, convoluted analysis is an important one and that all of these counteracting effects need to be taken into account. They believe (incorrectly) that the supply and demand analysis fails to do this. Second, they simply will not see any reason why the supply and demand analysis should be preferred to the more naive approach. To address these questions, I sometimes ask students to volunteer the various direct and indirect ways in which the price of bread is affected by an increase in the price of butter. (In fact, this works even better if you use a slightly more complicated example in which both supply and demand change simultaneously.) I list them on the blackboard 1–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. (1: lower demand leads to lower price; 2: less bread produced causes price to be bid up, etc.) When the list is long enough, I point out that no one could possibly sort out all of these countervailing effects and come to a conclusion without some additional device. I then point out that supply and demand analysis is such a device. The key (and for many students, this must really be stressed) is that in the single shift of the demand curve, we really do take account of all of these effects simultaneously. The fact that all of the effects are important is exactly what makes it both correct and necessary to resort to curve-shifting. Teaching Suggestions 1) Regarding the seat belt example on pp. 8-9: Someone (I think Armen Alchian) has suggested that the best way to prevent highway deaths might be to require that every car have a spear mounted on the steering wheel aimed directly at the driver’s heart. Surely this would reduce the number of accidents. This observation always gets a laugh and makes the point. 2) For another example of how people react to prices in non-market situations: There is apparently a psychology experiment in which subjects are given cups of coffee and told that they can keep the cups. They are not warned that the cups are extremely hot. When the cup is clearly inexpensive, subjects usually drop it; when it is made of fine china, they manage to hang on. I wanted to include this example in the book but was not able to track down a reference on time. 3) Along the same lines, you can cite a paper of Viscusi in the American Economic Review : Apparently when child safety caps on medicines are made more difficult to re- move, sufficiently many people stop using the caps at all that there is an increase in the number of accidental poisonings. 4) For some students it might be necessary to stress that equilibrium can occur at any price and quantity, and that unusually high or low prices do not imply disequilibrium. For example, if wages are very low and few people are working, some students want to jump to the conclusion that there is disequilibrium in the labor market. Point out to them that a low demand curve for labor explains the same phenomenon. 5) To drive home the inverse relationship between price and quantity demanded, you might mention that in August, 1990, East German taxicab drivers went on strike to demand lower fares. 6) Here is a slightly different way to present the material in Exhibit 1–10 (the economic incidence of a tax is independent of its legal incidence). Begin by drawing a graph showing just the original supply and demand curves. Note that ultimately the suppliers must be on their supply curve and the demanders must be on their demand curve; otherwise prices will adjust. Now note that a 5 cent tax, regardless of its legal nature, drives a 5 cent “wedge” between the suppliers’ price and the demanders’ price. Take a piece of chalk, hold it vertically, and say that its length is “5 cents.” Then hold the chalk vertically between the supply and demand curves near the price axis, and slowly move it rightward until its top and bottom just touch the demand and supply curves. Conclude that you have found the post-tax equilibrium. Now note that in order to find this equilibrium, you never had to ask what sort of tax was being imposed; thus such information must be irrelevant. 1–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Suppose a new fat substitute comes on the market, making it easy to produce low- calorie hamburgers, french fries, milkshakes, and so forth. True or False: The average American will weigh less after this product appears on the market. 2. True or False: If 1000 potatoes per day are sold in Des Moines, Iowa, and if a new supplier decides to sell 200 potatoes per day, then 1200 potatoes per day will be sold. 3. True or False: If a frost wipes out half the Florida orange crop, then some people who want to buy oranges will not be able to. 4. True or False: If we observe a reduction in the number of cars being purchased, then we should expect this change in demand to lead to a fall in price. 5. True or False: If the demand for lettuce falls, the price will fall, causing the demand to go back up. 6. True or False: According to the laws of supply and demand, when the price of a good rises, less of that good will be sold. 7. True or False: In the cities, there are more medical services provided than there are in rural areas. Nevertheless, the price of medical services is higher in the cities. This indicates that our simple “supply and demand” story does not apply to markets for things like medical care. 8. True or False : If both the quantity consumed and the price of medical services have risen in the last fifteen years, then the demand curve for medical services must have shifted. 9. A major daily newspaper reports that “although home sales are down, home prices continue to rise, in apparent violation of the law of supply and demand.” Does this observation in fact violate the laws of supply and demand? 10. Ice cream is more expensive in New York than in Iowa, but nevertheless New Yorkers eat more ice cream than Iowans do. True or False: This is contrary to what a simple “supply and demand” analysis would predict. 11. If the price of ice cream is higher in New York than in Iowa, it must be because the demand for ice cream is higher in New York. 12. In 2003, mad cow disease was first detected in American cattle. a) What do you expect happened to the demand for American beef? b) What do you expect happened to the price of American beef? c) In fact, in the aftermath of the mad cow scare, the price of American beef fell by about 15% and Americans’ beef consumption increased. Can you reconcile this observation with the laws of supply and demand? (Hint: the price of beef is determined in a world market, whereas the demand curve is the sum of American demand and foreign demand.) 13. If the demand curve for avocados is horizontal, then an excise tax on avocados will be passed on entirely to demanders. 14. If the supply curve for corn is perfectly horizontal, how will an excise tax affect the market price of corn? What about a sales tax? 15. If the supply curve for corn is perfectly vertical, how will an excise tax affect the market price of corn? What about a sales tax? 1–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 16. The following diagram shows the supply and demand for cupcakes (with quantity measured in dozens). Price ($) 8 S 7 6 5 4 3 2 1 D Quantity a) Suppose the government imposes a new sales tax of $6 per dozen cupcakes. What will the new price of cupcakes be? b) Suppose the government imposes a new excise tax of $6 per dozen cupcakes. What will the new price of cupcakes be? 17. The demand and supply curves for oranges in Lower Slobbovia are identical to the demand and supply curves for oranges in Upper Slobbovia. One day, the Lower Slobbovian demand curve shifts right by 150 oranges, while the Upper Slobbovian supply curve shifts left by 150 oranges. a) Use a diagram to illustrate the effect on the price of eggs in Lower Slobbovia. Use a separate diagram to illustrate the effect on the price of eggs in Upper Slobbovia. b) In which country does the price change by more? Justify your answer by referring to the locations of specific points in your diagrams. 18. The demand and supply curves for widgets in Upper Slobbovia are identical to the demand and supply curves for widgets in Lower Slobbovia. In Upper Slobbovia, every buyer of widgets receives a 5-cent-per-widget subsidy from the government. In Upper Slobbovia, every seller of widgets receives a 5-cent-per-widget subsidy from the government. True or False: The price of a widget in Upper Slobbovia is exactly five cents more than the price of a widget in Lower Slobbovia. Use a graph to justify your answer. 19. True or False: Some cities raise revenue by levying a tax on employers equal to a certain number of dollars per employee per year. This is a good thing for workers, because workers are not taxed. 20. Coconino County raises revenue through a tax on workers: everybody who has a job in Coconino County must pay a tax of $25 per year. It has been proposed that this tax be abolished and replaced by a tax on businesses equal to $25 per employee per year. True or False: Although this change sounds like a good thing for workers, it might actually turn out to be bad for them, since the number of jobs would go down. 1–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 21. Coconino County raises revenue through a tax on workers: everybody who has a job in Coconino County must pay a tax of $25 per year. It has been proposed that this tax be abolished and replaced by a tax on businesses equal to $25 per employee per year. True or False: Although this change sounds like a good thing for workers, it might actually turn out to be bad for them, since it could cause wages to fall. 22. The government of Fredonia wants to increase employment and is deciding between two plans. Plan I is to encourage hiring by giving employers $1 for each hour of labor that they hire. Plan II is to encourage entry into the labor market by giving workers $1 (in addition to their salary) for every hour that they work. a) Show separately how each plan affects the demand for labor, the supply of labor, and the equilibrium wage rate. b) Which plan is better for workers? Which plan is better for employers? c) Referring to your graphs from part a), carefully explain how you were able to draw the conclusion in part b). 23. The government of Coconino County wants to encourage firms to hire more workers. To accomplish this, each firm receives a government subsidy of $100 per year for each worker on the payroll. To raise the funds for this program, everybody who has a job in Coconino County must pay a $100 per year “employment tax”. Recently, a city councilman has proposed abolishing the entire program (eliminating both the subsidies to firms and the tax on workers). True or False: If the councilman has his way, there will be fewer jobs in Coconino County. Justify your answer carefully, by looking at the effects on both the supply and demand for labor. 24. Suppose that for some reason, Canadian companies want to sell exactly 100 widgets per year in the U.S., regardless of the price. American widget producers like to produce more widgets when the price goes up. a) In the U.S. widget market, draw the Canadian companies’ supply curve and the overall supply curve. Now suppose that the U.S. government wants to improve the fortunes of U.S. widget- makers, and is considering two plans to accomplish this. Under Plan A, all Canadian imports will be banned. Under Plan B, the U.S. government will purchase 100 widgets per year from American manufacturers at whatever is the going price. b) Use supply and demand diagrams to illustrate the effects of these two plans. Which is better for the widget-makers? How do you know? 25. Suppose that the only way to reach a certain restaurant is by train, and the train fare is $3. One day a law is passed requiring the restaurant owner to provide free transportation to his restaurant, which he does by making an arrangement with the railroad whereby his customers ride free and he pays the $3 fare per customer directly to the railroad. a) What does this do to the supply curve for restaurant meals? b) What does this do the demand curve for restaurant meals (Hint: It does not stay fixed.) c) What does this do to the price and quantity served of restaurant meals? d) Of the following, who benefits and who loses as a result of this law: The restau- rant owner, the restaurant customers, the railroad? 26. Apples are currently subject to a sales tax of 10 cents per apple. They sell for 25 cents apiece (that is, to buy an apple, the consumer must pay 25 cents plus 10 cents sales tax). 1–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) Suppose the sales tax is eliminated. How much can you say about the new price of apples? b) Suppose the sales tax is replaced by an excise tax of 10 cents per apple. How much can you say about the new price of apples? 27. At a price of $15,000 apiece, Japanese producers are willing to sell any quantity of compact cars that Americans want to buy. True or False: An excise tax on Toyotas sold in the United States would be paid entirely by Americans. 28. The following diagram shows the demand and supply for widgets: a) Suppose the government imposes a sales tax of $5 per widget. What is the new price of widgets, and how many are sold? Briefly explain how you got your answer. b) Suppose instead that the government imposes an excise tax of $5 per widget. What is the new price of widgets, and how many are sold? c) Which tax is better for consumers? Explain your answer in one sentence, based on your answers to parts a) and b). 29. The market for yachts is in equilibrium at a quantity of 500 per year; all 500 are bought by private citizens. Suppose the U.S. government announces that henceforth it will buy 150 yachts per year (regardless of the price). a) What happens to the demand for yachts? b) Now how many yachts are bought by private citizens? (Hint: The number bought by private citizens is equal to the total number bought minus the the number bought by the government.) If it is possible to answer this question with an exact number, do so. Otherwise, give a range of numbers (like “between 1,000 and 2,000”). Explain how you got your answer. 30. Suppose that a sales tax would cause the price of an apple to fall by 3 cents. What would be the effect of an excise tax of 10 cents per apple? (Remember that “price” means the pre-tax price.) 1–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 31. Suppose that a 40 cent excise tax on apples would lead to a 35 cent increase in the market price of apples. How would a 40 cent sales tax affect the market price of apples? (The “market price” means the price paid by the buyer to the seller, not including any taxes paid by the buyer.) 32. True or False: If the demand curve for rabbit fur is perfectly horizontal, then an excise tax on rabbit fur would be passed on entirely to demanders. 33. Two presidential candidates have offered different economic platforms. Paul Simon, a Democrat, proposes to help the working class by giving each worker an income tax reduction of $1 for each hour that he works. Art Garfunkel, a Republican, proposes to encourage employment by giving every firm a subsidy of $1 for each hour of labor that it hires. a) Illustrate the effects of the Simon plan on the demand and supply curves for labor. b) Illustrate the effects of the Garfunkel plan on the demand and supply curves for labor. c) True or False: Workers might actually prefer the Garfunkel plan because it encourages firms to offer more jobs at higher wages. Justify your answer carefully. 34. The government is considering an economic plan under which consumers will pay a new sales tax of 50 cents per gallon of gasoline. The revenue will be used to pay subsidies to gas station owners, who will receive 50 cents from the government for every gallon of gas that they sell. a) How does this plan affect the demand curve for gasoline? b) How does this plan affect the supply curve for gasoline? c) True or False: Although this plan looks like a good thing for gas station owners, it might actually hurt them because demanders will buy less gasoline. 35. Suppose that it costs car manufacturers $1,000 to install an air bag in a car, and that each customer values an air bag at $500. A new law requires every car to have an air bag. a) Show how the new law affects the demand and supply curves for cars. b) What happens to the price of a car after the law is passed? Does it go up or down? Does it change by more or less than $500? Does it change by more or less than $1,000? c) Are consumers made better or worse off by this law? Justify your answer. 36. Suppose that wheat is purchased only by poor people, whose demand for wheat is given by the following chart: Price Quantity $1 8 bushels 2 7 3 6 4 5 In the spirit of Christmas, a coalition of rich people has decided to buy wheat at the going market price (whatever that price happens to be) and resell it to poor people at half that price. Moreover, they will buy and resell as much wheat as poor people care to purchase. a) List the coordinates of four points on the new demand curve (that is, the rich people’s demand curve) for wheat. b) Suppose that the supply curve for wheat is vertical at a quantity of 7. Do the poor benefit from the generosity of the rich? 1–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. c) Suppose instead that the supply curve for wheat is horizontal at a price of $2. Do the poor benefit from the generosity of the rich? 37. Apples currently sell for 20 cents apiece. Label each of the following statements certainly true, possibly true or certainly false and justify your answers: a) A 10 cent sales tax would cause the price to fall to 15 cents, and a 10 cent excise tax would cause the price to rise to 25 cents. b) A 10 cent sales tax would cause the price to fall to 14 cents, and a 10 cent excise tax would cause the price to rise to 26 cents. c) A 10 cent sales tax would cause the price to fall to 11 cents and a 10 cent excise tax would cause the price to rise to 21 cents. d) Neither tax would affect the price. 38. Cars currently sell for $1500 apiece, plus $500 sales tax. a) If the sales tax is eliminated, what can you say about the new price of cars? b) If the sales tax is eliminated and replaced by a $500 excise tax, what can you say about the new price of cars? c) If the sales tax is eliminated and replaced by a $1000 excise tax, what can you say about the new price of cars? co 39. Suppose a new law requires students to give each of their professors a $100 tip at the end of the semester. a) What happens to the demand for college courses? b) What happens to the supply of college courses? c) Are students made better or worse off as a result of this law? What about professors? Justify your answer. 40. Apples currently sell for 50 cents apiece. The government is considering three different plans. Plan A is to subsidize apple purchases; every time you buy an apple, you get a dime back from the government. Plan B is to subsidize apple sales; every time you sell an apple, you get a dime back from the government. Plan C is to tax apple sales: Every time you sell an apple, you pay a dime to the government. When Plan A is instituted, the price of apples rises to 57 cents. a) What would have happened to the price of apples if the government had insti- tuted Plan B instead of Plan A? b) What would have happened to the price of apples if the government had in- stituted Plans A and C simultaneously instead of Plan A alone? Justify your answer. 41. Suppose a new law requires every college professor in your city to wear a special uniform while teaching. These uniforms must be rented from the mayor’s brother at a cost of $1 per hour. With the law in effect, universities pay professors $5.40 per hour. a) If the law were repealed, how much would professors get paid? b) If the law were replaced by a new law requiring the universities to pay for the uniforms (at the same $1 per hour), how much would professors get paid? Each part your answer should be an exact number if possible, or a range of numbers otherwise. (Hint: Remember that the professors are the suppliers of teaching services and universities are the demanders.) 42. The federal government wants to improve the fortunes of domestic car manufacturers and is considering two plans to accomplish this. Under Plan A, every purchaser of a domestic car would receive a $100 rebate from the government. Under Plan B, car manufacturers would receive a $100 rebate from the government for every car they sell. 1–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) How does Plan A affect the demand for cars? b) How does Plan B affect the supply of cars? c) Compare and contrast the effects of the two plans. 43. Gasoline currently sells for $3 a gallon. Suppose the government simultaneously institutes a sales tax of 10 cents per gallon and an excise subsidy of 10 cents per gallon. (The “excise subsidy” means that every time you sell a gallon of gasoline, you get a dime from the government.) What is the new price of gasoline? Are demanders helped or hurt by this pair of policies? What about suppliers? 44. The diagram below shows the demand and supply for hamburgers on your college campus. Price ($) 11 10 9 8 S 7 6 5 4 3 2 1 D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Quantity a) Suppose your college announces a new plan to improve student life: Any time you buy a hamburger anywhere on campus, you can bring your receipt to the administration building and trade it for a $5 bill. How much does the price of hamburgers change? b) Suppose instead that the college announces a different plan: It will pay $5 per hamburger to anyone who sells hamburgers on campus. How much does the price of hamburgers change? c) Which plan is better for the students who like to eat hamburgers? Explain your reasoning. 45. A new law requires each firm to provide its workers with free parking spaces. These spaces are worth $200 a year to the workers and cost firms $500 a year to provide. Is this law good for workers? Is it good for firms? Justify your answers. 46. On Monday, the equilibrium quantity of widgets is 200. On Tuesday, the supply curve shifts right by 50 widgets, and the new equilibrium quantity is 230. On Wednesday, the supply curve returns to its Monday position, and the demand curve shifts left by 30 widgets. a) Draw separate graphs to illustrate the situations on Tuesday and Wednesday. b) What is the equilibrium quantity on Wednesday? c) Carefully justify your answer to part b) by comparing the locations of specific points on your graphs from part a). 1–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 1–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 1 1. False, in the sense of “not necessarily true.” A fuel-efficient car reduces the price of “miles driven,” so people choose to drive more miles. More driving with greater fuel efficiency could lead to either an increase or a decrease in the amount of gasoline consumed. If the demand curve for “miles driven” is particularly steep, do Americans increase or decrease their use of gasoline? What if it is particularly shallow? 2. False (in the sense of: not necessarily true). The existence of the new birth control method lowers the “price” of those activities that are capable of producing unwanted babies, and so leads to greater participation in those activities. Since more sexual encounters take place, but each encounter has a lowered probability of leading to an unwanted birth, the number of unwanted births could go either up or down. To put it another way: after the discovery, there are two sorts of occasions on which people will use the new method of birth control. First there are those occasions when they would have otherwise used a less effective method. Second, there are those occasions on which they would otherwise have refrained from sex altogether. On the first sort of occasion, the new method leads to fewer unwanted pregnancies than previously, but on the second sort of occasion it leads to more. The example is analogous to the “reckless driving” example in the text. Some- times students attempt to carry the analogy too far by asserting that the number of unwanted babies must stay about the same (just as, after safety equipment was introduced, the number of driver deaths stayed about the same). But there is no reason why this needs to be true. We have one reason to believe that unwanted pregnancies will decrease (better birth control) and another to believe that they will increase (more people taking chances). Either effect could be bigger than the other, or they might just happen to cancel each other out, as appears to have been the case with auto safety. Sometimes students attempt to argue that the new method might have no effect since some people will refuse to use it, for reasons of religion or aesthetics. But this is not a good answer, since the fact that some people will not use the method doesn’t prove anything. In order to draw any conclusions from this sort of argument, it would be necessary to maintain that nobody will use the new method, and this seems implausible. 3. Some other “goods” may be sexual relations, clean air, warm weather or marriage. 4. False. A rise in price leads to a fall in quantity demanded, not a fall in demand. The initial price rise must be caused by either a shift in demand or a shift in supply. The new equilibrium is reached, and no further shifts are needed. 5. a) Supply falls so price rises and quantity falls. b) Demand rises so price rises and quantity rises. c) Demand and supply both fall. Quantity falls and price could go either way. d) As farm workers move to the city to earn the higher wages, the supply of corn falls. Price rises and quantity falls. Sometimes students argue that wealthier industrial workers will demand more corn and therefore the demand curve shifts out as well. This is a commendable insight, but it overlooks the fact that those higher wages 1–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. are paid by employers, who might now reduce their demand for corn, offsetting the additional demand by the workers. Therefore, unless we know more about why wages went up, we need not expect the market demand curve to shift. 6. a) Demand falls, price falls and quantity falls. b) Supply increases, price falls and quantity rises. c) Demand increases, price increases and quantity increases. d) Demand increases, price increases and quantity increases. e) Supply increases, price falls and quantity rises. 7. False. The demand curve for apartments shifts downward; therefore the price falls. 8. False. This could be explained, for example, if the supply curves are identical in both places, but the demand curve is higher in New York than in Iowa. 9. False. We are told only that the quantity has fallen. This might equally well be caused by a decrease in demand (in which case price must fall) or by an decrease in supply (in which case the price must rise.) 10. The demand curve for cigarettes shifts rightward by 10 cigarettes per year. The equilibrium quantity of cigarettes increases by less than 10 per year. The number of cigarettes smoked by others is equal to the new equilibrium quantity minus the ten that are thrown away. Thus Nosmo is correct in believing that he reduces the number of cigarettes that other people smoke, but incorrect in believing that he reduces that number by 10 per year. 11. False, the fall in demand would reduce the equilibrium price which would in turn reduce the quantity supplied. As a result, there will not be an additional pound of meat for someone else to eat. 12. False. The supply of housing shifts rightward by 1000, so the equilibrium quantity of housing shifts rightward by less than 1000. 13. P= $ 2.00 and Q= 7 lbs. 14. a) $.50 $2.00. 4 pounds. b) $2.50, $.50. 4 pounds. c) In either case you would not care. 15. a) After the demand curve drops vertically $5, it crosses the supply curve at a quantity of 3 and price of $3. Therefore the new price is $3. b) After the supply curve rises vertically $5, it crosses the demand curve at a quantity of 3 and a price of $8. Therefore the new price is $8. c) With a sales tax, consumers pay $3 plus $5 tax. With an excise tax, they pay $8 plus $0 tax. Either way they pay $8, so both taxes are equally bad for consumers. 16. False. The Upper Slobbovian demand curve is steeper, so quantity falls by less in Upper Slobbovia. 17. A sales tax has no effect on the price; an excise tax is passed on entirely to the consumer. So, for example, an excise tax of $1 per head of lettuce causes the price to rise by $1. Regarding the excise tax, students commonly reach the correct answer while offering a reason that is quite mistaken. Their (incorrect) argument is this: A ver- tical demand curve indicates that demanders will pay any price at all for avocados; therefore suppliers are able to pass the tax on completely without losing any sales. The argument is incorrect because it overlooks the fact that suppliers compete with each other. Any given supplier will indeed lose sales if he fails to match the going market price. 1–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Indeed, to see that the argument cannot possibly be correct, ask yourself why suppliers don’t raise their prices prior to the tax increase. If suppliers charge $1 originally and $1.25 after the imposition of a $.25 tax, why don’t they charge $1.25 (or more) even before the tax is imposed? The reason is that price is determined not by individual suppliers, but by the intersection of supply and demand. 18. a) The demand curve shifts vertically upward a distance $50. The quick way to see this is to remmember that a $10 sales tax shifts the demand curve down $10, and a $20 sales tax shifts the demand curve down $20, so a sales tax of minus $50 (as in the problem) should shift the demand curve down a distance -$50, which is to say, up a distance $50. If that’s too glib for you, you should be able to make an argument from first principles, mimicking the argument in Exhibit 1.3. b) The new price is higher than the old price, but less than $50 higher. 19. a) The supply curve shifts downward a vertical distance $50. b) The new price is lower than the old price, but less than $50 lower. 20. The diagram below shows the effects of the subsidy to buyers from problem 18 and the subsidy to sellers from problem 19. The two darkened points in the left-hand panel are identical to the two darkened points in the right-hand panel, because in each case they are located exactly $50 apart, with one on the old demand curve and one on the old supply curve. In the left-hand panel, consumers care about the price minus the subsidy, i.e. the price at the lower of the two darkened points. In the right-hand panel, consumers care about the price, i.e. the price at the lower of the two darkened points. Because these two prices are the same, consumers are equally well off under either subsidy. 21. The excise tax shifts the supply curve, which now crosses the demand curve at a lower quantity but still at the original price. So the price does not change and demanders (who care only about the price, not the tax) are unaffected. 22. False. This is true if “high” is replaced with steep and “low” is replaced with flat. 23. The price would fall to 13 cents apiece. 24. a) and e) are possibly true. b) and d) are certainly false because a sales tax cannot cause a price increase. c) is certainly false because an excise tax cannot cause a price decrease. 25. a) The excise tax has caused the price to rise by less than $15, which means the original price is between $15 and $20. When the excise tax is repealed, the price falls back to this original price, i.e. somewhere between $15 and $20. b) The new price will be $5 lower than it is under the excise tax, i.e. it will be $15. c) Starting from a graph that shows the $5 excise tax, the supply curve now shifts upward another $3, so the price rises, but by less than $3. The new price is between $20 and $23. 1–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 26. The new price will be somewhere between $5 and $9. Here is the picture: S Price S' 10 9 New Price 5 D D' Quantity 27. False. The supply and demand curves both shift downward a distance 50 cents. Therefore the entire picture shifts down 50 cents, so the new equilibrium is 50 cents directly below the old one. In other words, the quantity hasn’t changed. 28. False. The excise tax causes the supply curve to shift upward and the sales tax causes the demand curve to shift downward. If you draw some pictures with, for example a very flat demand curve and a very steep supply curve (or vice versa) you’ll see that the price can go either up or down. 29. a) The price rises. b) The price rises. c) Both price increases are equal. This is because they both occur at that price where the horizontal distance between the original supply and demand curves is exactly 100. 30. a) It means that everyone will have exactly the same take-home pay regardless of which plan is chosen. Also, employers will have exactly the same labor costs re- gardless of which plan is chosen. For example, if a tax on workers causes wages to rise to $6 per hour, then a tax on employers will cause wages to fall to $5 per hour; either way, workers receive a take-home (after-tax) pay of $5 per hour and employers spend $6 per hour to hire labor. b) You should draw the demand and supply curves for labor. A tax on workers causes the supply curve to rise vertically by $1 and a tax on employers causes the demand curve to fall vertically by $1. The resulting prices to suppliers and demanders can be shown to be independent of the choice of tax via reasoning as in Exhibit 1-10. 1–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 31. a) Demand shifts up by $50. Supply shifts vertically up by $200. b) The new price of a shower is between $550 and $700. (See the picture below.) c It is bad for consumers, who pay more than $50 for a digital control they value at $50. It is also bad for suppliers, who enjoy a price increase of less than $200 though their costs increase by $200. PRICE S' S 700 NEW PRICE 550 500 D' D QUANTITY Answers to Numerical Exercises N1. P = $1, Q = 800 oranges/day. N2. Supply: Q = 800 · P − 400; Demand: Q = −200 · P + 1, 000. P = $1.40, Q = 720 oranges/day. $ .90. N3. Supply: Q = 800 · P ; Demand: Q = −200 · P + 900. P=$.90, Q = 720 oranges/day. $ .90. N4. Supply: Q = 800 · P − 160; Demand: Q = −200 · P + 940. P = $1.10, Q = 720 oranges/day. $ .90. 1–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Two: Prices, Costs, and the Gains from Trade General Discussion and Teaching Suggestions 1. The carpenter-electrician example is cooked up to come out neatly, so that there are gains from trade when the two tasks are exchanged at a relative price of one for one. Some ambitious students will try it with other numbers and will be distressed to find that things don’t work out so well. Refer them to the numerical exercise at the end of the chapter for a full explanation. 2. A majority of students find the carpenter-electrician example surprising but clear. A few will argue vehemently against the conclusion. Often their arguments will revolve around the possibility of one agent’s “paying” the other to perform a task. (For example, the electrician, who has become wealthy through his superior skills, pays the carpenter to do all of the work while he goes to the Riviera; or, the carpenter, who is such a bumbler, pays the electrician to get all of the jobs done right.) The correct response is that “payment” must consist of the delivery of some good. For simplicity, we have assumed that the only two goods in the world are rewiring jobs and paneling jobs. If the student insists on introducing another good to be used as a medium of exchange—say, bananas—then we must add another row to the tables in Exhibit 2–2, for “growing bananas” (in addition to paneling and rewiring). This will complicate the example, but will not change the essential conclusion. 2–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Comment briefly on the merits of the proposal in the following letter to the editor of the Des Moines Register : One of the reasons Iowa farmers are suffering economically is because we are buying too much food which has been processed in other places while we are selling our raw products, i.e., corn, soybeans and livestock, for whatever “the market” dictates. The solution is for groups of agreeable Iowans, including women and older teenagers, to incorporate and start producing a finished food, i.e., specials breads or pastries, canned or frozen foods or vegetables, corn meal, tofu, etc. Sell these at farmer’s markets, for school lunches, for food stamps, per- haps the World Trade Center, eventually! —Mildred Conley 2. True or False: A rational society will use its most fertile land for agriculture. 3. Dell computers contain hard drives made by other manufacturers. True or False: If Dell made its own hard drives, Dell computers would be cheaper. 4. True or False: Consumers pay higher prices in retail markets than they would if they could buy directly from wholesalers, because they have to pay enough to cover two profit margins. 5. Explain exactly where the following argument goes wrong: The Anderson- Little clothing store buys clothes directly from the manufacturers, whereas Brand X clothing stores buy from middlemen. In each case, there are the same costs of producing, shipping, and marketing the clothes, but with Brand X’s system there is also the additional cost of supporting the middlemen. Therefore, clothes will be cheaper at Anderson-Little. 2–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 2 1. The relative price of tea decreased. The relative price of Civics increased. 2. You may conclude that he is confused. If the relative price of widgets in terms of gadgets has risen, then the relative price of gadgets in terms of widgets must have fallen. 3. The difference will be smaller. 4. The logic of the “good and bad oranges” example (at the end of Section 2.1) suggests that the average quality of liquor should have risen. But that logic need not apply. It costs about the same to ship a good orange or a bad orange. It does not cost about the same to hide the Jack Daniels distillery and a bathtub full of gin. So: Not necessarily true. 5. There will be a greater percentage of childless couples at the cheap movie. For a childless couple, a show might cost 10 times as much as a movie; add the cost of a babysitter and the show now costs less than ten times as much. So for a childless couple, the show is more expensive relative to the movie (and the movie is cheaper relative to the show) than it is for a couple with children. 6. False. The gains from trade arise from comparative advantages, not absolute advantages. 7. False. If it costs Dryden $10 an hour to rent time on printing presses, then it costs West $10 an hour to use its own presses — because the cost of using them is the forgone opportunity to rent them to Dryden. 8. False. Suppose that the going wage for child labor on farms is $5 per hour. Then the farmer without children must pay $5 to employ someone else’s children; the farmer with children must forgo $5 per hour (which he could earn by renting his children out to neighboring farmers) to employ his own children. Both face the same cost of $5 per hour. Some students argue that the farmer with children incurs the costs of feeding, housing, and education. However, it is not correct to count these among the costs of putting the children to work, since they must be paid whether the children work or not. Other students argue that the farmer with children is wealthier at the end of the year since he makes no cash payments to hire labor. Whether or not this is true, it is irrelevant to the question. The question does not ask which farmer is wealthier; it asks only which farmer has higher costs of harvesting. The answer is that both have the same costs. 9. False, in the sense of “not necessarily true.” The statement of the problem omits the key information that Mary is a highly skilled neurosurgeon, whereas George can do nothing except type. Mary’s greater typing speed does not imply that she has a comparative advantage at typing. Some students argue that if you are an employer who only wants to hire a typist, and if George and Mary are available at the same wage rate, then yes, it makes more sense to hire Mary as a typist than to hire George. But even this strained interpretation does not lead to the alleged conclusion. If you can really hire Mary at typist’s wages, then you should set her to performing brain surgery, 2–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. collect her fees as revenue to your firm, and use a small part of that revenue to hire George to do the typing. 10. False. The students with the most talent for medicine need not have a comparative advantage in medicine. 11. False, in the sense of not necessarily (or even probably) true. If the people of the country are desperate for food, they ought to engage in that activity which will produce the most food. That activity might be growing food, or it might be producing decorative jewelry and trading it for food. 12. a) 400 bushels of corn. 300 bushels of corn. Oklahoma. b) Iowa. c) In Iowa 7.6 acres must be used while in Oklahoma 22 acres must be used. d) Iowa has .4 extra acres and Oklahoma has 2 extra acres. 13. False. Except in the hairline case in which each country has the same costs for all activities, the country must have a comparative advantage in something (see Exhibit 2.2). 14. False. This puts the Winkies at a comparative disadvantage in producing auto- mobiles but a comparative advantage in producing other goods. Thus, the gains from trade makes both the Winkies and the Munchkins better off. 15. False. People trade for two reasons, one of which is different tastes. Some people will choose inferior housing in order to have better cars, or more books, or fancier vacations. One student answered this question by saying “False, because there are some people who, no matter how high their incomes, would still choose to live in the most disgusting, degrading, infested, and putrid environments imaginable.” An asterisk pointed to a footnote at the bottom of the exam paper which read, “For example, my uncle.” Answers to Numerical Exercises N1.a) Rewiring Paneling Electrician 1/2 Paneling 2 Rewirings Carpenter 2/3 Panelings 3/2 Rewirings b) The electrician. The carpenter. c) Without Trade With Trade Electrician 15 hours 10 hours Carpenter 25 hours 30 hours The electrician benefits from this trade, but the carpenter does not. 2–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. d) Without Trade With Trade Electrician 15 hours 12 hours Carpenter 25 hours 24 hours Both gain from this trade. 2–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Three: The Behavior of Consumers What’s New in This Edition Much of this chapter has been spruced up for this edition. The overall flow of ideas remains unchanged, but I think the presentation is substantially crisper now. Some of the rather difficult material on different tax regimes has been moved from the text to the problem set. General Discussion and Teaching Suggestions 1) Although the text stresses that opportunities and constraints are determined entirely independently, the point can never be overstressed. 2) My own teaching strategy has been to cover the basics (Sections 3.1 and 3.2) and then to assign some challenging problems that force students to think about the meaning of it all. Since many students have no idea where to begin, I have them work in groups of 4 or 5, with about a week to turn in their solutions. I then go over the solutions in class, and work some additional challenging problems. Students are much better able to follow the additional problems after having worked a few on their own. 3–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Juan buys 10 turnips each year. True or False: If the price of turnips rises by 10 cents apiece, and if Juan’s tastes and income remain unchanged, then he will have $1 a year less to spend on other things. 2. It is possible for a community to have too little crime. (Hint: What is the cost of crime prevention?) 3. Writing in the New York Times, radio commentator Ira Eisenberg described the innovative voucher program recently initiated in Berkeley, California: Instead of shunning street beggars, or grudgingly handing them cash, Berkeley residents can now offer panhandlers vouchers purchased from local merchants. The vouchers are as good as real money for buying food, laundry services, bus fares, even hot showers. They can’t be exchanged for alcohol or cigarettes, let alone illegal drugs. What do you think of Berkeley’s voucher plan, and of Mr. Eisenberg’s analysis? 4. Assuming that you like to drive, but dislike breathing polluted air, draw your indifference curves between car rides and air pollution. Assuming that you have to breathe one unit of polluted air for each ten miles that you drive, draw the appropriate constraint. What is the optimal amount of pollution for you to breathe? Under what circumstances would it be zero? 5. Draw a typical set of indifference curves between “Smoking” and “Lung Dam- age” for a person who likes to smoke. Draw the relevant budget constraint. Now suppose that a new cigarette is invented that is identical to currently available cigarettes in every way except that it causes less lung damage per cigarette. Show the new budget line and the new optimum. Could this in- vention lead to an increase in the number of people who get lung cancer from smoking? 6. Suppose you like driving fast but you hate getting injured. a) Draw a graph with “speed” on the horizontal axis and “probability of in- jury” on the vertical. Do your indifference curves slope upward or down- ward? Why? b) Suppose you drive to work every day 40 miles per hour (mph) and have a 5% annual chance of being injured. You are aware that in general your chance of being injured (measured in percent) is always equal to 1/8 of your driving speed (measured in mph). Draw the relevant budget constraint, and draw a set of indifference curves that could have led to your decision to drive at 40mph. c) In order for your chosen speed to be an optimum, what must be true about the shape of your indifference curves? Must they be concave or convex? d) Suppose that because of a new kind of safety device, the probability of injury falls to 1/10 of your driving speed. Draw the new budget constraint and the new optimum. Can you determine whether the device causes a fall in your probability of being injured? Can you determine whether the device makes you happier? 7. Suppose you have an income of $10 and are offered the opportunity to purchase dog collars at $1 apiece. However, if you buy at least 5 dog collars at that price, then you can buy any number of additional collars at 50 cents a piece. Draw your budget constraint between dog collars and all other goods. 3–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8. Louie consumes only two goods, X and Y . His indifference curves have the usual (convex) shape. He prefers basket (2, 2) to basket (1, 3). a) Is it possible to tell whether Louie prefers (2, 2) to (3, 1)? b) Is it possible to tell whether Louie prefers (1, 3) to (3, 1)? 9. Daisy consumes only two goods, X and Y . Her indifference curves have the usual (convex) shape. She is exactly indifferent between baskets (1, 3) and (2, 2). Which does she prefer between (2, 2) and (3, 1)? 10. Marco has an income of $12. In Year 1, when buttons and bows each sold for $1 apiece, he bought 4 buttons and 8 bows. In Year 2, when buttons cost $.50 apiece and bows cost $4 apiece, he bought 8 buttons and 2 bows. True or False: It is not possible to tell from this information in which year Marco was better off. 11. Akbar and Jeff consume only eggs and wine. With eggs on the horizontal axis and wine on the vertical, Akbar is indifferent between the baskets (1, 3) and (2, 2). Jeff is indifferent between the baskets (2, 2) and (3, 1). They both choose to consume basket (2, 2). They each buy wine for $1 per bottle. Which one pays the higher price for eggs? 12. Suppose the only goods you buy are bread and circus tickets. When bread sells for $1 a loaf and circus tickets sell for $1 apiece, you buy 7 loaves of bread and 3 circus tickets to exhaust your income of $10. One day the price of bread falls to 50 cents a loaf while the price of circus tickets rises to $2 apiece and your income remains unchanged. Is it possible to say with certainty whether you are better off? Why or why not? 13. Suppose you divide your income between cheese and other goods. Cheese costs $4 a pound and you buy 10 pounds a day. One day the price of cheese rises to $6 a pound and at the same time your income rises by $20 a day. Do these changes make you better off, worse off, or neither? Illustrate your answer with indifference curves. 14. Dizzyland Amusement Park has begun sellling a VIP pass that costs $20 and entitles the bearer to a discount price on rides. Mickey Duck, as Dizzyland patron, has decided he is definitely happier buying a VIP pass than not buying one. a) In a diagram with “Rides” on the horizontal axis and “All Other Goods” on the vertical axis, illustrate the shift in Mickey’s budget line when he buys the pass. b) True or False: Mickey will certainly go on more rides now that he has a VIP pass. 15. Your income is $100 a week. The grocery store where you shop sells eggs for $10 apiece and wine for $20 a bottle. But, starting in June, your Aunt Agnes offers to pay for half your egg purchases, so eggs only cost you $5 a week. With Aunt Agnes’s offer in place, you buy 12 eggs and 2 bottles of wine each week. a) Draw a diagram that illustrates your budget lines in May and June. b) In June, how much is Aunt Agnes spending on you per week? (Your answer should be a number of dollars.) c) In July, Aunt Agnes stops subsidizing your egg purchases and instead gives you a weekly cash gift equal to the amount you calculated in part b). Add your July budget line to the picture. 3–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. d) True or False: You are exactly as happy in July as in June. Use your diagram to justify your answer. 16. Herman has an income of $10, which he spends on fishheads and all other goods. Fishheads cost $1 apiece. a) Suppose the government agrees to pay half of Herman’s fishhead bill, so that fishheads now cost him only 50 cents apiece. He now chooses to buy 8 fishheads. Show how the government program affects Herman’s budget line, and show his new optimum point. Call it P . What are the coordinates of the point P ? b) Now suppose the government ends the program in part a) and replaces it with a new and simpler program: Herman just gets a cash gift of $4. Show his new budget line. Does it go above, below or through point P ? How do you know? c) Of the two programs in parts a) and b), which is more expensive for the government? Which does Herman prefer? Justify your answers. 17. On Monday, eggs sell for $2 each and wine sells for $4 a bottle. On Tuesday, the price of eggs rises to $3 each and the price of wine falls to $3 a bottle. Amanda and Jeter both have incomes of $24 on Monday and on Tuesday. On Monday, Amanda buys 4 eggs and 4 bottles of wine. On Tuesday, Jeter buys 2 eggs and 6 bottles of wine. a) On which day is Amanda happier? Use a graph to justify your answer. b) Can you determine whether Amanda and Jeter have identical tastes? 18. Kramden’s Grocery advertises “We randomly chose 10 of our customers and calculated how much they’d have paid for their market baskets at Norton’s Supermarket. At Norton’s they were an average of 6% higher.” Does this convince you that wise shoppers will shop at Kramden’s? Why or why not? 19. Suppose that the only items you consume are bread and wine. One day the price of wine increases, and simultaneously your income increases. You notice that you are exactly as happy as you were before either change took place. a) What happens to the quantity of wine that you consume? To the quantity of bread? b) Can you still afford your original market basket if you want it? Illustrate your answer with indifference curves. (Note: After Chapter Four has been covered, this problem is much easier. Assigning it now forces the students to develop for themselves some skills that will be useful in Chapter Four. It does appear in the textbook at the end of Chapter Four.) 20. Suppose that the only goods you consume are apples and peaches. One day the price of apples goes up, and the price of peaches goes down, and you find that you can still just afford to buy the same combination of apples and peaches that you were buying all along. True or False: The price changes leave you neither better nor worse off. 21. True or False: It makes no sense to say that an hour of your time is worth exactly $10, since you engage in many different activities, and the value of an hour devoted to one of them might be quite different than the value of an hour devoted to another. 22. Consider the baskets A = (1, 3), B = (2, 2) and C = (3, 1). Notice that these baskets lie along a straight line. Jack is indifferent between baskets A and B. Jill is indifferent between baskets B and C. Is it possible that Jack and Jill 3–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. could have identical tastes? Justify your answer. (You should assume that indifference curves have the usual shape.) 23. Basket A contains 1 X and 5 Y’s. Basket B contains 5 X’s and 1 Y. Basket C contains 3 X’s and 3 Y’s. On Monday you are offered a choice between Basket A and Basket C, and you choose A. On Tuesday, you are offered a choice between Basket B and Basket C, and you choose B. True or False: We may infer that your tastes changed overnight. 24. Suppose the basket of goods you buy in 2014 costs more, at 2013 prices, than the basket you bought in 2013 would cost at those prices. Can you say for certain in which year you are better off? 25. Cassie shops at Wegmans supermarket, where she spends $20 per week to buy 10 apples and 5 bananas. If she bought the same 10 apples and 5 bananas at Tops supermarket, she’d pay $30. True or False: Cassie is wise to continue shopping at Wegmans. 26. John buys eggs for $2 a dozen and bacon for $5 a pound. Sarah buys eggs for $5 a dozen and bacon for $2 a pound. Can you determine whether John and Sarah have identical tastes? 27. John buys shoes for $1 a pair and socks for $1 a pair. His annual income is $20. a) Draw John’s budget line. b) Now suppose the government institutes two new programs. First, it taxes shoes, so that shoes now cost John $2 a pair. Second, it gives John an annual cash gift of $10. Draw his new budget line. c) Suppose that with the new programs in place, John chooses to buy 10 pairs of socks and 10 pairs of shoes. Has the pair of government programs made him better off, worse off, or neither? 28. The Pullman Company has a lot of pull in the town of Pullman, Illinois. Everybody in town is identical, and they all work for the company, which pays them each $10 a day. Their favorite food is apples, which they get from a mail order catalogue for $1 apiece. a) Draw the typical resident’s budget line between “apples” and “all other goods” (measured in dollars). Draw in the optimum point. b) Pullman plans to lower the wage rate to $8 a day. Draw the new budget line. c) Pullman has discovered that if residents are less happy than they were at $10 a day, they will all leave town. To prevent this, Pullman has offered to subsidize everyone’s apple purchases: From now on, if you are a Pullmanite who buys an apple, you will pay only a fraction of the cost and the company will pay the rest. Pullman plans to choose a fraction which is just large enough to keep people from leaving town. Draw the new budget line. Indicate the new budget point. Label the corresponding quantity of apples A. d) Use your graph to illustrate the amount that Pullman spends on the apple subsidy. (Hint: How much of your $8 income do you have left over after buying A apples? How much of your $8 income would you have left over if you bought A apples at the unsubsidized price of $1 apiece? Where is the difference coming from? e) True or False: Pullman could end up spending just as much on the apple subsidy as it saves by lowering wages. 3–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 29. The Pullman Company has a lot of pull in the town of Pullman, Illinois. Everybody in town is identical, and they all work for the company, which pays them each $10 a day. The company runs the government, pocketing all tax revenue for itself. Residents eat apples, which they purchase from a mail order company for $1 apiece. But the company imposes a 100% sales tax, so residents actually pay $2 apiece for apples. a) Draw the typical resident’s budget line between “apples” and “all other goods” (measured in dollars). Draw in the optimum point. Label the corresponding quantity of apples A. b) Use your graph to illustrate the amount of revenue that Pullman derives from the apple tax. (Hint: How much income do you have left after buying A apples? How much income would you have left if you had bought the same number of apples at the untaxed price of $1 apiece? Where is the difference going? c) Pullman wants to lower the wage rate to $8 a day. Unfortunately, if resi- dents become any less happy, they will all leave town. However, Pullman has calculated that eliminating the apple tax would be just enough to convince people to stay in town at a wage of $8 a day. Assuming that Pullman lowers the wage and eliminates the tax, draw the new budget line. d) True or False: The combined changes described in part (c) leave Pullman neither better nor worse off than before. Warning to instructors: The following three problems are considerably more difficult than the preceding two, although all have more or less the same flavor. 30. The Pullman Company has a lot of pull in the town of Pullman, Illinois. Everybody in town is identical, and they all work for the company, which pays them each $10 a day. Their favorite food is apples, which they get from a mail order catalogue for $1 apiece. However, the company subsidizes apple purchases, so that every time you pay $1 for an apple, you get back 50 cents from the company. a) Draw the typical resident’s budget line between apples and dollars. b) Pullman has decided to eliminate the apple subsidy. But to avoid discon- tent among the workers, it plans to simultaneously raise the wage rate by just enough to keep workers exactly as happy as they have always been. Draw the typical worker’s new budget line. c) On your graph, illustrate the amount that Pullman spends per worker in the original situation (be sure to count the wage plus the amount spent on the subsidy!). Illustrate the amount Pullman spends per worker after the subsidy is cut and the wage is raised. Was Pullman wise to institute these changes? 31. The Pullman Company has a lot of pull in the town of Pullman, Illinois. Everybody in town is identical, and they all work for the company, which pays them each $10 a day. Their favorite food is apples, which they buy at the company-owned grocery store for $1 apiece. The company buys its apples for $1 apiece and therefore earns no profit at the grocery store. a) Draw the typical resident’s budget line between apples and dollars. b) Pullman has decided to raise the price of apples to $2 apiece. But to pre- vent dissatisfied workers from leaving town, Pullman must simultaneously 3–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. raise wages so that workers are just as happy as before. Draw the new budget line. c) True or False: Although Pullman is now paying higher wages, it is also earning profits at the grocery store. Thus increasing the price of apples might or might not have been a wise move. 32. Suppose you have 24 hours per day to allocate between leisure and working at a wage of $1 per hour. Draw your budget line between leisure and dollars. One day the government simultaneously institutes two new programs: a 50% income tax and a plan whereby everybody in the country receives a gift from the government of $6 per year. a) Draw your new budget line. b) Suppose the government chose the level of $6 for the gift because it pre- cisely exhausts the income from the tax. Explain why this means that the average taxpayer must be paying exactly $6 in tax. c) Assume that you are the average taxpayer, and draw your new optimum. Is it on, above, or below your original budget line? d) As the average taxpayer, are you working harder or less hard than before the programs went into effect? Are you happier or less happy? How do you know? 33. Suppose you have 30 years of life which can be allocated between leisure and working at a wage of $10,000 per year. a) Draw your budget constraint between “leisure” and “lifetime income”. b) Suppose now that you are given the option to attend college, in which case you will have only 26 years available for leisure and working, but your wage will be higher than $10,000 a year. Suppose also that you are exactly indifferent between attending college and not attending college. Illustrate this situation with budget lines and indifference curves. c) True or False: If you attend college, you will definitely spend more time working than if you do not attend college. Justify your answer. 34. Suppose you have an income of $15 per month and can buy meat for $1 per pound. a) Draw your budget constraint between meat and dollars. b) Now suppose the government imposes a sales tax that raises the (after- tax) price of meat to $1.50 per pound. After the tax is imposed, you buy 4 pounds of meat per month. Draw your new budget line and your new optimum point. c) Now suppose that, while continung to collect the sales tax, the government gives you a cash gift of $2 per month. Draw your new budget line and the new optimum. d) In part c), the combination of the sales tax and the cash gift leaves you just as happy as you were to begin with. 35. Your income is $50 a week and you can buy meat at $10 a pound. a) Draw your budget line between “meat” on the horizontal axis and “dol- lars” on the vertical. b) Suppose that the government starts a new program that will allow you to buy as much meat as you want to, with the government paying half of the cost. Draw your new budget line and your new optimum point. Call it A. c) Now suppose that the government cancels the program but replaces it by a new program, under which you are given just enough cash each week so 3–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. that you can just afford to buy basket A. Draw your new budget line. d) Which government program do you like better, the one where they pay for half your meat or the one where they give you the cash? Use your graph to justify your answer. The next two problems are somewhat more difficult. They can be made easier by replacing the phrase “Show the location of your new optimum point” with “Explain why your new optimum point must occur at the intersection between your old and new budget lines.” 36. Suppose the government imposes a sales tax on food and simultaneously gives you a cash gift every year. Suppose the amount collected in tax is exactly equal to the size of the gift. a) Use a graph showing how this combined program affects your budget line between “food” and “all other goods” (measured in dollars). Show the location of your new optimum point. b) True or False: The combined program leaves you neither better nor worse off than before it was instituted. 37. Suppose the government imposes an annual head tax and simultaneously be- gins subsidizing food purchases. Suppose the amount collected in tax is exactly equal to the size of the subsidy. a) Use a graph showing how this combined program affects your budget line between “food” and “all other goods” (measured in dollars). Show the location of your new optimum point. b) True or False: The combined program leaves you neither better nor worse off than before it was instituted. 38. Suppose you have a choice between attending two colleges. At Eli College, you pay $100 per credit hour, and can take as many or as few credit hours as you like. At Leland College, you pay $500 per year and are required to take exactly 10 credit hours. a) Assuming you have $2,000 to spend, draw your budget constraint between credit hours and dollars. (Hint: The constraint includes all those points you can reach by attending Eli and all those points you can reach by attending Leland.) b) Suppose you choose to attend Leland College. True or False: If Eli lowers its price to $50 per credit hour, you will surely transfer to Eli. (Assume that both colleges are identical except for the price, and that it costs you nothing to transfer.) 39. You have an income of $120 per week and own a car that costs $2 per mile to drive. You choose to drive 50 miles per week. a) Draw your budget constraint between “miles driven” and “all other goods”, with “all other goods” measured in dollars. Show your optimum point. b) Suppose you are offered the opportunity to purchase for $60 a car that costs 50 cents a mile to drive. If you do this, you’ll throw your old car away. Draw the budget constraint that results if you buy the new car. Note that the two budget constraints cross at (40, 40). c) Would you buy the new car? Defend your answer using indifference curves. 40. Suppose you get rid of your old gas-guzzler and buy an new, fuel efficient car. Driving is now cheaper, but on the other hand, you have to make monthly car payments. You find that on balance, you are exactly as happy as you were 3–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. before. Illustrate this situation using indifference curves between “car rides” and “all other goods”. Are you driving more or less than you did before? 41. Suppose that eggs sell for $1 a dozen, wine sells for $1 a bottle, and your income is $12. a Draw your budget line. b Suppose that the government imposes a sales tax on eggs, causing the price (to demanders) to rise to $2 a dozen. At the same time, the government sends everybody in America a check for $4. You now choose to buy 4 dozen eggs and 8 bottles of wine. Draw your new budget line and your new optimum point. c How much does the sales tax add to the cost of the basket (4, 8)? d True or False: Because you get $4 back from the government, you end up just as happy as you were to begin with. Use your diagram to justify your answer. 42. Suppose that the government issues $100 worth of food stamps to everybody in your city. These food stamps are coupons that can be exchanged for $100 worth of food at the grocery store, but they can be used only by the person to whom they are issued. a) Draw your budget constraint between food and all other goods both before and after the food stamps are issued. In doing so, measure food in units such that 1 unit of food sells for $1, and assume that your income before the food stamps were issued was $500. b) Suppose that you find that you would prefer to sell some of your food stamps for their dollar value, if only you were allowed to. What can we conclude about the marginal value of food? 43. Suppose that you have 16 waking hours per day, which you can allocate be- tween working for a wage of $1 per hour and relaxing. Draw your budget constraint between “dollars” and “hours of relaxation.” Now suppose that you invent a pill that enables you to get by on 4 hours sleep per night, and therefore have 20 waking hours per day. Draw your new constraint. Is it possible that you will now choose to work fewer hours than you did before? Now suppose that at the same time, the pill stops working (so that you’re back to 16 waking hours a day) and your wage goes up to $1.50 per hour. Draw your new budget constraint. Suppose you find that the wage increase makes it possible for you to attain the same combination of dollars and relaxation that you chose when you had the pill. How much will you work after the wage increase, compared with how much you worked when you had the pill? 44. (Warning: This is a hard problem.) Suppose that you have available 16 work- ing hours per day, which you can allocate between growing apples and relaxing. Show how you decide on your allocation. Now the government decides to in- stitute a tax whereby x% of your apples are taken away and discarded. Show your new allocation of time. Suppose that the government wants to acquire exactly A apples through this tax. How will they choose x? Now suppose that a change in your metabolism causes you to have 20 waking hours per day instead of 16. The government wishes to change the tax rate x so as to still collect A apples from you. How do they choose the new x, and where is your new optimum? Could you be worse off at your new 20 hour a day optimum than at your old 16 hour a day optimum? 3–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 45. Suppose you expect to earn $10 this year and $10 next year. Each dollar you earn this year can be be either spent, or saved at an interest rate of 10%. If you want to spend more than $10 this year, you can borrow money at 10% interest and repay it next year. Next year, you plan to pay off your debts (if any), then spend all your earnings and all your savings (if any). a) Draw your budget line between “dollars spent this year” and “dollars spent next year”. b) Suppose the government imposes a 50% income tax on all your earnings this year and next year (not including your interest earnings). Draw your new budget line. c) Suppose the government imposes a 50% sales tax on everything you buy this year and next year. Draw your new budget line. d) Suppose the government imposes a 50% income tax on all your earnings this year and next year, including your interest earnings. Draw your new budget line. d) True or False: If interest earnings are not subject to income tax, then an income tax and a sales tax will lead you to spend exactly the same amount both this year and next year. 46. Suppose the government imposes a temporary sales tax—one that is in ef- fect for a short time, but will disappear in the future. The government is considering two different tax policies: A. A big excise tax on eggs. This would cause the price of eggs to triple. B. A smaller excise tax on both eggs and wine. This would cause the price of both eggs and wine to double. a) Illustrate your original (no-tax) budget line and your budget line under Policy A. Mark your optimum point. b) Suppose that, coincidentally, the government would collect exactly as much money from you under Policy B as under Policy A. Illustrate your budget line under Policy B . How does your graph illustrate the fact that the two policies cost you equal amounts of money? c) Which policy do you prefer? Why? 47. Suppose the government imposes a temporary sales tax—one that is in effect for a short time, but will disappear in the future. In a diagram relating current consumption to future consumption, how does your budget line shift? Which is preferable: a permanent sales tax or a temporary sales tax (assuming the rates are adjusted so they collect equivalent revenues)? 48. Mr. Smith has a very low income and Mr. Jones has a very high income. They both purchase education from the same private school. a) In a single diagram, draw budget lines between “education” and “all other goods” for both Mr. Smith and Mr. Jones. Now suppose the government offers a certain quantity of free education with the proviso that if you acept the offer, you must consume exactly that quantity, no more and no less. Draw Mr. Smith’s new budget constraint and Mr. Jones’s new budget constraint. (Hint: Mr. Smith’s new budget constraint is no longer a line, but a line and a point; likewise for Mr. Jones.) c) Suppose Mr. Smith accepts the government’s offer and Mr. Jones rejects it. Is it possible that Mr. Smith and Mr. Jones have identical tastes? 49. Suppose you are a government policymaker and your goal is to make poor people happier. You can do so by subsidizing their food, education and medical care, or you can do so by giving them cash. 3–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) On the basis of your answer to Problem 22 in the textbook, make an argument in favor of giving cash. b) On the basis of your answer to the preceding problem in this manual, make an argument for subsidizing education instead of giving cash. (Hint: Suppose you want to help only the poor, but it’s difficult for you to tell who’s poor and who’s rich, and you are worried that rich people will try to claim a share of the cash giveaways.) c) Can you think of a reason why governments would want deliberately to limit the quantity or quality of education available at public schools? 50. Mr. Jones can purchase varying quantities of education from private schools at a going price. One day there opens in Mr.Jones’s neighborhood a public school that he may attend for free if he wants to. However, if he attends the public school, he must accept the amount of education that it offers. He can no longer take any private school classes because the public and private schools are in session at the same time. a) Draw Mr. Jones’s old and new budget constraints. b) Draw a set of indifference curves that implies Mr. Jones will increase his consumption of education when the public school opens. Draw a set that implies his consumption of education will not change. Draw a set that implies he will decrease his consumption of education. Call these the indifference curves of Mr. A. Jones, Mr. B. Jones and Mr. C. Jones. Can you rank Mr. A., Mr. B., and Mr. C. in terms of how much they seem to like education? c) True or False: If most people are reasonably but not fanatically fond of education, then an offer of free public education could reduce the quantity of education consumed. 3–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. THIS PAGE SHOULD BE LEFT BLANK 3–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 3 1. False. This statement confuses a change in opportunities with a change in tastes. 2. The indifference curves are parallel lines with slope −1/2 (assuming you’ve put nickels on the horizontal axis). The marginal value of a nickel is 1/2 dime. 3. The indifference curves are L-shaped, with corners at (1, 1), (2, 2), etc. 4. DOGS FISH FISH CATS CATS DOGS In each case, the arrows point in the "upward" direction. 5. Drawing an indifference curve through both (1,3) and (2,2), you will find that it must pass above (3,1). Therefore Huey prefers both (1,3) and (2,2) to (3,1). 6. a) You should be able to draw an indifference curve through (1, 3), passing above (3, 1) and also above (2, 2), and a different indifference curve through (1, 3) passing above (3, 1) but passing below (2, 2). Since either of these indifference curves might belong to Dewey, it is impossible to tell whether he prefers (1, 3) to (2, 2). (See the picture below.) b) If Dewey’s indifference curve through (3, 1) passes above (2, 2), it must also pass above (1, 3), contrary to the assumption in the problem. Thus Dewey can’t prefer (3, 1) to (2, 2). (See the picture below.) 3 3 2 2 1 1 1 2 3 1 2 3 a) Either curve is possible. b) In order for the curve to pass below (1,3), it must also pass below (2,2) 3–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7. The picture looks like this: All Other Goods 20 10 10 30 Ice Cream 8. a) You can have up to 6 hours at the carnival or up to 6 hours at the circus, so your budget constraint is the line through (6, 0) and (0, 6) in the picture below. b) If you had unlimited time, you could afford up to 10 hours at the carnival or up to 5 at the circus, giving you the budget line that stretches from (0, 10) to (5, 0). But because you must be either on or inside both your “time” budget line and your “money” budget line, you are constrained to the bold-faced segments in the picture below; those segments constitute your overall budget line. Hours at Circus 6 5 10 6 Hours at carnival 9. True: With nonconvex indifference curves you always specialize in the consump- tion of either X or Y. A small price change might or might not induce you to switch specializations. If you are specialized in Y and remain specialized in Y, then your consumption of X is left unchanged. If you are specialized in Y and switch to being specialized in X, then your consumption of X changes dramatically. A third possibility is that you are specialized in X and remain specialized in X, in which case your consumption of X will change by a small amount. 3–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 10. a) Because typing and filing are not “goods,” we need to rethink the shape of the indifference curves. First, notice that for a given basket A, baskets to the southwest of A are preferred to A and baskets to the northeast of A are inferior to A. Thus no such baskets can be on the same indifference curve as A. The only baskets that can be on the same indifference curve as A are to the northwest and southeast of A; it follows that the indifference curves slope downward. b) The slope of the indifference curve is −2, indicating that you’d be willing to trade 1 hour of typing for 2 hours of filing. If you hated typing even more, you’d be willing to trade 1 hour of typing for even more hours of filing; thus the indifference curve would be steeper (with a slope, for example, of −3 or −4). c) When you’re doing a lot of typing, you’re likely to be willing to make bigger sac- rifices to avoid yet another hour of it. Thus the indfference curve is steeper near baskets with a lot of typing and little filing, and shallower near baskets with less typing and much filing. In other words, they bow outward from the origin. d) The line has slope −1 and intersects both axes at 8 hours. e) At (3, 5), the indifference curve is steeper than the budget line. Thus your optimum point—the tangency of an indifference curve with the budget line—must occur below and to the right of (3, 5). In other words, you will now type more than 3 hours per day. 11. Y X a) Filbert’s and Lychee’s indifference curves cross; therefore they have different tastes. b) Filbert and Lychee’s budget lines have different slopes; therefore they pay different prices. 12. Both budget lines pass through the point (6,4), and there is an indifference curve through the 2013 budget line at that point. The 2014 budget line is steeper, which requires its tangency with an indifference curve to lie above and to the left of (6,4); moreover this indifference curve must lie above the curve through (6,4). Therefore 2014 is the year in which you eat more pizza and the year in which you are happier. 13. The picture below shows last week’s budget line and this week’s budget line. This week Susan chooses point A = (3, 2). We can check that this basket is on this year’s budget line: 3 × $6 + 2 × $2 = $22. (If this equation weren’t true, we could conclude that there was a mistake in the problem.) We can also verify that this basket is on last week’s budget line: 3 × $4 + 2 × $5 = $22. Therefore the point A is on both budget lines, which means it must be at the intersection of the budget lines. We know that Susan chooses point A this week, so her indifference curve through A must be tangent to this week’s budget line, as shown. To avoid crossings, the tangent to last week’s budget line must be somewhere between points A and B, 3–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. necessarily on a higher indifference curve than the one pictured. Therefore Susan was happier last week than this week. MEAT 11 This week 4.4 A Last week B CHEESE 3.67 5.5 14. Note: the diagram below is not to scale. In 2013 you choose the marked tangency at (12,6). In 2014 you choose a point on the darkened part of the flatter budget line. The entire darkened portion lies to the right of the crossing at (10,10). Therefore you definitely buy more than 10 pairs of shoes in 2014. But the darkened portion lies partly to the left of the tangency at (12,6). Therefore you might buy either more or fewer than 12 pairs of shoes in 2014. 2010 2011 2011. 2011. 15. With eggs on the horizontal axis and other goods (measured in dollars’ worth) on the vertical, your original budget line passes through (12,0) and (0,48), with your optimum at (5,28). If you join the egg club, your new budget line passes through (19,0) and (0,38) (thus it is flatter than the original) and it passes through your original optimum at (5,28). Therefore it is tangent to a higher indifference curve (somewhere below and to the right of (5,28)), which means you should join the egg club. 3–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 16. Other goods When the price of eggs doubles, Freddy moves from A to B. If he'd lost six dollars, he could just have afforded B. Therefore, the "lost six dollars" budget line (shown dashed) passes through B, and there must be a tangency somewhere between B and C. This tangency would be on a higher indifference curve than the one passing through B, so Freddy prefers losing $6. A 6 B C Eggs 17. a) Peaches a) If Aubrey is equally happy in both months, a single indifference curve must be tangent to both budget lines as shown. She therefore definitely eats more apples in July, i.e. TRUE. June July Apples b,c) Peaches b) If Aubrey eats exactly 8 apples in June, the picture looks like this. Her July tangency must lie on a higher indifference curve (like the dashed one), so TRUE. c) The dashed indifference curve could in fact be tangent to the July line slightly LEFT of the quantity 8, (as inidicated by the arrow) so FALSE. June July 8 Apples 3–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 18. a) 1. b) 3. c) 2. 19. TEA 4 TEA 4 2 2 2 4 2 4 COFFEE COFFEE TEA 4 TEA 4 2 2 2 4 2 4 COFFEE COFFEE The pictures show four possible configurations. In the first of the four, Amelia and Bernard have crossing indifference curves, and hence different tastes. In the last of the four, Amelia and Bernard share an indifference curve, but this doesn't prove they share all their indifference curves; hence they might or might not have different tastes. In the other two pictures, Amelia and Bernard might or might not have different tastes for multiple reasons: first, we can't tell whether the pictured indifference curves cross after they are extended further, and second, even if the pictured curves don't cross, we can't infer anything about all the unpictured curves. So reviewing the four pictures, we see that the answer to the "same tastes" question is: Maybe no, or maybe maybe, or maybe maybe, or maybe maybe. Which adds up to maybe. 20. Drawing the picture, you should see that Chris’s indifference curve through (2, 1) crosses David’s indifference curve through (1, 2). Therefore their tastes must differ. 3–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 21. Evelyn and Frederick could have identical preferences. 22. Inez’s consumption point is on Homer’s budget line and Homer’s is below Inez’s budget line, so the picture looks like this (with Inez consuming at point I and Homer at point H): Wine 8 Homer J 6 I Inez H Eggs 12 8 a) The pictured indifference curves cross, so Homer and Inez do not have the same tastes. b) If Inez could pay the same prices as Homer, she’d have Homer’s budget line and would choose a point between I and J, which would make her happier. 3–19 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 23. Kareem can just afford Jessica’s basket, so her basket must be at the intersection of the budget lines as shown: TEA JESSICA KAREEM COFFEE We are not told where Kareem’s basket is, so we have to consider various possibilities. If his basket is on the red part of his budget line, then certainly his indifference curve and Jessica’s must cross, so their tastes are different. If his basket is on the blue part of his budget line, there are the following two illustrated possibilities: TEA JESSICA KAREEM COFFEE TEA KAREEM JESSICA COFFEE In the bottom panel, Kareem is happier with his own budget line than he would be with Jessica’s, which is contrary to what’s given in the problem, so we can rule this case out. In the bottom panel, which is consistent with what’s given in the problem, the indifference curves cross. Therefore in all cases consistent with the problem specification, Kareem and Jessica must have different tastes. 3–20 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 24. The picture looks like this: BANANAS T S APPLES It’s true, as Tops advertises, that the Tops basket would be more expensive at Star (that is, it’s outside the Star budget line). But it’s equally true that the Star basket would be more expensive at Tops. The insight is that when Cassia goes to Tops, she buys more bananas, because Tops is where bananas are relatively cheap. She can’t afford this basket at Star, where bananas are relatively expensive. But when she goes to Star, she buys more of what’s relatively cheap at Star, and ends up with a basket she can’t afford at Tops. 25. a) Here is the graph: bananas bananas Acme Star Acme Star GREGORIAN apples BOUDICCA apples b) The key difference is that Gregorian’s indifference curve through (6,18) passes above the Acme budget line, while Boudicca’s passes below the Acme budget line. c) True; you can see in the picture that her new tangency must lie to the right of the point (10,10) where the budget lines cross. 3–21 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 26. a) In the diagram below, your new budget line is shown in blue. All other goods 10 P Q original 10 Sodas b) Your new budget line is the red line above, passing through P . You can now achieve a point between P and Q and are therefore better off. 27. In the diagram below, the head tax shifts your budget line to the red line; then the subsidy pivots it out to the blue line. If you buy 6 apples, you pay $3 and have $4 left over for other goods, so you’re at the point (6, 4), which is also on your original budget line. Therefore the tangency is as shown. Your Monday budget line must therefore be on a higher indifference curve, i.e. you are worse off on Tuesday. Oranges 10 7 Monday Tuesday 10 14 Apples 3–22 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 28. In the diagram below, the sales tax pivots your budget line in to the red line; then the cash gift shifts it out to the blue line. When you purchase 5 apples, you have $5 left over, so your new tangency is at (5, 5), which is also on the original line. Therefore the tangency is as shown, and you are worse off on Tuesday than on Monday. 15 Oranges 10 Tuesday Monday 5 10 Apples 29. In the diagram below, the sales tax gives you the red budget line; the head tax gives you the blue. Because it’s assumed that both taxes cost you the same amount, the head tax must be set so that the red line passes through the tangency point P . Therefore you can reach a higher indifference curve on the blue line, i.e. you prefer the head tax. Oranges P Apples 30. You can use exactly the same diagram as in problem 29. Combined sales taxes of 10% on both goods cause your budget line to shift inward parallel to itself, just like a head tax. So you still prefer the blue line (with the combined sales taxes) to the red line (with the sales tax on apples only). 3–23 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 31. The pictures below show the answers to parts b), c) and d). In each case the new budget line is shown in blue and the government’s revenue (measured in future dollars) is the length of the red line segment. Goods 11 Goods 11 Goods 11 Next Next Next Year Year Year 10 10 10 b) c) d) Goods Today Goods Today Goods Today 32. The temporary sales tax is shown in blue and the permanent sales tax is shown in red. The permanent sales tax is preferred. Goods Next Year Original Goods Today 33. The next-year-only tax is shown in blue and the permanent tax is shown in red. The permanent tax is preferred. Goods Next Year Original Goods Today 3–24 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 34. You can use the same picture we used for problem 33. The tax on interest is shown in blue and the permanent sales tax is shown in red. The permanent sales tax is preferred. 35. The old tangency is the marked point; the new tangency can be anywhere on the blackened part of the new budget line. You might choose either more or less leisure than before, hence either less or more time spent working. INCOME $200 160 16 20 LEISURE 36. Workers are initially at point O. The sales tax causes the budget line to pivot in and the raise causes the budget line to shift out parallel to itself. The new optimum is at X. The size of the raise is the vertical distance from X to Z. The amount of sales tax collected is the vertical distance from W to X and the raise is the vertical distance from W to Z. The raise exceeds the tax revenue, so Pullman is unwise to institute the tax. W AOG 10 X Z O 10 APPLES 3–25 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 37. a) The broken line L is your budget line. $ M L 14.50 7.50 L M LEISURE 14 24 b) Your new budget line is M , and your new tangency must be northwest of the old one, so you work more hours. Therefore tax revenue increases. c) The new one as it allows you to attain a higher indifference curve. 3–26 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1.a) Pairs of Wax Lips Packs of Candy Cigarettes 0 20 1 18 2 16 3 14 4 12 5 10 6 8 7 6 8 4 9 2 10 0 b) Fred chooses the basket (5, 10). c) Pairs of Wax Lips Packs of Candy Cigarettes MV 0 20 1 18 ∞ 2 16 16 3 14 7 4 12 4 5 10 2 1/2 6 8 1 3/5 7 6 1 8 4 4/7 9 2 1/4 10 0 1/9 Fred chooses the basket for which the MV of a pair of wax lips is equal to its relative price, which is 2. Thus he takes either the basket (5,10) or the basket (6,8); this is consistent with our answer to (b). Actually, the apparent ambiguity in the answer to this question results from the fact that we have only allowed Fred to count candy cigarettes and wax lips in whole number quantities. If we had allowed fractional quantities, we would argue as follows: suppose that Fred now has w pairs of wax lips and p packs of candy cigarettes. Now we reduce his wax lip holdings by h pairs (where h is a very small fraction), and then increase his candy cigarette holdings by m packs, where m is chosen to keep Fred just as happy as he was before. Thus we have w · p = (w − h) · (p + m). Solving this gives p m≈ · h. w (We ignore the term h · m, which is small. It follows that the marginal value of wax lips is m = (p/w) · h packs of candy cigarettes per h pairs of wax lips, or p/w packs of candy cigarettes per pair of wax lips. With this, we can replace the approximations in the table above by the following exact figures: 3–27 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Pairs of Wax Lips Packs of Candy Cigarettes MV 0 20 ∞ 1 18 18 2 16 8 3 14 4 2/3 4 12 3 5 10 2 6 8 1 1/3 7 6 6/7 8 4 1/2 9 2 2/9 10 0 0 Now we can see that with 5 pairs of wax lips and 10 packs of candy cigarettes, For Fred, the MV of a pair of wax lips is exactly 2 packs of candy cigarettes, so that this is the basket he will choose. 3–28 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Four: Consumers in the Marketplace General Discussion and Teaching Suggestions 1) To give students an idea of where we’re going, it can be helpful to point out that in Chapter Three we studied the behavior of a consumer with a given budget line, while in Chapter Four we will study how that consumer’s behavior changes when his budget line changes. In the solved problems in Section 3.3 and the problems at the end of Chapter Three, we have already seen a lot of examples of changing budget lines; in this chapter we will systematize that knowledge and try to make some general statements about the directions of changes. 2) The text discusses only the Hicksian version of the compensated demand curve (holding utility fixed) and the corresponding decomposition into substitution and income effects. Good students can be challenged to work out the details of the Slutsky compensation (holding fixed a Laspeyres index of the price level) and the corresponding Slutsky decomposition. For the right students, you can make additional assignments such as: define a “Hicksian” decomposition that consists of an income effect followed by a substitution effect (as opposed to the substitution effect followed by income effect that is traditional), illustrate its geometry, and say whatever else you can about it. Or: do the same thing with a “Slutsky-style” decomposition. Although I’ve never tried it, it seems a worthwhile experiment to assign such problems as topics for short papers. With several variants of the problem available, the threat of collusion is substantially reduced. Alternatively, the “mix and match” problems beginning on page 4-6 of this manual lead the students through every possible variation of such problems, with enough coaching so they can be used as exam problems rather than short paper topics. 3) Students will want to know why we study the compensated demand curve. One response is that it allows us to isolate the substitution effect and to demon- strate that its direction is unambiguous; this allows us to draw the non-obvious conclusion that all Giffen goods are inferior, and in fact that the Giffen phenomenon requires in some sense a “large” income effect in order to occur. A second response is that there are other theoretical applications of the com- pensated demand curve, for example to the theory of consumers’ surplus in Chapter Eight. But this will not be very satisfying to students at this point in the course. Yet a third response invokes the notion of the representative agent (without the need to introduce that piece of jargon). It is true that many consumers of apples experience no change in their money income when the price of apples goes up. If you want to know how many apples such a consumer will buy at a given price, you must look along his uncompensated demand curve. However, there are some situations in which it is reasonable to expect people to be income- compensated for a price change. Suppose, for example, that you own an apple orchard. In that case, whenever the price of apples goes up, your income goes up as well. However, this is still not a good justification for studying the compensated demand curve, because it is unlikely that your income will go up by exactly enough to compensate you for the higher price of apples. Indeed, if your income is derived primarily from your orchard, then you are likely to be considerably over compensated for any price change. In general, a rise in the price of apples is helpful to apple sellers and harmful to 4–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. apple buyers. How does it affect people on average? The complete answer depends on the exact meaning that we attach to the phrase “on average”, but one way to think about it is this: Since the total number of apples bought must equal the total number of apples sold, the gains to sellers must in some sense just balance the gains to buyers. Therefore, on average, people are made neither better nor worse off by a change in the price of apples, which is to say that on average, people are income– compensated for the price change. Thus if we are attempting to model the behavior of an individual consumer or of a small part of the economy, the uncompensated demand curve is the right one to use. But in certain models that attempt to take account of all of the activities of everyone in the economy (you might even want to introduce the phrase “general equilibrium”, or to mention that such models are increasingly important in macroe- conomics), the compensated demand curve provides the appropriate description of consumer behavior on average. 4–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. True or False: For a rich man and a poor man, a Mercedes-Benz is equally expensive. 2. The only good Hiram ever buys is potatoes; he would never consider buying any other good. a) True or False: Potatoes cannot possibly be an inferior good for Hiram. b) What is the shape of Hiram’s Engel curve for potatoes? 3. The only good Hiram ever buys is potatoes; he would never consider buying any other good. a) True or False: Potatoes cannot possibly be a Giffen good for Hiram. b) What is the shape of Hiram’s demand curve for potatoes? 4. You buy only beer and pizza. One day the price of beer goes down, the price of pizza goes up, and you discover that you can just exactly afford to continue buying the basket you were buying all along. Do these changes leave you happier, less happy, or equally happy? Illustrate your answer with indifference curves. 5. Suppose that the federal government issues $100 worth of food stamps to everyone in your city. These food stamps are coupons that can be exchanged for $100 worth of food at the grocery store, but can only be used by the person to whom they are issued. a) Draw your budget constraint between “Food” and “All Other Goods” both before and after the food stamps are issued. b) True or False: If food is a normal (as opposed to inferior) good, then the food stamps will surely lead to more food being eaten. c) Suppose that you lose your $100 worth of food stamps but at the same time, your income increases by $200. True or False: If food is a normal (as opposed to inferior) good, this will surely lead to an increase in your food consumption. 6. True or False: All Giffen goods are inferior goods, but not all inferior goods are Giffen goods. 7. Homer consumes beer and donuts. Beer is an inferior good. One day the price of donuts falls. Use a graph to show what happens to Homer’s beer consumption. Does Homer end up drinking more or less beer than before? Justify your answer carefully. 8. In the following diagrams, the black dots represent points where the illustrated lines are tangent to indifference curves. X X X X X FIGURE A FIGURE B FIGURE C FIGURE D FIGURE E a) In which figures(s) is X a normal good? b) In which figures(s) is X a Giffen good? c) In which figure(s) is Y an inferior good? d) In which figure(s) is Y a Giffen good? 9. Suppose that when the price of X goes up, you respond by consuming less Y . 4–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) Illustrate the income and substitution effects of a rise in the price of X. How does your graph illustrate the information in italics above? b) looking at the effects on your consumption of Y , which is bigger — the income effect or the substitution effect? Carefully explain how you can tell. 10. The only goods you consume are eggs and wine. On Monday, you consume basket M . On Tuesday, the price of eggs goes up and you consume basket T . On Wednesday, the price of eggs returns to its Monday level and the price of wine goes up. On Wednesday, you consume basket W and you are exactly as happy as you were on Tuesday. True or False: If you consume fewer eggs on Wednesday than on Monday, then eggs cannot possibly be a Giffen good. 11. The only goods you consume are eggs and wine. On Tuesday, your income rises. On Wednesday, you are just able to afford Monday’s basket. a) Illustrate your Monday, Tuesday and Wednesday budget points and op- tima. Label the optima M , T and W . b) A Neffig good is a good that you buy less of when the other good’s price rises. True or False: Every Neffig good is a normal good. Justify your answer by referring to your labeled points. 12. The only two goods you consume are X and Y. Y is an inferior good. Suppose that the price of X goes down. a) Illustrate the substitution and income effects. b) True or False: Your consumption of Y must go down. Justify your answer in terms of the effects you illustrated in part a). 13. The only two goods you consume are X and Y. X is a Giffen good. Suppose that the price of X goes up. a) Illustrate the substitution and income effects. b) True or False: Your consumption of Y must go down. Justify your answer. 14. Suppose the only two goods you consume are X and Y. On Tuesday, the price of Y (not X!) goes up. On Wednesday, there are no new price changes, but your income rises by just enough so that you can exactly afford Monday’s basket. a) Use a diagram, with X on the horizontal axis and Y on the vertical, to illustrate your budget lines and optimum points on Monday, Tuesday, and Wednesday. Label the optimum points M , T , and W . b) In terms of the locations of points M , T , and W , what would it mean for X to be an inferior good? c) Is it true that W is always to the right of M ? If so, how do you know? If not, what would your answer depend on? d) Call X a Figgen good if it is true that “when the price of Y goes up, the quantity demanded of X goes up.” In terms of points M , T , and W , what would it mean for X to be a Figgen good? e) True or False: Every inferior good is a Figgen good. f) True or False: Every Giffen good is a Figgen good. 15. You consume two goods, X and Y . On Tuesday, the price of Y (not X!!) rises. On Wednesday, there are no new price changes, but your income rises until you are just as happy as you were on Monday. a) Draw your budget lines and optimum points on all three days. Label the optima M , T and W . 4–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) In terms of the locations of the optimum points, what would it mean for Y to be a Giffen good? c) In terms of the locations of the optimum points, what would it mean for X to be a normal good? d) Suppose that X is a normal good, and suppose also that you consume more X on Tuesday than on Monday. When the price of Y changes, which effect on your X-consumption is larger: the income effect or the substitution effect? Justify your answer in terms of the locations of the points on your graph. 16. On Monday, apples and peaches sell for $1 each. Your income is $10, with which you buy 2 apples and 8 peaches. On Tuesday, the price of apples rises to $2 and the price of peaches falls to 50 cents (and your income remains $10). a) Draw your Monday and Tuesday budget lines and show your Monday optimum point. Label it M . b) Suppose your optimum point on Tuesday is to the right of M . Are apples a normal good? Use your diagram to fully justify your answer. 17. Suppose you allocate all your wealth to “housing” and “savings”. Housing costs $40 per square foot. You have $100,000 in wealth and have elected to build a 1000 square foot house. a) Draw your budget line between housing (on the horizontal axis) and sav- ings (on the vertical). Draw the indifference curve you are on. b) Now suppose the price of housing falls to $30 per square foot. Draw your new budget line. (Hint: You can keep your existing house if you want to.) c) True or False: The fall in housing prices makes you happier. d) Assume that housing is an inferior good and illustrate the substitution and income effects from a fall in housing prices. e) True or False: If housing is an inferior good, then in this problem the substitution effect must be larger than the income effect. 18. Suppose you buy only X and Y, both of which are normal goods. Suppose also that almost all of your income is spent on Y. When the price of X goes up, does the quantity of Y go up or down? 19. Homer consumes only donuts and coffee. One day the price of donuts falls, and Homer responds by increasing his coffee consumption. a) Show how the fall in the price of donuts affects Homer’s budget line. b) Show Homer’s old and new optimum, and label them A and B. How does your graph illustrate the fact that Homer now consumes more coffee? c) Shortly after the price of donuts falls, Homer is informed that his salary has been cut. He finds that he is now exactly as happy as he was before any of the changes took place. Show his new budget line and his new optimum point. Label it C. d) Use your graph to determine whether coffee is an inferior good. Justify your answer in terms of the relative locations of points A, B and C. Be careful to note that although the price of donuts has changed, the question asks whether coffee is inferior. e) Is it possible to tell whether coffee is a Giffen good? Why or why not? 20. William consumes meat and potatoes. When the price of meat goes up, William continues to consume exactly the same number of potatoes as be- fore. 4–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) Draw a picture showing William’s budget lines before and after the price of meat goes up. Show his optimum points on both budget lines. How does your picture reflect the fact that William’s potato consumption is unchanged? b) Draw a compensated budget line and indicate the substitution and income effects of the price change. c) Can you tell whether potatoes are a normal or an inferior good for William? Justify your answer thoroughly. d) Can you tell whether potatoes are a Giffen good for William? Justify your answer thoroughly. 21. In each of the following pictures, the black dots represent tangencies with indifference curves. In which pictures is X normal? In which pictures is Y normal? In which pictures is X Giffen? In which pictures is Y Giffen? 4–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 22. The darkened points in the following diagram indicate places where indifference curves are tangent to the illustrated lines: Determine whether each of the following statements is true or false and in each case justify your answer by referring to the relative locations of the illustrated points. a) Eggs are a normal good. b) Eggs are an ordinary good. c) Wine is a normal good. d) Wine is an ordinary good. 23. Suppose you consume only cakes and ale. You currently have 5 cakes and 7 pints of ale. Now someone starts giving you additional cakes, while your ale consumption remains unchanged. You find that each additional cake has a lower marginal value than the previous one. a) True or False: Ale must be a normal good. b) True or False: Cakes must be a normal good. 24. Bugs consumes only carrots and lettuce, both of which are normal goods for Bugs. One day the price of carrots goes up. a) Illustrate Bugs’ old and new optimum points, and show the substitution and income effects. How does your graph reflect the fact that carrots are a normal good? How does it reflect the fact that lettuce is a normal good? b) Can you say for certain whether the substitution effect causes Bugs to buy more or less lettuce than before? If so, use your graph to explain why. If not, explain on what your answer would depend. (Warning: The question asks about quantities of lettuce, not of carrots.) c) Can you say for certain whether the income effect causes Bugs to buy more or less lettuce than before? If so, use your graph to explain why. If not, explain on what your answer would depend. d) When the price of carrots goes up, can you say for certain whether Bugs would buy more or less lettuce than before? If so, justify your answer; if not, explain on what the answer would depend. e) Suppose that almost all of Bugs’s income is spent on lettuce. Now when the price of carrots goes up, do you expect him to buy more or less lettuce than before? Carefully justify your answer in terms of the substitution and income effects. 25. Can a good be simultaneously inferior and non-Giffen? Justify your answer using a diagram that illustrates the income and substitution effects of a price increase. 26. Suppose you consume only X and Y . Both goods are normal. When the price of X goes up, which of the following is true? i) Your consumption of Y definitely goes up. 4–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. ii) Your consumption of Y definitely goes down. iii) Your consumption of Y could go either up or down. If you answered (i) or (ii), give a complete justification for your answer. If you answered (iii), state what additional piece of information you would need to determine what happens to your consumption of Y . In any case, your answer should be in terms of substitution and income effects. 27. Sam consumes only green eggs and ham. a) Draw a diagram with green eggs on the horizontal axis and ham on the vertical. Illustrate how Sam’s budget line is affected by a rise in the price of ham. b) Show the indifference curve that Sam was on before the price change, and draw in a compensated budget line. c) Suppose that green eggs are an inferior good for Sam, and show Sam’s new optimum point. How does your graph reflect the fact that green eggs are an inferior good? d) In terms of your graph, identify the substitution and the income effects. e) True or False: If green eggs are an inferior good, then when the price of ham goes up, Sam consumes more green eggs. Carefully justify your answer in terms of the substitution effect and the income effect. 28. The only goods you consume are X and Y. Assume that both X and Y are normal goods. One day the price of X goes down. a) Illustrate your old and new budget lines and your old and new consump- tion points. Illustrate the substitution and income effects from the fall in the price of X. Make sure I can tell what’s what on your graph, either with labels or with explanation nearby. b) Can you say for certain whether the substitution effect causes you to con- sume more Y or less Y? If so, use your graph to explain why. If not, explain what the answer would depend on. (Please take note that although the price of X has fallen, the question asks about your consumption of Y , not of X.) c) Can you say for certain whether the income effect causes you to consume more Y or less Y? If so, use your graph to explain why. If not, explain what the answer would depend on. d) When the price of X goes down, can you say for certain whether you buy more Y or less Y? If so, carefully justify your answer. If not, explain what the answer would depend on. e) Suppose that almost all of your income is spent on Y. Now when the price of X goes up, do you expect to buy more Y or less Y? Carefully justify your answer in terms of income and substitution effects. 29. Suppose that there are two kinds of cars: cheap cars that get lousy gas mileage and expensive cars that get good mileage. a) Considering that you get to decide which kind of car to own, draw your budget constraint between “miles driven” and “all other goods”. b) Suppose that the price of gasoline goes up, and you respond by increasing your purchases of gasoline. True or False: This means that gasoline is a Giffen good for you. 30. Freddie’s income is $20 a month. In June, cookies cost $1 apiece, crackers cost $1 apiece, and Freddie buys 5 cookies and 15 crackers. In July, cookies cost $1.50 apiece, crackers cost $.50 apiece, and Freddie buys 9 cookies and 13 crackers. Can you determine whether cookies are a normal or an inferior good 4–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. for Freddie? What about crackers? Fully justify your answers. 31. You consume only beer and pizza. Beer is a normal good. One day the price of beer goes down and the price of pizza goes up. Must you consume more beer? Justify your answer with indifference curves. 32. Herman Munster eats ten cheese sandwiches every day for lunch, and he would continue eating ten cheese sandwiches every day even if the price of cheese doubled. Can you determine whether cheese sandwiches are an inferior good for Herman? Justify your answer. 33. Your income is $100 a month. You sign up for a telephone plan that costs $10 a month plus 10 cents per call. a) Once you’ve signed up for the phone plan, draw your budget constraint between phone calls and “all other goods”, with “all other goods” mea- sured in dollars. b) Now suppose the phone company offers an alternative plan that costs $20 a month plus 5 cents per phone call. You like this plan better so you switch; after switching, you make fewer calls per month. Illustrate this situtation with indifference curves. c) True or False: Given the information in part b), phone calls must be a Giffen good for you. d) True or False: Given the information in part b), phone calls must be an inferior good for you. 34. Suppose apples are an ordinary (non-Giffen) inferior good and oranges are a Giffen good. Which do you expect to have the steeper Engel curve, apples or oranges? Explain why. 35. If your indifference curves between X and Y are shaped as in Exhibit 3-10, what is your income elasticity of demand for X? What is your price elasticity of demand for X? 36. Gina’s demand curve for chocolate bars has the same elasticity at all points. True or False: That elasticity must be equal to 1. (Note: This problem is hard.) 37. Suppose that your price elasticity of demand for carrots is -2 and the price of carrots goes up 1%. What happens to your total expenditure on carrots? 38. When the price of carrots goes up, Maeve’s total expenditure on carrots goes down. What can you conclude about her price elasticity of demand for carrots? 39. True or False: For a normal good, the price elasticity of demand must be greater in absolute value than the income elasticity of demand. Hint: Imagine a 1% change in price, and think about income and substitution effects. Which of these effects is reflected in the income elasticity of demand? Which in the price elasticity of demand? 40. In August, 1990, East German taxicab drivers were on strike demanding lower cab fares. What must the drivers have believed about the price elasticity of demand for taxicab rides? 41. In 2003, tolls were raised on seven bridges across the Delaware River, connect- ing Pennsylvania to New Jersey. In the first two months of the year, bridge traffic fell by 17%, but revenue increased by 123% because of the higher tolls. What is the price elasticity of demand for using these bridges to cross the Delaware River? 4–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Mix and Match Problems The following “mix and match” procedure produces 192 variations on problems 9 and 10 in the textbook. At the end of this section (beginning on page 4-10) I give some illustrations of the problems you can create via the mix and match procedure. STEP I: Choose an “opening” from among choices A − L below. (Twelve choices.) STEP II: Each of the twelve openings contains contains the phrase “just as happy as”. Either leave this phrase unchanged, or replace it with “just able to afford the same basket that you bought”. (Two choices.) STEP III: Choose a “closing” from among choices P − S below. (Four choices.) STEP IV: Either do or do not interchange X’s and Y ’s throughout the prob- lem. (Two choices.) For example, the following set of choices essentially reproduces problem 9 from the text. I: Opening A; II: Leave phrase unchanged; III: Closing P ; IV: Do not interchange X and Y . Likewise, the following set of choices essentially reproduces problem 10 from the text. I: Opening H; II: Replace the phrase; III: Closing S; IV: Do interchange X and Y . The following sets of choices essentially ask students to reproduce the argu- ments in the main body of the textbook. I: Opening H; II: Don’t replace the phrase; III: Closing P or Q; IV: Do not interchange X and Y . In this case, you should delete the part of closing P or Q that asks the student to produce an argument different from the one in the text. NOTE: If in Step IV, you elect to switch X’s and Y ’s, I think it’s a good idea to include a “don’t get confused” warning. For example, in problem 10 in the textbook, I have changed “the price of Y goes up” to “the price of Y (not X! ) goes up”. The Openings A. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X goes up (while your income and the price of Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the price of X returns to its Monday level, but at the same moment your income falls by just enough so that you are just as happy on Wednesday as on Tuesday. Draw your new budget line and your new optimum point. Label the optimum W . B. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X falls (while your income and the price of Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the prices of X and Y remain at their Tuesday levels, but at the same moment your income falls by just enough so that you are just as happy on Wednesday as on Monday. Draw your 4–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. new budget line and your new optimum point. Label the optimum W . C. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, your income falls (while the prices of X and Y remain fixed). Draw a diagram, with X on the horizon- tal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income returns to its Monday level, while the price of X rises by enough so that you are just as happy on Wednesday as on Tuesday. Draw your new budget line and your new optimum point. Label the optimum W . D. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, your income rises (while the prices of X and Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income remains at its Tuesday level, while the price of X rises by enough so that you are just as happy on Wednesday as on Monday. Draw your new budget line and your new optimum point. Label the optimum W . E. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, your income rises (while the prices of X and Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income returns to its Monday level, while the price of X falls by enough so that you are just as happy on Wednesday as on Tuesday. Draw your new budget line and your new optimum point. Label the optimum W . F. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, your income falls (while the prices of X and Y remain fixed). Draw a diagram, with X on the horizon- tal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income remains at its Tuesday level, while the price of X falls by enough so that you are just as happy on Wednesday as on Monday. Draw your new budget line and your new optimum point. Label the optimum W . G. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X falls (while your income and the price of Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the price of X returns to its Monday level, while your income increases by enough so that you are just as happy 4–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. on Wednesday as on Tuesday. Draw your new budget line and your new optimum point. Label the optimum W . H. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X rises (while your income and the price of Y remain fixed). Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the price of X remains at its Tuesday level, while your income increases by enough so that you are just as happy on Wednesday as on Monday. Draw your new budget line and your new optimum point. Label the optimum W . I. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X falls and the price of Y rises. You find that on Tuesday you are just as happy as on Monday. Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the Tuesday prices remain in effect, but your income increases. In fact, Wednesday’s percentage increase in your income is equal to Tuesday’s percentage increase in the price of Y . Draw your new budget line and your new optimum point. Label the optimum W. J. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X rises and the price of Y falls. You find that on Tuesday you are just as happy as on Monday. Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the price of X falls by just enough so that the relative price of X in terms of Y is the same on Wednesday as on Monday. Draw your new budget line and your new optimum point. Label the optimum W . K. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X rises and the price of Y falls. You find that on Tuesday you are just as happy as on Monday. Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the Tuesday prices remain in effect, but your income falls. In fact, Wednesday’s percentage decrease in your income is equal to Tuesday’s percentage decrease in the price of Y . Draw your new budget line and your new optimum point. Label the optimum W. L. Suppose the only goods you buy are X and Y . a) Suppose that between Monday and Tuesday, the price of X falls and the 4–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. price of Y rises. You find that on Tuesday you are just as happy as on Monday. Draw a diagram, with X on the horizontal axis and Y on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, the price of X rises by just enough so that the relative price of X in terms of Y is the same on Wednesday as on Monday. Draw your new budget line and your new optimum point. Label the optimum W . The Closings P. In each of parts (c), (d) and (e), determine whether the statement is (1) true always, (2) false always, (3) true if X is an inferior good, but otherwise false, (4) false if X is an inferior good but otherwise true, (5) true if X is a Giffen good, but otherwise false, or (6) false if X is a Giffen good but otherwise true: c) M is to the left of T . d) T is to the left of W . e) M is to the left of W . f) True or False: Every Giffen good is an inferior good. Justify your answer by using the earlier parts of this problem, not by using the argument given in the text. Note to instructors: For a slight variation on closing P , change “Every Giffen good is an inferior good” to “A normal good cannot be Giffen” in part f). This is of course logically equivalent, but to a certain class of students it will appear to be a very different problem. Q. Answer the following questions: c) In terms of the locations of points M , T , and W , what does it mean for X to be an inferior good? d) In terms of the locations of points M , T , and W , what does it mean for X to be a Giffen good? e) Which of the following statements is always true and why: M is to the left of T ; M is to the right of T ; M is to the left of W ; M is to the right of W ; T is to the left of W ; T is to the right of W . f) True or False: Every Giffen good is an inferior good. Justify your answer by using the earlier parts of this problem, not by using the argument given in class. Note to instructors: As with closing P , closing Q has another slight variation: change “Every Giffen good is an inferior good” to “A normal good cannot be Giffen” in part f). This is of course logically equivalent, but to a certain class of students it will appear to be a very different problem. R. Answer the following questions: c) In terms of the locations of points M , T , and W , what does it mean for X to be a normal (as opposed to inferior) good? What does it mean for Y to be a normal good? d) Y is called a Figgen good if it is true that “when the price of X goes down, the quantity demanded of Y goes up” (or equivalently, “when the price of X goes up, the quantity of Y demanded goes down”). In terms 4–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. of points M , T and W , what would it mean for Y to be a Figgen good? (Be careful to keep your X’s and Y ’s straight!) e) True or False: Every Figgen good is a normal good. Give a complete justification for your answer. f) True or False: A Figgen good cannot be Giffen. Give a complete justifi- cation for your answer. Note to instructors: For a further variation on closing R, change “Every Figgen good is a normal good” to “An inferior good cannot be Figgen” in part e). S. Answer the following questions: c) In terms of the locations of points M , T , and W , what does it mean for X to be a normal (as opposed to inferior) good? What does it mean for Y to be a normal good? d) Y is called a Neffig good if it is true that “when the price of X goes up, the quantity demanded of Y goes up” (or equivalently, “when the price of X goes down, the quantity demanded of Y goes down”). In terms of points M , T and W , what would it mean for X to be a Neffig good? e) True or False: Every inferior good is a Neffig good. Fully justify your answer. f) True or False: Every Giffen good is a Neffig good. Fully justify your answer. Illustrations The following problems illustrate the results of the mix-and-match procedure. In some cases I have changed X and Y to, e.g. wine and roses, just for variety. 1. (STEP I: F. STEP II: no switch. STEP III: P. STEP IV: no switch) Suppose that the only goods you buy are wine and roses. a) Suppose that between Monday and Tuesday, your income falls (while the prices of wine and roses remain fixed). Draw a diagram, with wine on the horizontal axis and roses on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income remains at its Tuesday level, but the price of wine falls. In fact, it happens to fall by just enough so that you are equally as happy on Wednesday as on Monday. Draw your new budget line and your new optimum. Label it W . In each of parts (c), (d) and (e), determine whether the statement is (1) true always, (2) false always, (3) true if wine is an inferior good, but otherwise false, (4) false if wine is an inferior good but otherwise true, (5) true if wine is a Giffen good, but otherwise false, or (6) false if wine is a Giffen good but otherwise true: c) M is to the left of T . d) T is to the left of W . e) M is to the left of W . f) True or False: Every Giffen good is an inferior good. Justify your an- swer by using the earlier parts of this problem, not by using other arguments we gave in class. 2. (STEP I: E; STEP II: no switch; STEP III P (variant); STEP IV: no switch) 4–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Suppose the only goods you buy are bread and circus tickets. a) Suppose that between Monday and Tuesday, your income rises (while the prices of both bread and circus tickets remain fixed). Draw a diagram, with bread on the horizontal axis and circus tickets on the vertical, to illustrate how your budget line moves. Illustrate your optimum points on the two budget lines, labeling Monday’s optimum M and Tuesday’s optimum T . b) Now suppose that on Wednesday, your income returns to its Monday level, but at the same moment the price of bread falls by exactly enough so that you are just as happy on Wednesday as on Tuesday. Draw your new budget line and your new optimum. In each of parts (c), (d) and (e), determine whether the statement is (1) true always, (2) false always, (3) true if bread is an inferior good, but otherwise false, (4) false if bread is an inferior good but otherwise true, (5) true if bread is a Giffen good, but otherwise false, or (6) false if bread is a Giffen good but otherwise true: c) M is to the left of T . d) T is to the left of W . e) M is to the left of W . f) True or False: A normal good cannot be Giffen. Justify your answer by using the earlier parts of this problem, not by using other arguments we gave in class. 3. (STEP I: D; STEP II: no switch; STEP III: Q; STEP IV: no switch) You consume two goods, X and Y . From Monday to Tuesday, your income rises. On Wednesday, your income remains at its Tuesday level, but the price of X rises. On Wednesday you are exactly as happy as on Monday. a) Draw your budget lines for all three days. Be sure to label which is which. Label the three days’ optimum points M , T and W (for Monday, Tuesday and Wednesday). b) In terms of the locations of M , T and W , what does it mean for X to be inferior? c) In terms of the locations of M , T and W , what does it mean for X to be Giffen? d) Which of the following is always true, and why?: M is to the left of T ; M is to the right of T ; M is to the left of W ; M is to the right of W ; T is to the left of W ; T is to the right of W . e) Using your answers to the earlier parts of this problem, prove that a Giffen good must be inferior. 4. (STEP I: F; STEP II: no switch; STEP III: R; STEP IV: no switch) You consume two goods, X and Y . Suppose that from Monday to Tuesday, your income falls. From Tuesday to Wednesday, the price of X falls. You are exactly as happy on Wednesday as on Monday. a) Draw your budget lines for all three days. Label the three days’ optimum points M for Monday, T for Tuesday, and W for Wednesday. b) In terms of the points M , T and W , what would it mean for X to be a normal (as opposed to inferior) good? What would it mean for Y to be a normal good? c) Y is called a Figgen good if it is true that “when the price of X goes down, the quantity demanded of Y goes up”. In terms of points M , T and W , 4–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. what would it mean for Y to be a Figgen good? (Be careful to keep your X’s and Y ’s straight!) d) True or False: Every Figgen good is a normal good. Give a complete justification for your answer. 4–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 4 1. a) Fewer. b) No. 2. The full picture is: ROSES T M TUESDAY WEDNESDAY MONDAY WINE with the Wednesday optimum somewhere on the darkened part of the Wednes- day budget line. a) In going from the Monday optimum M to the Tuesday optimum T, consumption of wine must go down. b) No, because the Monday optimum M is outside the Tuesday budget line. c) Wednesday. d) Yes. You certainly buy less on Wednesday. If you bought more wine on Wednesday, the Wednesday optimum would have ‘to be to the right of (and consequently below) the Monday optimum M; this would require the two indifference curves to cross. e) No. The change from Tuesday to Wednesday is a pure income effect. Thus its direction depends on whether wine is a normal or an inferior good. 3. a) A, C, D b) B c) C,D d) D 4–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 4. The picture is: OTHER GOODS C A B Eggs are inferior because B is to the right of C. Eggs are EGGS not Giffen because B is to the left of A. 5. The picture is: ROSES W T M WINE M must be to the right of W because it is at a steeper point on the same indifference curve. It is given that W is to the right of T. Therefore M is to the right of T, which makes wine a normal good. So true. 4–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 6. a) The picture shows your old and new budget lines. Y A B C NEW OLD COMPENSATED X b) The substitution effect is the move from A to C and the income effect is the move from C to B. c) The substitution effect is a rightward move from A to C; C is at a flatter place on the same indifference curve. d) If X is normal, the income effect is a rightward move from C to B. e) If X is inferior, the income effect is a leftward move from C to B. f) False; the opposite is true. If X is normal, then B is left of C is left of A, so B is left of A, so consumption must rise. If X is inferior, B could be either left or right of A, so consumption could rise or fall. 7. The picture is: Roses M T W Wine M is to the left of T when wine is Giffen; T is to the left of W always; M is to the left of W when wine is inferior. Part f) is true: If wine is Giffen then M is left of T, and T is always left of W, so if wine is Giffen then M is left of W, which is to say that if wine is Giffen then wine is inferior. 4–19 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8. a) See the graph below. Note that Wednesday’s budget line passes through the point M , to reflect the fact that you can just afford M on Wednesday. Wine T M W Eggs b) If eggs are Neffig, then W is left of T . M is surely left of W to avoid a crossing. So if eggs are Neffig, then M is left of T , i.e. eggs are normal. So true. c) An inferior good can’t be normal, so (because of part b) an inferior good can’t be Neffig. So true. 9. WINE M,T and W are your optima on Monday, Tuesday and Wednesday. W T M is below W because it is at a flatter point on the same indifference curve. If wine is inferior, then T is below M M. So if wine is inferior, then T is below W. That is, if wine is inferior, you buy less wine on Tuesday than Wednesday. So true. EGGS 4–20 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 10. WINE M,T and W are your optima on Monday, Tuesday and Wednesday. T is right of W because it is at a M W flatter point on the same indifference curve. If eggs are Giffen, then W is right of M. So if eggs are Giffen, then T is right of M. That is, if eggs are Giffen, T you buy more eggs on Tuesday than Monday. So true. EGGS 11. The picture shows that X is Giffen, so it must also be inferior. The points ($3,4) and ($6,5) are on the demand curve for X. 12. AOG pp C pp A B is directly below A (given) and C is left of A (geometry). Thus C is left of B so shoes are definitely inferior for Tara. So false. pp B SHOES 13. SOCKS pp C B is directly to the left of A (given) and C is above A A pp B pp (geometry). Thus C is above A, so socks must be normal. So true. SHOES 4–21 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 14. HAM pp B Original optimum is at A; new C pp optimum is at B. Substitution effect is from A to C ; income effect is from C to B. The graph reflects the inferiority of pp A ham by the fact that B is above C . Also, C is above A by geometry. It follows that B is above A, so the statement in part b) is True. GREEN EGGS 15. LIVER a) C is above A by geometry; B is C pp below A (given). Therefore B is below C , so liver must be a normal good for Leopold. pp A b) Because liver is normal, it cannot be Giffen. B pp KIDNEYS 16. LETTUCE The substitution effect is from A to C and the income effect is from C to B. C is on the same indifference C curve as A but at a steeper point, so C is above A; thus the substitution B A effect leads to more lettuce. B is below C because lettuce is normal; thus the income effect leads to less lettuce. CARROTS If Bugs spends very little on carrots, then a rise in the price of carrots probably has a small income effect. Thus the substitution effect is (probably) bigger than the income effect, so when the price of carrots rises, Bugs's lettuce consumption goes up. 4–22 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 17. When the price of X goes up, you move from point A to point B: Y C B A X It is given in the problem that B lies above A, and that C lies above B. Therefore the vertical distance from A to C (the substitution effect) must be greater than the vertical distance from C to B (the income effect). 18. We are told in the first sentence that there is no income effect. Therefore when the price of eggs rises, there is only a substitution effect, which surely leads you to consume fewer eggs. 19. First, we are given that on Tuesday you can no longer afford Monday’s basket, and on Tuesday you are happier than Monday. That tells us that the graph looks like this: Y T M X 4–23 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Now let’s add in a compensated budget line so we can see the income and substitution effects: Y X T M X The combined substitution effect is the move from M to X and the combined income effect is the move from X to T . Because X is a normal good, T must be right of X. Because of the configuration of the original graph, M must be right of T . Thus the horizontal distance from X to M is greater than the horizontal distance from T to M . In other words, the combined substitution effect is greater than the combined income effect. 20. ORANGE SODA Judith starts at A and ends at B. To ' determine whether root beer is normal we have to look at the effect of a parallel shift, so we add the dashed A budget line for comparison. Now we observe that point C is to the C right of A (flatter point; same indifference B curve) and that B is vertically aligned with A (given in the problem). Thus C is right of B, so root beer is normal. 5 ROOT BEER 4–24 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 21. SODAS (DRAWING IS NOT TO SCALE!) In April, Frieda chooses point A. In May, she chooses pointM. The indifference curve tangent at A must pass to the left of M; otherwise the curves tangent at A and M would cross. Therefore M is on a higher indifference curve, and the answer to part a) is that Frieda is happier in May. For part B, there are two ways to get the answer: Method I: Draw the budget line shown, parallel to the May line but tangent to the April curve. Note that X is right of A by geometry and A is right of M (given) so X is right of M, making eggs inferior. Method II (not shown): Draw a budget line tangent to the higher indifference curve but parallel to the (steeper) April budget line. The tangency Y will lie to the left of M, which is left of A. Y left of A makes eggs inferior. The underlying intuition: Eggs got cheaper, so the substitution effect says "buy more eggs". ButFrieda buys fewer eggs, which can only be due to the income effect. She's effectively richer, M and the income effect is saying "fewer eggs". Thus eggs must be inferior. A X EGGS 22. Without a seat belt, the driver is at A and with a seat belt the driver is at B. Assuming speed and safety are normal, SPEED B is above and to the right of C . By geometry,C is above and to the left of A. Thus B must be above A (people certainly drive faster). But B could be either left or right of A (either more or pp B fewer lives might be saved). So true. C pp A pp SAFETY 4–25 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 23. 72 INCOME The substitution effect (A to C ) is leftward. The income effect (C to B) is rightward if leisure is a normal good; leftward if leisure is an inferior good. If leisure is inferior, then B is surely left of A. That is, a higher wage leads to less leisure, hence 48 more labor. So in this case the labor supply curve certainly slopes B upward. pp C If leisure is normal, B could be pp left or right of A, so the labor A supply curve could slope either pp direction. So part e) is True. 24 LEISURE HOURS The person whose income is derived entirely from wages feels a large income effect from a wage change. In that case (assuming leisure normal) B is far to the right of C , hence likely to be far to the right of A, so labor hours respond strongly to a wage change; that person's labor supply curve is relatively flat. 24. a) $2250. $0. b) $0. c) The budget line is the flatter line in this picture: SPENDING NEXT YEAR 2500 2250 1667 1800 SPENDING TODAY d) Finding $400 shifts the budget line out parallel to itself till it passes through ($2200,$0) and ($0,$2350). Being informed of a $500 raise next year does the same thing. A rise in the interest rate to 50% shifts the budget line to the steeper line in the above picture. e) Both would lead to the same budget line, hence the same optimum point, hence the same amount of spending both today and tomorrow. f) The tangency is at ($1000,$1000). 4–26 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. g) As already noted, the budget line shifts as in the above picture. You decrease current spending, increase future spending, and are happier. h) The substitution effect is leftward and upward along the illustrated indifference curve. You cannot determine the direction of the income effect. 25. a) True. When his income goes up, Herman must by more Munster cheese, because there’s nothing else to buy. b) True. When the price of Munster cheese goes up, Herman is surely forced to buy less of it. There’s nothing else to cut back on. 26. a) It is a hyperbola. b) It is a vertical line. c) −1 27. In these circumstances, you consume either no X or only X. When you consume no X, a change in the price of X has no effect on your well–being, so no compensation is called for. When you consume only X, a change in the price makes you better off if it allows you to consume any more X at all, and worse off it it allows you to consume less X. Thus your income must be compensated by just enough to keep your consumption of X constant. For example, if the price of X were to double, your income would also be doubled in the imaginary experiment described in the textbook. It follows that your compensated demand curve looks like this: P Q 28. True. The compensated demand curve eliminates the income effect. For a normal good, this means that a price increase yields a smaller quantity reduction along the compensated demand curve than along the uncompensated demand curve. For an inferior good, the reverse is true. 29. True, since the uncompensated demand curve differs from the compensated de- mand curve only by the incorporation of the income effect, and the income effect from a change in the price of bubblegum is likely to be a small one. (Even if the price of bubblegum were to multiply tenfold, it is unlikely that your lifestyle would change appreciably.) On the other hand, housing consumes a large part of most people’s budgets, so that even a modest rise in the cost of housing could have a substantial income effect. 30. Your income elasticity of demand is 1. Your (uncompensated) price elasticity of demand is −1. 31. It means that when your income goes up, your consumption of the luxury good increases by a greater proportion than your income does. If your income increases by 1%, your consumption of luxury goods increases by more than 1%. But you cannot increase your consumption of all goods by more than 1% without violating the budget constraint. Therefore not all goods can be luxuries. 4–27 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. In fact, this can be made more precise. When your income increases by 1%, your expenditures on goods must increase by exactly 1% “on average.” Thus the average income elasticity of demand for all goods must be 1. In the averaging process, goods must be weighted according to the share of your income that is spent on them. Suppose that you consume only X and Y. Write kX and kY for the fraction of your income that you spend on X and the fraction that you spend on Y. Write ηX and ηY for your income elasticities of demand for X and Y. Then we must have kX · ηX + kY · ηY = 1. If you want to prove this formula, start with the expressions PX · X kX = I PY · Y kY = I PX · ∆X + PY · ∆Y = ∆I. (First explain what each of these expressions means and why it is true.) Then insert the expressions for kX , kY , ηX and ηY into the formula and use algebra to simplify. 32. The demand for gasoline from Gus’s, because it has more substitutes (such as gasoline from the competing gas station across the street). Answers to Numerical Exercises N1.a) The equation of the indifference curve can be written y = c/x for some constant c. Differentiating gives the slope as −c/x2 = −y/x. b) The equation of the budget line is x + y = 40. The equality between the slope of the indifference curve and the slope of the budget line can be written −y/x = −1. Combining these equations gives x = y = 20. Thus the answer is 20. c) Now the equations are 4x + y = 40 and −y/x = −4. This gives x = 5 and y = 20. Thus the answer is 5. d) Your demand curve goes through (P = 1, Q = 20) and (P = 4, Q = 5). e) The original indifference curve passes through (20, 20), so its equation must be xy = 400. The slope of the compensated budget line is −4; at a tangency between this line and the indifference curve we must have −y/x = −4. Solving these equations together gives x = 10 and y = 40. So the answer is 10. f) Your consumption falls by 15, from 20 to 5. Of this, the fall from 20 to 10 (10 units) is due to the substitution effect and the fall from 10 to 5 (5 units) is due to the income effect. N2.a) b∆I. I · ∆X I · b∆I bI b) η = = = . X · ∆I X · ∆I X c) η = 1 − a/X. d) η → 1 e) 1 N3.a) 1 − c/X = η. b) If X = 0, η = −∞, and if P = 0, η = 0. N4. −1. 4–28 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Five: The Behavior of Firms General Discussion In teaching the theory of the firm, it is common to begin with production, derive the various cost curves, and then derive the firm’s supply behavior. While this order is the “logical” one, it presents significant pedagogical difficulties. The most serious is that, for the duration of several lectures, students are utterly baffled as to what all of the production machinery is for . The present chapter seeks to address this difficulty, by showing students “up front” how the firm’s supply behavior is determined by its marginal cost curve. This has the added advantage of reinforcing one of the important lessons of consumer theory—the principle of equimarginality— and showing students that the same principle underlies the behavior of both consumers and firms. Once students have seen the importance of the marginal cost curve, they tend to be far more tolerant of the time taken in later chapters to determine how it arises. Because the goal is a quick appreciation of the fact that optimization is the same thing as equating costs and benefits at the margin, almost no time at all is devoted to discussing why marginal cost should be upward sloping. A single example—that of a farm on which some acres are more fertile than others—is more than enough to satisfy students at this stage. Talk of diminishing marginal returns will come soon enough in Chapter 6. Section 6.1 derives an upward sloping (or U-shaped) marginal cost curve from the assumption of diminishing marginal returns. Thus Chapter 5 plus Section 6.1 constitutes a complete treatment of the firm’s supply behavior in the short run. Some instructors will want to cover part or all of Chapter 6 before returning to Chapter 5, and the structure of the book makes this easy to do. Indeed, once Chapter 6 has been covered, the main ideas of Chapter 5 should take less than a lecture. Although logical purists will want to cover production before mentioning costs, and although, as I have said, the book can easily accommodate this viewpoint, I would like to make one more argument against extreme logical purity. The argu- ment is that the usual order of things is really no more “logical” than the order in the textbook. If we were true logical purists, we would never mention supply until after a full treatment of the firm, we would never mention demand until af- ter consumer theory, and we would never use mathematics without first insisting on a complete logical foundation for the real number system. The latter would disqualify many outstanding economists from ever publishing anything. In practice, we never insist on truly logical orders of presentation in any ma- terial. Nobody seriously suggests that school children should understand Cauchy convergence before learning to perform decimal arithmetic, although it is certainly a logical prerequisite. It seems to me to be less extreme, but no more defensible, to insist that students learn details of production without the motivation of first seeing cost curves in use. If you agree, cover chapter 5 before chapter 6. If you disagree, go to chapter 6 directly. Let a thousand flowers bloom. 5–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Which of the following circumstances might affect the prices charged by a young doctor just out of medical school and why? a) The high cost of tongue depressors. b) The high cost of X-ray machines (assume that every doctor must have one X-ray machine in his office). c) The high cost of a medical education. d) The fact that this particular young doctor is heavily in debt due to student loans. e) The doctor’s discovery that his loan payments will be higher than he had expected. f) The fact that only a limited number of people are permitted to become doctors. g) An epidemic. h) The fact that this doctor has recently been sued for malpractice. Fortu- nately for him, the public is unaware of the lawsuit, but unfortunately for him, his insurance company is well aware of it and has raised his rates. i) It becomes generally known that this doctor’s insurance company has raised his rates. j) Malpractice insurance rates for all doctors go up. k) The doctor in the office next door suffers fatal consequences when he attempts to remove his own appendix. l) The doctor decides to join a very expensive country club. 2. The RH Snippet company has one president and 1000 assembly line workers. Which of the following events would have a bigger impact on the price of Snippets and why? a) The president gets a raise of $1,000,000 a year. b) A new union contract raises each worker’s wages by $1,000 a year, but allows the firm to fire as many workers as it wants to. 3. Kate runs the only dress shop in Hooterville. To make a dress, she uses $1 worth of fabric. She sells 100 dresses per month. One day, she learns that the price of fabric has doubled and that the landlord is reducing her rent by $100 per month. Do you expect the price of Kate’s dresses to rise or to fall? Why? 5–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 5 1. If the benefits are still $1.5 billion and the cost of continuing is $1.2 billion with certainty then the project should be completed. 2. Vandalism at ABC is a fixed cost and does not affect prices. Pilferage at XYZ is a marginal cost. So true. 3. The rent on the factory is a fixed cost and has no effect on the price of drapes. The price of fabric is a variable cost and does affect the price of drapes. 4. Plan A affects variable cost and hence price; Plan B affects a fixed cost and hence does not affect price. The patients benefit from Plan A but not Plan B. 5. The retraining course is a fixed cost, so it will not affect the price of eye exams. But if some dentists are driven out of dentistry (or out of Smallville) by this new expense, then the price of a dental exam can rise. 6. True. One department store does not change its prices in response to a rise in fixed costs. But if there are initially many stores and some are driven from the industry, then prices will rise. 7. a) This increases the marginal cost of producing hamburgers and so can affect Waldo’s behavior, including his prices. b) This is equivalent to a). A tax of 50 cents per hamburger is, from Waldo’s point of view, no different than an increase in the price of meat. Therefore the price of a hamburger can be affected. c) This is a fixed cost, and therefore has no effect on Waldo’s behavior unless it drives him out of business. d) This appears at first to be equivalent to c), but it is not. The difference is that in c), only Waldo pays the fine, whereas here every restaurant in town pays it. If some of those other restaurants leave the marketplace, the demand for Waldo’s hamburgers will rise, leading to a change in his marginal revenue curve and a change in his price. e) This cost is completely sunk and has no effect on behavior. Note that this sunk cost is not equivalent to the fixed cost in part c). The fixed cost in c) does not become sunk until Waldo decides to keep the restaurant open another year. Thus it can affect his decision about whether to remain in business, but not the price of hamburgers if he remains. The cost here is sunk from the beginning, and so has no effect on anything. In other words, in part c) Waldo might go out of business, but in part e) he will not. f) This causes a change in demand, consequently a change in marginal revenue, con- sequently a change in quantity, and consequently a change in price. A few general comments about this problem are in order. One is that students sometimes think that Waldo gets to decide which costs to count as fixed and which to count as marginal, as though this were a matter of accounting procedures. But a cost either is fixed or it isn’t, regardless of how Waldo keeps his books. Another comment: Students sometimes say in response to part c) or part e) that although marginal cost is unchanged, meaning that price will not change, Waldo can attempt to compensate for his loss in some other way, by using cheaper meat or hiring fewer waitresses. These students have missed the point entirely. If Waldo is a profit maximizer, he is already using the profit–maximizing quantity of meat and hiring the profit–maximizing number of waitresses. Any change in this 5–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. strategy will make Waldo worse off, not better. Finally, students sometimes attempt to answer this question by using the sup- ply and demand apparatus that we learned in Chapter 1. This is illegitimate for the following reason: In Chapter 1, we made some reasonable guesses about when supply curves will shift. For example, we said that an increase in the price of fertilizer causes a leftward shift in the supply curve for wheat. Now, however, we are embarking on a more careful and rigorous examination of firm behavior, which will lead in forthcoming chapters to a more careful and rigorous examination of the sources of supply curves. Thus we no longer want to make guesses about changes in supply behavior; we want to deduce changes in supply behavior from first principles. The ultimate reward (which comes in Chapter 7) is this: we will use the ideas of this chapter to figure out how and when supply curves shift. Then we will combine these ideas with the ideas of Chapter 4, which tell us how and when demand curves shift, and with the ideas of Chapter 1, which tell us how shifts in supply and shifts in demand affect prices and quantities. This will enable us to make predictions about prices and quantities without resorting to any guesswork. 8. a) False. The salary increase does not affect the marginal cost of providing seats at the ballpark, nor does it affect marginal revenue (since it does not affect demand). Hence no effect on price. Sometimes students attempt to argue that there is an effect on the marginal cost of hiring ballplayers. But the team is not selling ballplayers; it is selling seats at the ballpark. Only the marginal cost of providing those seats is relevant. For example, it is probable that the number of janitors hired to clean up after the game goes up with the number of seats that are filled. Thus an increase in janitors’ salaries, unlike an increase in players’ salaries, could cause an increase in ticket prices. Of course, it remains the case that whenever a player gets a heavily publicized salary increase, sportswriters report that the fans will pay through higher ticket prices. This is why some people are sportswriters and other, different, people are economists. b) Now the demand for tickets is changed, leading to a change in marginal revenue and possibly a change in price. The change in price is due entirely to the change in demand, and is unaffected by the amount that the Cubs pay to acquire the player. If, contrary the Cubs’ hopes, the player has no effect on the demand for tickets, there will be no change in ticket prices. 9. False. Sunk costs are sunk. 10. (a), (b) and (d) are relevant; (c) is a sunk cost. 11. We have the following chart: Quantity Total Revenue Marginal Revenue Total Cost Marginal Cost 1 $20 $20 $2 $2 2 $36 $16 $6 $4 3 $48 $12 $11 $5 4 $56 $8 $18 $7 5 $60 $4 $26 $8 If the firm must produce a whole number of items, it produces 4 and sells them at a price of $14. If it can produce fractional numbers, it presumably produces some quantity between 4 and 5 and sells them at a price between $12 and $14. 5–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 12. a) Quantity 2 at a price of $18. b) Quantity 1 at a price of $20. c) Quantity 2 at a price of $18. d) It produces nothing. 13. If the area consists entirely of stores, then Wilma is correct. Rents are fixed costs that do not affect prices. The reason that rents are high is that stores are willing to pay a lot for this location, where prices are high. But if many of the buildings in the area are used for office space, or anything other than stores, then Fred might be right. The high rents (caused perhaps by a high demand for office space in this location) have driven some stores out of the area, raising the demand for the products of those that remain, and consequently increasing prices. Answers to Numerical Exercises N1. x2 − (x − 1)2 = 2 · x − 1 dollars per liter. N2. (y/100)2 . N3. (y/100)2 −((y −1)/100)2 = y/5000−1/10000 dollars per centiliter = y/50−1/100 dollars per liter. If the number of liters is x = y/100, then we can write this as 2 · x − 1/100 dollars per liter. N4. This is correct within a penny. N5. Let z be the number of milliliters, so that x = z/1000. Total cost is (z/1000)2 . Marginal cost is (z/1000)2 − ((z − 1)/1000)2 = z/500000 − 1/1000000 dollars per milliliter = z/500 − 1/10000 dollars per liter = 2 · x − 1/10000 dollars per liter. We now see that when we estimate marginal cost by $2 · x, we are off by no more than one one– hundredth of a cent. If you measure in even smaller units, you will find that the error in the approximation can be made arbitrarily small. Thus when there is no limit to the divisibility of the orange juice, we can say that the marginal cost is exactly $2 · x per liter. 5–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Six: Production and Costs General Discussion The chapter introduction uses simple and concrete examples to explain the distinction between short-run and long-run decision-making, and then explains that we will study the short run and the long run as separate topics. Section 6.1 develops the complete short-run theory without reference to the long run. Section 6.2 develops the complete long-run theory without reference to the short-run. Section 6.3 ties the two theories together. This organization offers the instructor a lot of options. Some will want to cover only 6.1, moving on directly from there to Chapter 7 (Competition). This has the advantage of deferring the more difficult material in 6.2 and 6.3 until after students have developed a little more sophistication. Others will want to cover 6.1 and 6.2, giving full accounts of short-run and long-run considerations, while deferring or skipping over the subtle relationships of 6.3. Those who prefer the traditional full-blown approach will want to use the entire chapter. A more radical option is to cover 6.1 but skip 6.2 and 6.3 completely. Although this omits a lot of important material, I believe that it is a reasonable approach for classes that do not consist primarily of economics majors. If a student does not go on in economics, I would far prefer that he come away with a good feeling for the workings of competitive markets, the functioning of the price system, and the role of property rights—the material of Chapters 7 through 14— than that he be able to derive a long run marginal cost curve directly from a production function. 6–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. True or False: An upward shift in the variable cost curve is always accompa- nied by an upward shift in the marginal cost curve. 2. Bob Thomason produces theorems using hours of labor and Big Machines. In the short run, his labor is a variable factor but the number of Big Machines is fixed. When he works for L hours using M Big Machines, Bob can produce L · M theorems. There are only 3 Big Machines in the world, and they can only be rented in whole number quantities (you can not employ 1/2 of a Big Machine). Bob’s time is worth $1 per hour, and it costs $1 per hour to rent a Big Machine. a) Draw Bob’s short run total cost curve on the assumption that he em- ploys 1 Big Machine. Do the same on the assumption that he employs 2 Big Machines. Do the same on the assumption that he employs 3 Big Machines. b) Draw Bob’s long run total cost curve. c) Repeat parts a) and b) with “total cost” replaced by “average cost.” d) Repeat parts a) and b) with “total cost” replaced by “marginal cost.” 3. True or False: When a firm’s short run and long run total costs are equal, the firm is on its expansion path. 4. True or False: A firm operating at the minimum point of its long run average cost curve must also be operating at the minimum point of its short run average cost curve. 5. True or False: In the long run, the firm always chooses the least expensive production process. Thus long run average cost is never greater than short run average cost. 6. True or False: In the long run, the firm always chooses the least expensive production process. Thus long run marginal cost is never greater than short run marginal cost. Warning: The above is a quite difficult problem for students. Don’t assign it unless you are prepared to spend a lot of time going over it. The following is even more difficult. 7. Suppose that a firm is operating at a point on its expansion path, producing the quantity Q. Show that the short-run and long-run marginal cost curves cross at quantity Q. 8. Suppose that a firm experiences constant returns to scale at all levels of output. True or False: Whenever the firm increases its use of inputs, its output ex- pands proportionately. Thus this firm never experiences diminishing marginal returns to labor. 9. True or False: If a firm only uses one input, then diminishing marginal returns and decreasing returns to scale will both set in at the same point. 6–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 6 1. The following pictures are all “per hour”: OUTPUT w (ENVELOPES) TP 50 AP=MP 500 10 LABOR (WORKERS) LABOR (WORKERS) $/ENVELOPE $ TC $.10 MC=AC=AVC $5 50 ENVELOPES ENVELOPES 2. The following pictures show the new curves in boldface, with the original curves reproduced for comparison: OUTPUT TP w (ENVELOPES) 100 AP=MP 1000 50 500 10 LABOR (WORKERS) LABOR (WORKERS) $/ENVELOPE $ TC $12.50 $10 $.10 $5 AC $.05 MC=AVC 50 ENVELOPES ENVELOPES 6–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 3. Let Q be the quantity of envelopes. If Q > 200 then it pays to rent the machine whereas if Q < 200 it pays not to rent the machine. The long-run total and average cost curves take the following form: $/ENVELOPE $ TC $.10 AC $.05 200 200 ENVELOPES ENVELOPES Quantity VC TC AC AVC 4. 1 $12 $42 $42/unit $12/unit 2 $20 $50 $25 $10 3 $26 $56 $18.67 $8.67 4 $30 $60 $15 $7.50 5 $36 $66 $13.20 $7.20 6 $46 $76 $12.67 $7.67 7 $60 $90 $12.86 $8.57 8 $80 $110 $13.67 $10 5. Average cost will rise; average variable cost and marginal cost will remain unaf- fected. 6. True. 7. False. The two prescriptions are equivalent. Either amounts to staying on the expansion path. 8. In this case the firm could reduce expenditures on L and increase expenditures on K and stay on the same isocost curve. In the process it could attain higher and higher isoquants until it reached the point where M RT SLK = PL /PK . The obvious reason for doing this is that a higher level of output (and presumably profits) could be attained for constant expenditures on inputs. 9. True. The firm will stay on the 3-unit isoquant, but move to a point where the slope reflects the new relative prices of the two inputs. 10. a) If the firm cuts back to 2 units of labor, it must increase capital by 2 units (to a total of 3 units) to maintain its output level of 193. Thus M RT SLK = 2. M PL = 215 − 193 = 22 and M PK = 237 − 193 = 44. b) SRT C = 2 × 4 + 4 × 10 = 48. In the long run, the firm employs 3 units of capital and 3 of labor so LRT C = 3 × 4 + 3 × 10 = 42. c) LRT C = 55, since the firm employs 1 unit of capital and 7 of labor. d) Decreasing returns to scale because 2 units of capital and 4 of labor would produce less than twice as much. Therefore the LRAC curve must be increasing. 6–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 11. The pictures are: Typewriters Lawn mowers 9 6 3 } Isoquants 2 4 6 Workers Workers Secretaries MANUSCRIPTS Lawns mowed Lawns mowed MANUSCRIPTS PERper worker SECRETARY MPL 5 TP 1 5 SECRETARIES Workers 5 SECRETARIES Workers $ $ TC LRTC 50 50 VC 30 MANUSCRIPTS Lawns mowed MANUSCRIPTS Lawns mowed 5 5 $ per lawn mowed per manuscript AC $$per perlawn mowed manuscript 10 LRAC=LRMC 6 MC=AVC Lawns mowed MANUSCRIPTS MANUSCRIPTS Lawns mowed 5 6–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 12. The isoquants and isocosts are as follows: BUCKETS 2 1 1 2 WORKERS The expansion path passes through the following points: Workers Buckets 1 1 1 2 2 3 2 4 3 5 3 6 The product and cost curves are as follows: Workers TP VC TC MPL (Buckets of Water) ($) ($) (Buckets of Water per Worker) 1 2 2 7 2 2 4 2 7 2 3 5 4 9 1 4 5 4 9 0 5 5 6 11 0 Buckets of Water AC MC LRTC LRAC LRMC ($/bucket) ($/bucket) ($) ($/bucket) ($/bucket) 1 7 1 3 3 3 2 3.50 0 4 2 1 3 3 1 7 2.33 3 4 2.25 0 8 2 1 5 2.20 1 11 2.25 3 6–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1.a) They are hyperbolas with equations KL = 1, KL = 4, KL = 9, KL = 16. b) To compute M RT SLK , suppose that the number of units of labor is reduced by 1, to 4. How much capital must the firm employ to produce 10 units of output? The answer is 25, which is an increase of 5 units. Thus the M RT SLK is 5 units of capital per worker. √ √ The M PL is given by √20 · 5 − √20 · 4 ≈ 1.06. The M PK is given by 20 · 5 − 19 · 5 ≈ .25. c) Yes. d) To produce 10 units of output, the firm must employ 5 units of labor, for a total cost of $20 + $5 = $25. e) The condition M PK = M PL can be written as √ p √ p K ·L− (K − 1) · L = K ·L− K · (L − 1) which √ implies that K = L. Thus the firm must choose K and L so that K = L and K · L = 10. This forces K = 10, L = 10. The long run total cost is $10 + $10 = $20. f) Constant. 6–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Seven: Competition General Discussion and Teaching Suggestions 1) I believe that the best test of understanding this material is the ability to work problems in comparative statics. (For example: When the price of steel goes down, what happens to the price and quantity of Ford automobiles, in the short run and in the long run?) I believe that one of the primary goals of a chapter on competition should be to develop that ability. Therefore I have included several worked examples in the chapter, a wealth of problems at the end (see especially problems 1, 10, 11 and 12), and a special section summarizing the basic principles that the student must master (Section 7.7). 2) For many students, it can be helpful to present a taxonomy of costs, clas- sifying them according to the time periods over which they are fixed or variable, and according to whether they are felt by one firm or the entire industry. All of this is implicit in the text, of course, but it can be useful to place an explicit chart on the blackboard, something like this: A. Industry-Wide B. Firm-Specific 1. Sunk 2. Avoidable only by exit 3. Fixed in short run Variable in long run 4. Variable One can then fill in the boxes with examples, such as: In Box 1A a one-time- only surprise tax on firms in the industry; in Box 1B a one-time-only fine to be paid by the firm; in Box 2A an annual license fee; in Box 2B a yearly fine for a safety violation that the firm cannot correct; in Box 3A a rise in the price of capital; in Box 3B a rise in the cost of some firm-specific capital (e.g. the construction of a highway near land used by the firm, increasing the cost of land, which is substitutable with another factor in the long run); in Box 4A a rise in labor costs; in Box 4B a firm-specific fine per unit sold (e.g. a bar generates much noise and the owners agree to reimburse the neighbors with a fee of 5 cents per drink sold). Then one can work through the short-run and long-run consequences of a change in each kind of cost. Some cases are disposed of quickly; for example those in row 1 have no effect whatsoever and those in rows 2 and 3 have no short-run effects. In addition to the effects of changes in the various kinds of costs, students must also learn the effects of demand shifts. If they really know all of this, then they really understand the theory of competition. 7–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 3) It is traditional in this subject to assert that all costs are variable in the long run. It seems to me that there are some important exceptions (e.g. an annual license fee that does not vary with the size of the firm), and the text allows for this possibility. 4) Students who understand this chapter should be able to work the numerical exercises at the end. I tell my students that if they cannot perform these exercises, then they have missed a fundamental point. 7–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. True or False: If North Liberty, Iowa were to impose an excise tax on all corn grown in North Liberty, the consumers of corn would actually pay part of the tax. 2. True or False: In a competitive industry, some firms might be more efficient than others on average, but all firms are equally efficient at the margin. 3. True or False: In the short run, competitive firms choose output levels to minimize their short-run average costs. 4. True or False: In the short run, a firm will shut down if its total revenue fails to exceed its fixed costs. 5. True or False: A firm that shuts down must be earning negative profits, but a firm that earns negative profits might not shut down. 6. The Z.Z. Top Company earned zero profit in 2013 and, thanks to an increase in demand, a positive profit in 2014. True or False: The average cost of producing a Z.Z. Top was lower in 2014 than in 2013. 7. True or False: If the demand for beer increases, then beer makers will not only earn higher total profits in the short run, they will also earn higher average profits per bottle. 8. True or False: If a firm’s long run average and marginal cost curves are identi- cal to its short run average and marginal cost curves, then the firm’s shutdown price is always below its break even price. 9. True or False: In the long run, a rise in the wage rates of industrial workers will cause the price of haircuts to rise. 10. Books with many mathematical formulas and graphs are generally more ex- pensive than similar books written entirely in prose. True or False: Because typesetting is not part of the marginal cost of producing a book, the cost of typesetting mathematical formulas and graphs cannot explain this price difference. 11. Suppose a series of bombings destroys several of the coffee shops in your neigh- borhood. a) What happens to the price and quantity of cups of coffee sold at one of the remaining shops in the short run? b) What happens in the long run? 12. Every doctor in Coconino County uses disposable tongue depressors to examine patients, and also must keep exactly one X-ray machine in his office. The tongue depressors cost 10 cents each and the X-ray machine rents for $100 a year. The county is considering a plan to provide each doctor with unlimited free tongue depressors. An alternative plan is to provide each doctor with a free X-ray machine. a) If medicine is a competitive industry in Coconino County, compare and contrast the short-run effects of the two plans, both for the town as a whole and at each individual doctor’s office. b) If medicine is a constant-cost competitive industry in Coconino County, compare and contrast the long run effects of the two plans, both for the town as a whole and at each individual doctor’s office. c) If medicine is an increasing-cost competitive industry in Coconino County, 7–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. compare and contrast the long run effects of the two plans, both for the town as a whole and at each individual doctor’s office. 13. The Wall Street Journal reports that a number of Atlantic City casinos might shut down because of enormous outstanding debts. Comment. 14. True or False: If all people are equally efficient dishwashers, then a tax on dishwashing will be paid entirely by demanders. 15. True or False: A firm that wants to maximize its short-run profits would operate at the minimum point of its short-run average cost curve. 16. In the city of Rochester, taxi drivers form a competitive constant cost industry. Each cab driver always rents exactly one cab and also pays for gas. a) Suppose the city decides to pay half of all the drivers’ gas expenses. Fill in each box below with “goes up”, “goes down”, “unchanged”, or “uncer- tain”: Short Run Long Run Price Industry-Wide Quantity Quantity per Firm Profit per Firm Number of Firms b) Repeat part a), assuming that the city decides to pay for half of all the drivers’ cab rental expenses instead of their gas expenses. 17. The table below shows the market demand curve for widgets and the marginal cost curve of a typical firm. Each firm has fixed costs of $60. Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $10 975 1 $10 20 950 2 20 30 900 3 30 40 800 4 40 50 600 5 50 Answer the following questions, and be sure to show how you got your answers. a) What is the break-even price in this industry? b) In long run equilibrium, how many firms are in the industry? c) When the industry is in long run equilibrium, what point corresponds to a price of $20 on the short run industry supply curve? 18. Many supermarkets charge cereal manufacturers for the right to display their products prominently. True or False: If this practice were banned, cereal manufacturers would be better off in the long run. 19. Suppose there is an increase in the cost of fire insurance for department stores. a) In the short run, and assuming competition, could this affect prices of goods sold at department stores? Why or why not? b) In the long run, and assuming competition, could this affect prices of goods sold at department stores? Why or why not? c) Would your answers change if instead of competition there were only one department store in town? 7–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 20. By law, each private school in Rochester must have a standard-sized gym- nasium that costs $1,000,000 to construct. The Rochester City Council has decided to offer aid to the local private schools and is undecided about how to do it. One possibility is to subsidize teachers’ salaries; the other is to provide each school with the required gym. a) If there is only one private school in town, which plan is more beneficial to the families who send their children there? b) If private schools constitute a competitive industry, then how does subsi- dizing teachers’ salaries affect the price and quantity of schooling in the short run, both for an individual school and for the market as a whole? c) If private schools constitute a competitive industry, then how does pro- viding free gymnasia affect the price and quantity of schooling in the long run, both for an individual school and for the market as a whole? 21. Suppose there is a fall in the demand for shoes. In the long run, what happens to the price of shoes, the quantity produced by the entire industry, and the quantity produced by an individual shoemaker? Does your answer depend on whether the industry is constant-cost, increasing-cost or decreasing-cost? If so, how? 22. If the market for pizza is competitive, then a rise in the price of cheese and tomatoes could either increase or decrease the quantity of pizzas sold at a given pizza parlor. 23. If the restaurant industry is competitive and the wholesale price of food falls, then we can be sure that in the long run existing restaurants will serve more food than before. 24. Suppose that a decision is made to provide a government subsidy of $1000 per year to every restaurant in the town of Llareggub, regardless of how many meals that restaurant serves. In the long run, what happens to the number of meals per year served at any of the restaurants currently in business? Carefully explain your answer. 25. True or False: When a firm is able to earn positive profits, its average cost of production is lower than when it earns zero profits. 26. True or False: A competitive firm earns positive profits when it faces increas- ing returns to scale and negative profits when it faces decreasing returns to scale. 27. True or False: If a firm earns negative profits in the short run, it will leave the industry in the long run. 28. Suppose automobiles are produced competitively. In each of the following circumstances, determine the short-run effect on price and quantity of cars, both for the auto industry as a whole and at the Ford Motor Company: a) The price of steel goes down. b) A new government policy goes into effect whereby every producer of au- tomobiles is given a gift of $100,000 per year. c) An excellent new mass transportation system is developed. 29. Sweaters are provided by a competitive constant cost industry. Determine how each of the following circumstances would affect the price of sweaters and the quantity of sweaters sold by the Better Sweater Company. a) The government announces that it will pay $500 per year to any firm engaged in making sweaters. Answer both in the short run and in the 7–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. long run. b) The government announces that it will pay $5 per sweater to any company engaged in making sweaters. Answer in both the short run and the long run, and be as precise as possible about the size of the price change. 30. Suppose there is a fall in the price of factory space. How does this affect the price and quantity of baskets produced at the WorldWideWicker Company? a) Answer in the short run. b) Answer in the long run, assuming a constant-cost industry. 31. Suppose there is a new excise tax of $5 per haircut, and assume that barber shops form a competitive constant-cost industry. What happens to the price and quantity of haircuts at Beyond Salon? a) Answer in the short run. When you shift supply curves, use your knowl- edge of how far they must shift to get an unambiguous answer to whether quantity at Beyond Salon goes up, goes down, or remains the same. b) Answer in the long run. When you shift supply curves, use your knowledge of how far they must shift to determine whether quantity at Beyond Salon goes up, goes down, or remains the same. c) In the long run, what happens to industry-wide quantity? What happens to the number of firms in the industry? Support your answer, making use of your answer to part (b). 32. Widgets are supplied by a constant-cost industry. One day the government orders 50 gadget-makers to instantly start making widgets instead of gad- gets. (This all takes place in a country where the government can do such things.) These 50 new widget-makers have exactly the same costs as the ex- isting widget-makers. a) In the short run, what happens to the price of widgets, the industry-wide quantity, and the quantity produced at Herman’s widget farm? b) What happens in the long run? 33. Suppose that wheat is purchased only by poor people. Their demand for wheat is given by the following schedule: Price Quantity $1 per bushel 10 bushels 2 8 3 7 4 5 Now suppose that in the spirit of Christmas, a coalition of rich people decide to buy wheat and resell it to poor people for half of whatever the rich people have to pay. a) List some points on the new demand curve for wheat. b) Suppose that the rich announce their plan just before Christmas, and suppose that in the short run, the supply of wheat is fixed at 7 bushels. (That is, the supply curve for wheat is vertical at 7.) How much do poor people benefit from the generosity of the rich? c) Suppose instead that the rich announce their plan a year in advance, and suppose that wheat is supplied by a competitive constant-cost industry. Is this better or worse for poor people than if the rich had made a last- minute announcement as in part a)? 34. Suppose corn is produced only in Iowa and consumed only in California. Sup- pose there is a general rise in the incomes of Californians. True or False: In 7–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. order to predict the long-run effect on the price of corn, it is necessary to know whether corn is a normal or an inferior good for Californians. What additional assumptions might your answer depend on? 35. Apple pies are provided by a competitive constant cost industry. Granny’s Apple Pie Shop is one of the firms in this industry. In each of the following circumstances, determine which is greater: the number of pies per day that Granny sells in the short run or the number of pies per day that Granny sells in the long run. (Assume that Granny remains in the industry in the long run.) a) A new law requires all apple pie shops to purchase an annual license. b) The price of apples increases. c) The demand for apple pies increases. 36. Wally’s Widgets is a firm in the competitive constant-cost widget industry, where each firm rents exactly one widget press and uses it to convert sugar into widgets. Determine whether each of the following statements is true or false and use graphs to justify your answers. a) If the price of sugar falls, Wally will surely produce fewer widgets in the long run. b) If the rental rate for widget presses falls, Wally will surely produce fewer widgets in the long run. 37. Gregor’s Glassware is a firm in a competitive constant-cost industry. Suppose that an earthquake shuts down half of Gregor’s competitors. What happens to the price and quantity sold of Gregor’s merchandise, both in the short run and in the long run? Justify your answers. 38. A new government regulation requires each bicycle manufacturer to purchase an air purification system to reduce hazardous fumes in the workplace. What happens to the price of bicycles in the long run? Be sure to justify your answers. a) Answer assuming that bicycles are produced by a competitive industry. b) Answer assuming that bicycles are produced by a single monopolist. 39. Suppose that bicycles are produced by a competitive constant-cost industry. Suppose that bicycling declines in popularity as more people take up in-line skating. a) What happens to the profits of bicycle manufacturers in the short run? b) What happens to the number of bicycles produced per firm in the short run? c) What happens to the profits of bicycle manufacturers in the long run? d) What happens to the number of bicycles produced per firm in the long run? Justify all of your answers. 40. Suppose that ginseng tea is provided by a competitive constant-cost industry and that a new highly publicized study shows that drinking tea increases life expectancy. What happens to the amount of tea produced by a single manufacturer? a) Answer in the short run. b) Answer in the long run. 41. Suppose that the gizmo industry is in long-run equilibrium when the govern- ment suddenly orders a whole lot of new firms to enter the industry. They are forced to enter even if profits are driven below zero. 7–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) What happens in the short-run after the new firms enter? What hap- pens to price, industry-wide quantity, and quantity supplied by individual firms? b) What happens in the long run? (You may assume a constant-cost industry if that helps you.) 42. Determine whether each of the following statements is true or false and give reasons for your answers. a) True or False: In a competitive constant cost industry, an excise tax causes price to rise in the short run, and to rise even farther in the long run. b) True or False: In a competitive constant cost industry, a fall in demand causes each firm to supply less in the short run, and even less in the long run. 43. Determine whether each of the following statements is true or false and give reasons for your answers. a) If fixed costs rise in a competitive constant cost industry, the number of firms does not change in the short run but falls in the long run. b) If demand increases in a competitive constant cost industry, the output of a single firm increases in the short run but returns to its original level in the long run. 44. In each of the following situations, determine the effect on the price and quan- tity of drinks served at the Airliner Tavern. Answer first in the short run, then in the long run assuming that taverns form a constant cost industry, then in the long run assuming that taverns form an increasing cost industry, then in the long run assuming that taverns form a decreasing cost industry. (Obviously this problem can be shortened by, for example, omitting the case of decreasing costs.) a) The wholesale price of liquor goes up. b) The owners recalculate and discover that last month’s redecoration actu- ally cost 15% more than they’d thought. c) A disgruntled customer threatens to sue after being mistakenly served lye instead of rye. In exchange for a large payoff, the customer offers not only to withhold suit, but also to keep his mouth (or what is left of it) shut about the incident. d) The same incident occurs as in part c), but the newspapers have already found out about it. e) The yearly price of liquor licenses goes up. f) The city council passes a one-time emergency tax measure, requiring every local tavern owner to immediately contribute $30 to the town treasury. g) The owners of a neighboring establishment complain about the noise from the Airliner, and they win a court order requiring the Airliner to com- pensate them. The court rules that the Airliner must pay the neighbors 5 cents for each drink it serves. h) A general breakdown in family life leads to a lot more people going out to taverns. i) A wealthy couple decide they really want to build a house precisely on the site now occupied by the Airliner. j) There is a general rise in the price of land. 45. In each of the following situations, determine the effect on the price and quan- tity of car washes sold at Al’s Car Wash. Answer first in the short run, then in 7–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. the long run assuming that car washes form a constant cost industry, then in the long run assuming that car washes form an increasing cost industry, then in the long run assuming that car washes form a decreasing cost industry. (Obviously this problem can be shortened by, for example, omitting the case of decreasing costs.) a) The cost of mechanical car wash equipment goes up. b) The motel next door to Al’s wants to expand and offers to buy him out. c) One of Al’s major pieces of equipment breaks down and needs to be re- paired. d) There is an epidemic of equipment failures at car washes all over town. e) The mayor declares a one-time only Car Wash Appreciation Day, on which every car wash owner in the city is given $1000 out of city funds. f) The mayor declares that Car Wash Appreciation Day will become an annual event. g) An influential member of the city council invents an automatic car-polishing machine. When the council member discovers that no car wash wants to buy the machine, legislation is pushed through requiring every car wash to own one. (The council member’s supply curve for car-polishing equipment is upward sloping.) h) There is a general rise in wage rates. i) A story on 60 Minutes reveals that Al subscribes to the deconstructionist school of literary criticism. Workers throughout the city are so revolted that they will not work for Al unless he pays them 50 cents an hour more than they can earn at any other car wash. j) A large office building is constructed, making it impossible to see Al’s Car Wash from the road. k) The city begins using salt to clear ice off the roads in winter. (Salt causes cars to rust unless it is washed off frequently.) 46. In each of the following situations, determine the effect on the price and quan- tity of goose liver sold at Bambi’s House of Goose Liver. Answer first in the short run, then in the long run assuming that goose liver restaurants form a constant cost industry, then in the long run assuming that goose liver restau- rants form an increasing cost industry, then in the long run assuming that goose liver restaurants form a decreasing cost industry. (Obviously this prob- lem can be shortened by, for example, omitting the case of decreasing costs.) a) Due to a health scare, the city requires all goose liver purveyors to discard their inventory and replace it with fresh goose liver. b) An incompetent but enthusiastic health inspector takes office, and is ex- pected to periodically order all goose liver purveyors to discard their in- ventory at random times. c) Bambi’s vindictive ex-husband is appointed health inspector and is ex- pected to fine Bambi $5,000 per year for spurious health violations. d) Bambi’s vindictive ex-husband is appointed health inspector and is ex- pected to fine Bambi one-tenth of her revenues each year for spurious health violations. e) A careless employee leaves the freezer door open and all of Bambi’s goose liver needs to be replaced. f) A medical journal reports that goose liver can cause cancer. g) A medical journal reports that goose liver can prevent cancer. h) Bambi’s freezer needs to be replaced. i) Bambi has a fight with the owner of Tiny’s Discount Goose Liver Em- 7–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. porium, which supplies all of the goose liver restaurants in town. Conse- quently, she must now import all of her goose liver from the next county, and must pay additional shipping fees. j) Bambi and Tiny make up, and as a sign of friendship, Tiny agrees to supply Bambi with goose liver at half price from now on. k) Bambi and Tiny make up, and as a sign of friendship Tiny gives her 100 free pounds of goose liver (but continues to charge the usual price when Bambi orders more). l) A new law requires all restaurant owners who serve goose liver to pass a course on “The Role of Goose Liver in a Secular Society”. The local college charges $500 tuition for the course. m) There is a fall in the wage rate for restaurant dishwashing services. n) A new landfill comes to occupy the property next to Bambi’s. The odor from the landfill is offensive to customers. o) A new movie theater opens next door to Bambi’s, and is the only movie theater in town that allows movie-goers to bring in their own goose liver instead of buying it at the concession stand. 47. Widgets are supplied by a constant-cost competitive industry. Each individual firm faces a fixed cost of $6 and marginal costs given by the following table: Quantity Marginal Cost Quantity Marginal Cost 1 $1 5 5 2 2 6 6 3 3 7 7 4 4 8 8 Industry-wide demand is given by the following table: Price Quantity Price Quantity $1 1200 5 700 2 1000 6 500 3 900 7 300 4 800 8 200 a) What is the break-even price in this industry? (Hint: For each possible price, figure out what quantity each firm will provide and what its profit will be. Don’t forget the $6 fixed cost.) b) In long run equilibrium, how many firms are there in this industry? 48. Moose-nose pies are produced by a competitive constant-cost industry. The industry is in long-run equilibrium and there are exactly 100 firms. The follow- ing chart shows the industry-wide demand curve and the marginal cost curve of a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $5 250 1 $5 10 200 2 10 15 150 3 15 20 100 4 20 25 50 5 25 What are the firm’s fixed costs? 7–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 49. Widgets are produced by a competitive constant cost industry where each firm has fixed costs of $10. The following chart shows the industrywide demand curve and the marginal cost curve of a typical firm. Industrywide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $10 3000 1 $10 $20 2500 2 $20 $30 2000 3 $30 $40 1500 4 $40 $50 1000 5 $50 $60 500 6 $60 In long run equilibrium, how many firms are in the industry? 50. The following tables show the market demand curve for widgets and the marginal cost curve at a typical firm. The industry is constant-cost and each firm has fixed costs of $60. Answer the questions below. Firm’s Marginal Cost Curve Industry-Wide Demand Quantity MC Price Quantity 1 $40 per widget $40 per widget 1000 2 60 60 950 3 80 80 900 4 100 100 850 5 120 120 750 6 140 140 600 a) What is the break-even price in this industry? b) In long-run equilibrium, how many firms are in this industry? 7–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 51. The following charts show points on the industry-wide demand for widgets and the marginal cost curve of a typical firm. The industry is constant cost, each firm has fixed costs of $30, and the industry is in long run equilibrium. Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $1 1600 1 $1 3 1400 2 3 5 1200 3 5 7 1000 4 7 9 800 5 9 11 600 6 11 13 400 7 13 a) What is the price of a widget? b) Suppose the city imposes a sales tax of $6 per widget. In the short run, what is the new price of a widget? What is the new profit per firm? c) Suppose the city imposes a sales tax of $6 per widget. In the long run, what is the new price of a widget? What is the new profit per firm? d) Suppose the city imposes a license fee of $12 per firm. In the short run, what is the new price of a widget? What is the profit per firm? e) Suppose the city imposes a license fee of $12 per firm. In the long run, what is the new price of a widget? What is the profit per firm? f) Suppose the city offers an excise subsidy of $3 per widget. In the short run, what is the new price of a widget? What is the new profit per firm? (You might have to approximate.) g) Suppose the city offers an excise subsidy of $3 per widget. In the long run, what is the new price of a widget? How many firms enter the industry? (You might have to approximate.) 52. The widget industry is a constant-cost industry, so that all firms are identical. Each firm has fixed costs of $9. The following chart shows the industry wide demand curve and the marginal cost curve of a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $1 800 1 $1 4 700 2 4 7 600 3 7 10 500 4 10 13 400 5 13 16 300 6 16 19 200 7 19 22 100 8 22 25 60 9 25 The industry is in long-run equilibrium. Answer the following questions, mak- ing sure to show enough work so your instructor can tell how you got your answer : a) What is the price of a widget? (Your answer should be a number.) 7–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) Suppose the government imposes a sales tax of $9 per widget. In the short run, what is the new price of a widget? What is the profit per firm¿? What is the number of firms in the industry? c) Suppose the government imposes a sales tax of $9 per widget. In the long run, what is the new price of a widget? What is the profit per firm? What is the number of firms in the industry? d) Suppose the government offers an excise subsidy of $9 per widget. In the short run, what is the new price of a widget? What is the profit per firm? What is the number of firms in the industry? e) Suppose the government offers an excise subsidy of $6 per widget. In the long run, what is the new price of a widget? What is the profit per firm? What is the number of firms in the industry? f) Suppose the government gives every firm an annual subsidy of $4 (inde- pendent of how much the firm produces). In the short run, what is the new price of widgets? What is the profit per firm? What is the number of firms in the industry? g) Suppose the government gives each firm an annual subsidy of $4 (inde- pendent of how much the firm produces). In the long run, what is the new price of widgets? What is the profit per firm? What is the number of firms in the industry? i) Suppose the demand curve shifts right a distance 900. In the short run, what is the new price of widgets? What is the profit per firm? What is the number of firms in the industry? j) Suppose the demand curve shifts right a distance 900. In the long run, what is the new price of widgets? What is the profit per firm? What is the number of firms in the industry? 53. The widget industry is a constant-cost industry, so that all firms are identical. Each firm has fixed costs of $8. The following chart shows the industry wide demand curve and the marginal cost curve of a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $3 200 1 $3 5 175 2 5 8 150 3 8 12 125 4 12 20 100 5 20 30 75 6 30 The industry is in long run equilibrium. a) Suppose the demand curve shifts rightward a distance 150. In the short run what is the new price of a widget? b) Suppose the demand curve shifts rightward a distance 150. In the long run how many firms enter or exit the industry? c) Suppose the government imposes a sales tax of $15 per widget. What is the new price of widgets in the short run? d) Suppose the government imposes a sales tax of $22 per widget. How many firms leave the industry in the long run? 7–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 54. The widget industry is a constant-cost industry, so that all firms are identical. The following chart shows the industry wide demand curve and the marginal cost curve of a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Quantity Marginal Cost Price Quantity 1 $1 $1 700 2 2 2 600 3 5 5 500 3 5 8 400 4 8 9 300 5 9 12 120 6 12 15 100 7 15 The industry is in long run equilibrium, and widgets sell for $8 apiece. Now the government imposes an excise tax of $4 per widget. a) What is the new price in the short run? b) How much are the fixed costs at each firm? c) How many firms leave the industry in the long run? Be sure to show enough work so I can see how I got your answers. Your answer to each part of this question should be a number . 55. Each firm in the competitive constant-cost widget industry has $90 in fixed costs and the following marginal cost curve: Quantity Marginal Cost 1 $10 2 20 3 30 4 50 5 100 6 200 The industry is in long-run equilibrium and the industry-wide quantity is 800. How many firms are in the industry? You must show enough work so I can tell how you got your answer. 56. Pogs are supplied by a constant cost industry in which each firm has fixed costs of $2. The industry-wide demand curve and the typical firm’s marginal cost curve are as follows: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $10 1000 1 $10 12 800 2 12 14 600 3 14 16 400 4 16 18 200 5 18 20 100 6 20 On the short run supply curve, what quantity is associated with a price of $20? You must explain how you got your answer. 57. Pogs are supplied by a constant cost industry in which each firm has fixed costs of $25. The industry-wide demand curve and the typical firm’s marginal 7–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. cost curve are as follows: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $5 480 1 $5 20 400 2 20 25 360 3 25 30 320 4 30 40 240 5 40 45 120 6 45 a) Suppose that the industry is in long-run equilibrium. Now the government imposes a $20 excise tax on pogs. What is the new equilibrium quantity in the short run? b) Suppose that instead of the excise tax in part a), the government requires every pog seller to buy a pog-selling license. Only 80 licenses are created, and these are sold to the highest bidders; nobody else can sell pogs. What is the price of a pog-selling license? Show your work!! 58. Widgets are supplied by a competitive constant cost industry (so that all firms are identical .) Bobo’s House of Widgets is one firm in this industry. Answer each of the following questions if possible. If there’s not enough information to answer, then explain why not. a) Which of the following has the bigger effect on Bobo’s quantity supplied in the short run: A $100 increase in fixed costs, or a $1 per widget increase in variable costs? b) Which of the following has the bigger effect on Bobo’s quantity supplied in the long run: An increase in fixed costs that causes the price of widgets to rise by $3, or an increase in variable costs that causes the price of widgets to rise by $3? (All cost increases are assumed to be industry-wide.) 59. Pogs are provided by a competitive constant cost industry in which every firm has fixed costs of $12. Below are the industry-wide demand curve and the typical firm’s marginal cost curve. All quantities are per month: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $1 1000 1 $1 3 800 2 3 5 600 3 5 7 400 4 7 9 200 5 9 10 100 6 10 11 50 7 11 Pogs currently sell for $3. a) In the long run, how many firms will enter or exit? b) Suppose that the government requires all firms to pay a monthly license fee in order to sell pogs. In the short run (with pogs selling at $3), what is the largest monthly fee that firms would be willing to pay? You must show enough work so we can tell how you got your an- swers. 7–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 60. Widgets are supplied by a competitive constant-cost industry. Each firm has fixed costs of $20. Here are the industry-wide demand curve and a typical firm’s marginal cost curve: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $1 1000 1 $1 3 800 2 3 5 600 3 5 7 400 4 7 9 200 5 9 10 100 6 10 11 50 7 11 12 20 8 12 a) Suppose the industry is in long-run equilibrium. On the short-run supply curve, what quantity corresponds to a price of $5? b) Suppose that a new law requires each firm to produce exactly 2 widgets. In the long run, what is the price of a widget and how many firms remain in the industry? 61. Suppose in the widget industry, each firm has fixed costs of $3. Here are the industry demand curve and the typical firm’s marginal cost curve: Price ($) Firm's Marginal Costs 14 13 Quantity MC 12 11 10 1 $5 per widget 9 8 2 8 7 6 3 10 5 4 4 13 3 2 1 Quantity 50 100 150 200 250 300 350 400 450 500 INDUSTRY WIDE DEMAND The industry is in long run equilibrium. a) What is the price of a widget? b) How many firms are in the industry? Now suppose the government institutes a new $7 excise subsidy to widget makers (That is, firms receive $7 for each widget they sell.) c) In the short run, what is the new price of a widget? d) In the long run, what is the new price of a widget? 62. Mood rings are provided by a competitive constant-cost industry currently consisting of 100 identical firms. The following graphs show an individual firm’s Total Cost for producing various quantities of output, and the market demand curve: 7–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Firm’s Total Cost Industry Demand Quantity Total Cost $0 300 Price Quantity 1 400 $360 400 2 450 290 500 3 510 230 600 4 590 180 700 5 700 140 800 6 840 110 900 7 1020 80 1000 8 1250 a) What is the current price of a mood ring? b) In the long run, how many firms will enter or exit this industry? (Don’t worry if your answer is not a whole number.) 7–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 63. The following chart shows the industry-wide demand for widgets and the marginal cost curve of a typical firm. The industry is constant-cost and is in long run equilibrium. The price of a widget is $7. Industrywide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $10 500 1 $1 $9 1000 2 $2 $8 1500 3 $3 $7 2000 4 $5 $6 2500 5 $7 $5 3000 6 $9 a) On the industry’s short-run supply curve, what quanitity is associated with a price of $9? b) What are the firm’s fixed costs? (Your answer should be a number of dollars.) 64. Moose-nose pies are produced by a competitive constant-cost industry. The industry is in long-run equilibrium and Moose-Nose pies sell for $25 each. The following chart shows the industry-wide demand curve and the marginal cost curve of a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $5 100 1 $5 10 125 2 10 15 150 3 15 20 250 4 20 25 300 5 25 a) How much are the fixed costs at each firm? (Your answer should be a number.) b) Answer in the short run: If a fall in demand causes the equilibrium price of moose-nose pies to fall to $15, what is the new (industry-wide) equilib- rium quantity of moose-nose pies? By how much does the industry-wide quantity fall in the short run? (Your answer should be a number.) 65. Widgets are produced by a constant cost industry, where fixed costs are $12 per firm per year. The industry is in long-run equilibrium. The following charts show the industry-wide demand curve and the marginal cost curve at a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost ($/Widget) (Widgets/Year) (Widgets/Year) ($/Widget) $2 1200 1 $2 4 800 2 4 6 600 3 6 8 500 4 8 10 400 5 10 12 300 6 12 a) In long run equilibrium, how many widgets does the industry produce each year? 7–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) Suppose the government wants the industry to produce 800 widgets per year in the long run and plans to accomplish this by giving every widget firm an annual cash gift. How big should the gift be? (Your answer should be a number of dollars per firm.) c) Supose the government wants the industry to produce 800 widgets per year in the long run and plans to accomplish this by giving every widget firm a subsidy for each widget they produce. How big should the subsidy be? (Your answer should be a number of dollars per widget.) d) Between the annual cash gift and the subsidy per widget, which plan is more expensive for the taxpayers? 66. Widgets are provided by a competitive constant-cost industry where each firm has fixed costs of $30. The following charts show the industry-wide demand curve and the marginal cost curve of a typical firm. Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $5 1500 1 $5 10 1200 2 10 15 900 3 15 20 600 4 20 25 300 5 25 30 200 6 30 35 140 7 35 40 50 8 40 a) What is the price of a widget? b) How many firms are in the industry? For the remaining four parts of this problem, suppose the government imposes an excise tax of $15 per widget. c) In the short run, what is the new price of widgets? d) In the short run, how many firms leave the industry? e) In the long run, what is the new price of widgets? f) In the long run, how many firms leave the industry? 67. Widgets are provided by a constant cost industry, where fixed costs are $3 per firm per year. The industry is in long-run equilibrium. The following charts show the industry-wide demand curve and the marginal cost curve at a typical firm: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost ($/Widget) (Widgets/Year) (Widgets/Year) ($/Widget) $2 1200 1 $2 5 800 2 5 9 600 3 9 14 500 4 14 20 400 5 20 27 300 6 27 Suppose the government wants the industry to produce 1200 widgets per year in the short run, and plans to accomplish this by offering firms a subsidy for each widget they produce. How big should the subsidy be? (Your answer should be a number of dollars per widget.) 7–19 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 68. Dog food is provided by a competitive constant-cost industry in which each firm has the following marginal cost curve: Quantity Marginal Cost (# of Cans per Year) (Price per Can) 1 5 2 10 3 15 4 20 5 25 6 30 7 35 The industry is in long run equilibrium and dog food sells for $10 per can. Now a new law requires each dog food firm to buy a license for $25 a year. In the long run, what is the new price of dog food? 69. Widgets are provided by a constant-cost industry. The following charts show the foreign demand for American widgets and the marginal cost curve of a typical American widget firm. Foreign Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $3 150 1 $3 5 140 2 5 7 120 3 7 9 100 4 9 11 90 5 11 13 80 6 13 15 70 7 15 17 60 8 17 Initially, American firms are not allowed to sell to foreigners. In the U.S., widgets sell for $7 apiece. a) What is the fixed cost of running a widget firm? Now the government decides to issue 10 export licenses; a firm with an export license can sell as many widgets to foreigners as it wants to. The export licenses are sold at auction to the highest bidders. b) What is the price of an American widget sold on the foreign market? c) What is the price of an export license? d) After the export licenses are issued, what is the new price of an American widget sold in America? Be sure to justify your answer. 70. Suppose the wholesale price of gasoline falls by 50 cents a gallon. Does the retail price fall by more than 50 cents, by 50 cents, or by less than 50 cents? a) Answer assuming gas stations constitute a competitive constant-cost in- dustry. b) Answer assuming gas stations constitute a competitive increasing-cost industry. 7–20 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 7 1. a) This is a change in a fixed cost; nothing happens. b) This is a fall in marginal cost. Gus’s MC curve falls; that is, his supply curve shifts rightward. The industry supply curve also shifts rightward, leading to a lower price for cab rides and hence a lower (flat) demand curve for Gus’s services. Price is down; quantity can go either way. c) Normally, we expect that the demand for Gus’s cab rides is flat at the going market price for cab rides. This expectation is justified by the assumption that Gus’s cab rides are no different than anyone else’s. But in this problem, we depart from that assumption. The demand for cab rides generally is unchanged; likewise for supply; thus the industry price of cab rides is unchanged. But the demand for Gus’s cab rides falls, hence the price and quantity of Gus’s cab rides falls. d) Demand for cab rides falls; price of cab rides falls; therefore the (flat) demand curve for Gus’s cab rides falls. No change in supply curves. Quantity falls at Gus’s firm, and also falls industry-wide. e) Sunk cost; no effect. f) This increases the opportunity cost of driving a cab. To completely solve the prob- lem, you’ve got to decide whether it’s an increase in fixed costs or in marginal costs. The answer depends on what you assume about Gus’s alternative opportunities. Suppose first that Gus must choose between driving a cab and working in a factory; he can’t do both. In that case, the wages of factory workers are a fixed cost of driving a cab; you give up the same factory job whether you collect one fare a day or ten fares a day. A change in fixed cost has no effect on price or quantity. But suppose alternatively that Gus can moonlight, working in the factory for part of the day and driving the cab for the other part of the day. Then each additional cab fare requires him to lose more time in the factory, making factory wages a variable cost. In this case, the analysis is exactly as in Exhibit 7.9. g) Ordinarily, we expect exit to be impossible in the short run, but in this example, firms are forced to exit immediately. Therefore the industry supply curve shifts left, price rises, the (flat) demand curve for Gus’s cab rides rises accordingly, and his quantity rises also. h) Industry supply shifts leftward (because all the other firms’ supply curves shift leftward); price up; Gus’s quantity up. i) Change in fixed costs does not affect anything. j) Two ways to do this: Method I: Treat city-owned cabs as a separate good from private cabs. The city-owned cabs reduce demand for private cabs, so price falls, Gus’s (flat) demand curve falls, and his quantity falls. Method II: Treat city-owned cabs and private cabs as identical goods. Supply of cab rides increases, so price falls, Gus’s (flat) demand curve falls, and his quantity falls. k) Industry supply shifts rightward (because all other firm’s supply curves shift right- ward); price down; Gus’s quantity down. 7–21 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. l) Gus’s MC curve shifts up (that is, his supply curve shifts left). Very few firms are affected, so industry supply hardly moves; we can assume (to a good approxima- tion) that it doesn’t move at all. Therefore price unchanged and Gus’s quantity down. m)Sunk cost; no effect. 2. False; a competitive firm does not need to lower its price to “steal customers”. 3. False; the profit on the last item produced is zero, but that doesn’t make the firm’s total profit equal to zero. 4. False. In Exhibit 7.6, if the price is above P0 but below the minimum of the average cost curve, the firm earns negative profit but continues to produce in the short run. 5. False. More homeless people will move to New York, increasing crowding at shelters, making it more difficult to get handouts, and so forth, until New York is again no more attractive than the next best alternative. 6. People with no special skills must be indifferent between engraving gold jewelry and the next best opportunity. Therefore the opportunity to keep the gold dust must be exactly offset by lower wages in this industry. 7. True in the short run; false in the long run. 8. True. In either case the (industry) supply curve shifts vertically by an amount equal to the excise tax. In the long run, the supply curve is vertical, so the price rises by the full amount of the tax. 9. a) At a price of $6, the quantity of car washes demanded is 200 (2 car washes per consumer times 100 consumers) and the quantity supplied is also 200 (4 per supplier times 50 suppliers). Therefore $6 is an equilibrium price. b) Car washes must break even selling at $6. Variable costs are $(3 + 4 + 5 + 6) = $18 and revenue is $6 × 4 = $24, so fixed costs must be $(24 − 16) = $8. 10. a) This is a fall in variable cost. It lowers the break-even price, so the industry-wide supply curve shifts (vertically) down. Therefore the (flat) demand curve for Gus’s services shifts down. Gus’s supply (=MC) curve also shifts vertically down. From these observations, we can see that price is down, industry quantity is up, and Gus’s quantity might be either down or up. If we treat all cab rides as identical, it might be reasonable to assume that an increase in the price of gas adds a single constant to the marginal cost of each cab ride. (For example, if each ride uses two gallons of gas, and the price of gas goes up by 10 cents a gallon, the marginal cost of each cab ride goes up by 20 cents per ride.) (This assumption might be false if, for example, cabs use more gas per mile when they’re heavily used.) If we make this assumption, then both the industry supply curve and Gus’s supply curve shift vertically down by exactly the same amount. In that case, we can conclude that Gus’s quantity is unchanged. b) This is a fall in fixed cost. The break-even price drops, so the industry supply curve shifts vertically down, so the (flat) demand curve for Gus’s cab shifts vertically down. His supply curve does not shift. Price is down, industry quantity is up, Gus’s quantity is down. c) To keep customers, Gus must lower his price. But he was earning zero profit to begin with, so he won’t be willing to do this. Therefore Gus exits. d) Industry-wide demand falls; no change in price; no change in supply or demand for Gus’s cab, hence no change in Gus’s quantity. (Some firms, possibly including Gus’s, will exit.) 7–22 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. e) Sunk cost; no effect. f) As in the answer to problem 1, this can be interpreted either as an increase in fixed costs or an increase in variable costs. Under the first interpretation, see Exhibit 7.15; under the second, see Exhibit 7.16. g) No change in the cost of operating a cab service, so no change in anything. (In the short run, the remaining firms earn positive profits; these profits draw entry till the original equilibrium is restored. Entry must continue until price reaches its original equilibrium, because until that happens, firms are still earning positive profits.) h) Break-even price rises by $1 so price of cab rides rises by $1 and Gus supplies more rides. i) Break-even price up; price up; Gus supplies more rides. j) If you think of the city taxis as a separate industry that competes with private taxis, this can be analyzed just as in 10d). If you think of the city taxis as part of the private cab industry, then no curves move (no supply curves move because no costs have changed). The first method tells you that if the city operates 100 cabs, demand shifts left by 100 and the total number of private cabs falls by 100. The second method tells you that the total number of cabs (city plus private) remains unchanged. Notice that these are two ways of saying the same thing (as they must be because both methods are correct). Either way, price is unchanged and Gus’s supply curve is unchanged, so nothing changes at Gus’s cab company (unless he is one of the 100 who exit). k) Break-even price falls so price of cab rides falls; Gus, who was earning zero profit to begin with, exits. l) Gus’s marginal cost curve rises; his profits become negative and he exits. m)It might or might not be worth Gus’s while to make this one-time payment; the alternative is to leave the industry, which presumably is a costly procedure (adver- tising for someone to buy his cab, etc.) He’ll do whichever is cheaper. 11. a) Break-even prices fall so industry supply moves vertically down (i.e. leftward). Price falls, flat demand curve for Gus’s services falls, Gus’s quantity falls. b) Variable cost falls, so Gus’s MC curve falls. Break-even prices fall so industry supply moves vertically downward (i.e. leftward). Price down, flat demand curve for Gus’s services down. Price falls by more than the drop in MC; Gus’s supply curve falls vertically by exactly the drop in MC; therefore Gus supplies fewer rides. c) To keep customers, Gus must lower his price. He might either do this or leave the industry. If he lowers his price, he provides fewer rides. d) Industry-wide demand falls; price rises; quantity up. e) Sunk cost; no effect. f) As in the answer to problem 4, this can be interpreted either as an increase in fixed costs or an increase in variable costs. Under either interpretation, industry supply moves vertically upward and price rises, so flat demand curve for Gus’s services rises. On first interpretation he moves along his supply curve and supplies more rides; on second interpretation his supply curve moves also. g) No change in the cost of operating a cab service, so no change in anything. h) Break-even price rises so price of cab rides rises and Gus supplies more rides. i) Industry supply moves vertically up; price up; Gus supplies more rides. j) Can be analyzed just as in 11c). k) Industry supply moves vertically down so price of cab rides falls; Gus, either sup- plies fewer rides or exits. l) Gus’s marginal cost curve rises; he either supplies fewer rides or exits. 7–23 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. m)Gus either makes the payment, which becomes a sunk cost and has no further effect, or leaves the industry. 12. a) Break-even prices falls so industry supply falls. Price falls, flat demand curve for Gus’s services falls, Gus’s quantity falls. b) Variable cost falls, so Gus’s MC curve falls. Break-even price falls so industry supply falls. Price down, flat demand curve for Gus’s services down. A good answer: Demand for Gus’s services is down, his supply curve has shifted rightward, so quantity could move either way. A more in-depth answer: Assume the cost of gas per cab ride has fallen by, say, 50 cents. Then the break-even price has also fallen by 50 cents. Demand and supply fall by exactly the same distance, so quantity is unchanged. c) To keep customers, Gus must lower his price. He might either do this or leave the industry. If he lowers his price, he provides fewer rides. d) Industry-wide demand falls; price falls; quantity down. (Some firms, possibly in- cluding Gus’s, will exit.) e) Sunk cost; no effect. f) As in the answer to problem 4, this can be interpreted either as an increase in fixed costs or an increase in variable costs. Under the first interpretation, see Exhibit 7.20a; under the second, see Exhibit 7.20b. g) No change in the cost of operating a cab service, so no change in anything. h) Break-even price rises so price of cab rides rises and Gus supplies more rides. i) Industry supply moves vertically up; price up; Gus supplies more rides. j) Can be analyzed just as in 12c). k) Industry supply moves vertically down so price of cab rides falls; Gus, either sup- plies fewer rides or exits. l) Gus’s marginal cost curve rises; he either supplies fewer rides or exits. m)Gus either makes the payment, which becomes a sunk cost and has no further effect, or leaves the industry. 7–24 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 13. Price Price Supply(SR) Supply(SR) T T D' Supply(LR) D M W M,W D' D Quantity Quantity Industry Sally's Swordshop We see from the picture that swords are most expensive on Tuesday, that the most swords are bought on Wednesday, and that Sally's Swordshop sells the most swords on Tuesday. Sally's profits are highest when the price is highest, i.e. on Tuesday. Price Price 14. Supply(SR) Supply(SR) P' P' X Supply(LR) D Y D' D Quantity Quantity Industry Firm a) The quantity supplied shifts back to 40% of its equilibrium level, and the price rises accordingly, to P'. b) Profits increase because the price rises, but decrease because the quantity per firm is restricted. On balance, profit could either increase or decrease, so there might be either entry or exit. In Chapter 8, we will discover that the profit per firm increases by the amount X-Y, so there is entry if X>Y and exit if Y>X. 15. a) Price does not change in the long run. b) More in the long run, because we are moving along a flat supply curve. c) Quantity does not change in the long run. d) Profits do not change in the long run. 16. a) Price does not change in the short run. b) Quantity does not change in the short run. c) Quantity does not change in the short run. d) Profits do not change in the long run. 17. a) Price does not change in the long run. b) More in the long run, because we are moving along a flat supply curve. c) Quantity does not change in the long run. d) Profits do not change in the long run. 7–25 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 18. In both cases, the firm’s (flat) demand curve shifts $5 vertically upward. In Scenario A (a fixed cost) the firm’s supply curve doesn’t move. In Scenario B (a variable cost) the firm’s supply curve shifts leftward. Therefore the firm provides more widgets in Scenario A. 19. a) In the short run, the gift has no effect. So all that matters is the excise tax. This is an increase in a variable cost, so the picture is exactly as in Exhibit 7-9. b) The firm faces the same (flat) demand curve as before, but its supply curve is shifted left. Therefore each firm provides fewer shoes. Because the price is unchanged, demanders purchase the same number of shoes as before. Therefore the number of firms must increase. 20. a) Industry supply curves shifts rightward 800. Equilibrium quantity shifts rightward by less than 800; that is, more patients are served, but the increase is less than 800. b) In the long run, price must return to original level so quantity returns to original level. Thus private clinics serve exactly 800 fewer patients. 21. The firm’s short-run supply curve is equal to its marginal cost curve. The in- dustry’s short-run supply curve is derived from the firm’s marginal cost curve by multiplying all the quantities by 100 (the number of firms). So on the industry supply curve, a price of $2 goes with a quantity of 100, a price of $3 goes with a quantity of 200, etc. To find the point of equilibrium, we look for a point that is on both the industry’s (short-run) supply curve and the industry’s demand curve. That point occurs at a price of $5 and a quantity of 300. Thus each firm produces 3 widgets. Because the industry is in long-run equilibrium, each firm’s profit must equal zero. Now: Profit = TR - TC = (3 × $5) − (Fixed Costs + Variable Costs) a) At quantity 3, variable costs are $2 + 3 + 5 = 10, so profit is $15 − (F C + 10). For this to equal zero, FC must equal $5. b) as answered above, $5 c) 600 22. In the short run, this fixed cost has no effect. In the long run, the price of a widget must rise until firms can just break even given the new fixed cost of $5+11=16. Trial and error reveals that this occurs at the price of $8, where the firm produces quantity 5 (here T R = 8 × 5 = 40 and T C = 16 + 2 + 3 + 5 + 6 + 8 = 40.) At this price, 100 widgets are demanded, so in long run equilibrium there must be 20 firms producing 5 widgets each. Since there 100 firms to begin with, 80 must leave the industry. 7–26 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 23. a) $8 $5 $2 100 300 (Note: This is a stylized picture; the actual supply and demand curves are not straight lines.) Original equilibrium is at quantity = 300. New equilibrium must be at a point where the original supply and demand curves differ by $6. This occurs at quantity 100, where the demand price is $8 and the supply price is $2. So in the short run, the new widget price is $2. b,c) $11 $5 300 We know from problem 19 that the long run supply curve is flat at the break-even price of $5. When demand drops vertically a distance $6, the price of a widget remains at $5. The price-plus-tax paid by demanders is now $11, at which price demanders want approximately 30 (somewhere between 25 and 50). Suppliers continue to supply 3 widgets each, so approximately 10 firms remain, meaning that approximately 90 firms must exit. 7–27 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 24. a) $6 $5 $3 300 400 Original equilibrium is at quantity = 300. New equilibrium must be at a point where the original supply and demand curves differ by $3. This occurs at quantity 400, where the demand price is $3 and the supply price is $6. So in the short run, the new widget price is $3. b,c) $5 $2 300 500 In the long run, the excise subsidy pushes the break even price down by $3, so the supply curve drops $3 and is now flat at $2. At this price, demanders want quantity 500. Each firm continues to produce quantity 3 (because firms continue to receive $5 per widget), so the total number of firms is 500/3, or approximately 167. Thus approximately 67 firms must enter. 25. a) Supply now crosses demand at price=$6, quantity=400. b) In the long run, a change in demand won’t change the price. 26. a) The equilibrium price for sales to foreigners is $15. At this price, foreigners buy 70 widgets, and 10 American firms supply 7 widgets each. b) The price of an export license will be bid up until each firm earns zero profit, just as firms that sell to Americans do. To compute profit, we need to know the firm’s fixed costs. We can do this by 7–28 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. looking at the firms that sell to Americans. These firms produce 3 widgets per firm at a price of $7 each, so TR= $21. Their variable costs are $2+5+7=14, so their fixed costs must be $7. Now the firms that sell to foreigners sell 7 widgets each at $15 for total revenue of $105. Their variable costs are $2+5+7+9+11+ 13+15=62, so their total fixed costs must equal $43. In other words, their fixed costs are $36 greater than for firms that sell to the American market. That $36 must be accounted for by the price of the license. c) Initally, each firm sells 3 widgets and 75 widgets are demanded; thus there are 25 firms. Of these, 10 switch over to serving foreigners, so we are left with 15 firms in the American market. Thus to get points on the short-run supply curve, we must multiply quantities on the firm’s short-run supply curve by 15. This tells us that on the new short-run supply cure, the price of $9 goes with a quantity of 60; this point is also on the demand curve. So that’s the new equilibrium. d) In the long run, firms enter the American market until the original equilibrium is restored. Thus the price returns to $7. 27. a) Because Type A firms must earn zero profit, they must produce a quantity of 4 widgets each and face a price of $80 per widget. Type B firms face the same price, hence have total revenue $160 and variable costs of $140, which means, in order to earn zero profit, that their fixed costs are $20. b) At a price of $80, the quantity demanded is 50. Type A firms collectively produce 40, so Type B firms must collectively produce 10. Because each Type B firm produces 2 widgets, there must be 5 Type B firms. c) At price $100, the 10 Type A firms produce a total of 50 and the 5 Type B firms produce a total of 15, so the corresponding quantity is 50 + 15 = 65. 28. See problem 14. 29. False. They seek to maximize profit, period. In long run equilibrium, assuming a constant cost industry, average cost is minimized, but this is not the goal of any firm. 30. In Upper Slobbovia, the entire tax is passed on; in Middle Slobbovia, a portion of the tax is passed on; in Lower Slobbovia, none of the tax is passed on. 31. True. The long run supply curve shifts vertically upward by the amount of the tax. The new equilibrium point is to the left of the old one, and consequently higher than the old price plus the tax. 32. False. The first year’s entry causes the short run supply curve to shift rightward. Therefore the price will be below its original level. 7–29 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1.a) Each firm produces 5 widgets, earning revenue of $50, with total cost $36. Profit is $14, which is positive, so the industry is not in long run equilibrium. b) Positive profit draws entry till te price falls to $6, where each firm produces 3 widgets and profit is zero. N2. The price is $15. At this price, each firm produces 3 widgets and earns zero profit. Consumers demand 450 widgets so there are 150 firms in the industry. At a price of $10, each of 150 firms would produce 2 widgets, so the quantity on the short run supply curve is 300. N3.a) $20 (the price at which profit is zero) b) 150 (the quantity demanded divided by the quantity supplied per firm) c) Prior to the tax, the short-run supply curve contains points ($5, 150), ($10,300),($15,450), etc. With the tax, the short-run supply curve shifts vertically upward $15 and now contains points ($20,150),($25,300), etc. The point ($25,300) is on both the supply and demand curves, so it is the new equilibrium. The price is $25. d) No firms leave in the short run. e) In the long run, price must rise by the full amount of the tax, from $20 to $35. f) Each firm provides 4 widgets. 140 widgets are demanded. Therefore the number of firms must fall from 150 to 140/4=35. So 115 firms leave the industry. N4.a) At a price of $20, total cost and total revenue each equal $80. So $20 is the break-even price, and this is the price of a widget. b) Each firm produces 4 widgets; 600 are sold, so the number of firms is 600/4=150. c) Each firm’s supply curve shifts a distance $15, so the new supply curve is given by Price Quantity $20 1 25 2 30 3 35 4 40 5 With 150 firms, this gives an industry-wide supply curve of Price Quantity $20 1 25 300 30 450 35 600 40 750 $25 is now the price at which quantity supplied equals quantity demanded, so this is the new price of widgets. d) Nobody leaves the industry in the short run. e) The (flat) long-run supply curve shifts upward $15, so the new price is $35. f) Firms get to keep $20 per widget, so they supply 4 widgets each; 140 must be supplied altogether, so there are now 140/4=35 firms. Thus 115 leave the industry. N5.a) The break-even price is $7; at this price each firms’ total revenue and total costs are both equal to $28. b) Each firm produces 4 widgets. c) The industry-wide quantity is 24, so there must be 6 firms. d) The industry-wide supply curve is 7–30 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Quantity $2 6 4 12 5 18 7 24 11 30 13 36 This crosses industry-wide demand at a price of $13, so that is the new equi- librium price. At that price, each firm produces 6 widgets. d) In the long run, the price must return to the break-even level of $7. At that price, consumers demand 60 widgets, and each firm produces 4, so there must be 15 firms. N6. The equilibrium price is $5. At that price, there are 80 firms in the industry, each with fixed costs of $10 and total costs of $25. Also, each firm has a total revenue of $25, so profits are zero. N7.a) Profit maximization requires P = M C. Zero profits requires P = AC. Thus M C(Q) = AC(Q), where Q is the number of kites each firm produces. From the expressions given in the problem we get 100 2Q = Q + , Q so that Q = 10 and consequently P = 20. That is, each firm produces 10 kites and earns zero profit when P = 20. Consequently the long run industry supply curve is flat at P = 20. b) Since P = 20, we can solve for the equilibrium value of Q and get Q = 7000. The industry produces 7000 kites, of which 10 are produced at any given firm. It follows that there are 700 firms in the industry. c) In the short run, supply is fixed at Q = 7000. Solving for the equilibrium price, we get P = 40. Each kite maker supplies 10 kites at an average cost of 20 and sells them at a price of 40, for a profit of 20 per kite or 200 per firm. d) The new long-run equilibrium Q is 8000, so there must be 800 firms, of which 100 are new. All firms earn zero profit. N8.a) Fire extinguishers are a fixed cost, so M C does not change. The cost of a fire extinguisher is equal to the number of fire extinguishers, which equals the number of firms, so each firm’s T C is up by √ F , and consequently √ AC is up by F/Q. b) Solving for M√C = AC, we get Q = 100 + F , P = 2 100 + F . c) Since√P = 2 100 + F , we get F = P 2 /4 − 100. Each of the F firms produces Q = 100 + F = P/2 kites, so the industry supply is P2 P3 P Q= − 100 · = − 50 · P. 4 2 8 d) Using the above expression for industry supply and solving for the equilibrium gives P = 40, Q = 6000. Each firm produces 20 kites, so there are 300 firms in all. They earn zero profit. 7–31 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Eight: Welfare Economics and the Gains from Trade What’s New in This Edition Among many other innovations, I’ve highlighted four different ways of thinking about deadweight loss (as the excess of losses to losers over gains to winners, as the social value of forgone production, as the margin of victory in an election between policy choices in which voters are granted numbers of votes proportional to their stakes in the outcome, as measures of forgone opportunities for Pareto improvements). Of course each of these four notions serves to reinforce the others. Throughout the chapter, there are rewrites and reorganizations intended to make the material flow more smoothly and easily. Teaching Suggestions 1) Exhibit 8–13 shows “Another Way to Do It,” where “It” is the act of calculating consumers’ surplus in the face of a market distortion. Students who are having trouble with the first way to do it should not allow themselves to become distracted by this, and need reassurance that it is far more important to learn one way completely than to learn two ways partially. Those students who are on top of things will find this exhibit useful, because some problems to be encountered in future chapters are easier this way. (No prob- lems here in Chapter 8 have that characteristic.) There is of course an analogous “other way to do it” for producers’ surplus, and it is equally useful. Students can be assigned to work it out, or it can easily be presented in lecture. 2) In order to impress students with the power of the welfare theorem, it can be useful to present some simple situations in which the theorem does not hold. An obvious candidate is the prisoner’s dilemma, which appears in Chapter 11 but can be covered now. Quicker and easier examples arise from failures of collective action: Everybody on the street would be happier if everybody on the street spent an afternoon picking up trash, but it is not to any individual’s advantage to go out and pick up trash. (This is, of course, a prisoner’s dilemma, but in much less formal guise.) These make good intuitive sense to students. You can challenge the class to come up with other interesting examples. By pointing out that the welfare theorem fails in these cases—the equilibrium outcomes are not Pareto- optimal—you can drive home both the meaning of the theorem and the fact that its success in competitive markets is non- trivial. 3) In explaining the difference between the Pareto criterion and the efficiency criterion, it can be helpful to start with a simple one-good example. One way to do this is to start right off by working end-of-chapter problem 4 at the blackboard, or by assigning it early on for students to think about. 4) Students sometimes arrive with remarkable misconceptions about the Invis- ible Hand. One of the most pervasive is to equate it with “survival of the fittest” in some version of social Darwinism. They (incorrectly) believe that markets are efficient precisely because inefficient producers can not survive, in perfect analogy with biological evolution. Tell them that the truth is more subtle. The Invisible Hand Theorem relies (among other things) on the equalization of marginal cost across firms (as in the discussion back in Chapter 7), which in turn depends on the existence of competi- tive prices, i.e. going market rates of exchange that no individual can affect. There 8–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. is no biological analogue to the competitive price system. Some analogue of natural selection might very well be important in explaining some economic phenomena, but the Invisible Hand is quite a different thing. 5) If you want to discuss normative criteria, I think it can be instructive to push them to extremes. Ask your students whether the Rawlsian veil of ignorance (discussed in the appendix to the chapter) throws light on animal rights issues. E.g., if you are behind the veil and don’t yet know whether you’ll be born a person or a cow, do you want people to be permitted to eat cows? This question in itself seems less interesting to me than the meta-question: Do we learn anything from thinking about questions like this in this way? I don’t know the answer to the meta-question. But I do think we learn something from thinking about the meta- question. 6) The appendix to the chapter exposits some philosophical points that usually get briefer treatment in textbooks at this level. I think that the appendix is written at a level where students can easily read it on their own. 8–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. If the price of haircuts rises from $10 to $11, consumers’ surplus will fall by 10%. 2. If Jack Daniels whiskey sells for $10 a bottle and if 1,000 bottles were sold last year, then the total value of those bottles to consumers was $10,000. 3. Suppose that people buy diamond jewelry only because they welcome the opportunity to display their wealth. What would be the welfare effects of taxing diamond jewelry? 4. Michael Kinsley, writing in the New Republic of january 22, 1989, says “When an Impressionist painting thought to be worth $15 million is suddently worth $30 million, the world is not $15 million richer. However, the owner’s claim on the world’s existing wealth has doubled.” Is he right? (Extra credit: Look up the article in question. In what sentence does the first economic error occur?) 5. True or False: A firm that is required by law to cut its production in half will lose half its producers’ surplus. 6. Brownies sell for $2.50 apiece, and you are only permitted to buy them in whole number quantities. You buy one per day. Now sellers begin offering half-brownies at $1.25 per day. What can you say about the number you will buy? 7. If consumers buy 1000 heads of lettuce per week, and if the price of lettuce falls by 10 cents per head, then the consumers’ surplus will increase by $100. 8. Suppose that an effective price ceiling is imposed on bread at the wholesale level. a) In the wholesale market, where your grocer is the consumer, what happens to the actual price that he pays for bread? b) In the retail market, in which your grocer is the producer, what happens to the supply curve for bread? Why? c) True or False: A price ceiling on bread at the wholesale level will cause the retail price of bread to rise. 9. The U.S. supply and demand curves for cars cross at $10,000. Foreigners will purchase any quantity of American cars for $15,000 each. One day, the government imposes a tax of $2000 export tax on every American car sold to a foreigner. (Cars sold to Americans are not taxed.) Your friend Barry predicts that Americans will now pay $15,000 per car. Your friend Willard predicts that American buyers will now pay $13,000 per car. Who is right? Explain your answer in terms that Barry and Willard (neither of whom knows anything about economics) can understand. 10. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government imposes an export tax of $1 per bushel on all domestically grown wheat that is shipped abroad. a) What price must Americans pay for wheat before the tax is imposed? What price must Americans pay for wheat after the tax is imposed? b) Before and after the tax is imposed, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the tax? 8–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 11. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government imposes a tax of $1 per bushel on all wheat grown in the United States, regardless of whether it is sold domestically or abroad. a) What price must Americans pay for wheat before the tax is imposed? What price must Americans pay for wheat after the tax is imposed? b) Before and after the tax is imposed, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss from the tax? 12. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government imposes a sales tax of $1 per bushel on all wheat bought in America. a) What price must Americans pay for wheat before the tax is imposed? What price must Americans pay for wheat after the tax is imposed? b) Before and after the tax is imposed, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the tax? 13. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government imposes a sales tax of $1 per bushel on all wheat sold by American producers to American consumers. Suppose also that American consumers are free to buy wheat on the world market at the going $8 price if they want to. a) What price must Americans pay for wheat before the tax is imposed? What price must Americans pay for wheat after the tax is imposed? b) Before and after the tax is imposed, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the tax? 14. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government imposes a sales tax of $1 per bushel on all wheat sold by American producers to American consumers. Suppose also that American consumers are forbidden to buy wheat from foreigners, so all wheat sold in America must be produced in America. a) What price must Americans pay for wheat before the tax is imposed? What price must Americans pay for wheat after the tax is imposed? b) Before and after the tax is imposed, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the tax? c) Given the existence of the tax, what is the deadweight loss due to the prohibition on foreign wheat? 15. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government offers American farmers a subsidy of $1 for every bushel of wheat that they ship abroad. (Wheat sold in the U.S. earns no subsidy.) a) What price must Americans pay for wheat before the subsidy is imple- mented? What price must Americans pay for wheat after the subsidy is 8–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. implemented? b) Before and after the subsidy is implemented, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the subsidy? 16. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government offers American farmers a subsidy of $1 for every bushel of wheat they grow, regardless of where that wheat is sold. a) What price must Americans pay for wheat before the subsidy is imple- mented? What price must Americans pay for wheat after the subsidy is implemented? b) Before and after the subsidy is implemented, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the subsidy? 17. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 per bushel, but American producers can sell as much wheat as they want to on the world market at a price of $8 per bushel. Now suppose the government offers American farmers a subsidy of $1 for every bushel they sell in the U.S. (There is no subsidy for wheat that is shipped abroad.) a) What price must Americans pay for wheat before the subsidy is imple- mented? What price must Americans pay for wheat after the subsidy is implemented? b) Before and after the subsidy is implemented, calculate the gains and losses to all relevant groups of Americans. What is the deadweight loss due to the subsidy? 18. The U.S. supply and demand curves for cars cross at $15,000; coincidentally, $15,000 is also the price at which (identical) cars can be purchased from abroad (in any quantity). One day the government sets a new price ceiling of $10,000 per car. To prevent long lines from forming, the government agrees to sell cars for $10,000 apiece to any American buyer who can’t find an American car to buy. The government gets these cars by buying them from abroad. Illustrate the gains and losses to all relevant groups of Americans and illustrate the deadweight loss. 19. In the town of Rochester, widgets are sold by a competitive industry at an equilibrium price of $12 apiece. One day the city simultaneously imposes a price ceiling of $7 per widget and a sales tax of $5 per widget. a) Use a graph to illustrate the amount that consumers must pay, in price plus tax plus the value of waiting time, to acquire a widget. b) Use your graph to illustrate the total value of time spent waiting for widgets. c) Use your graph to illustrate the gains and losses to all relevant groups, and to show the deadweight loss. 20. Widgets are provided by a constant cost industry. The industry is in long- run equilibrium and each firm produces five widgets. If a new law restricts each widget firm to producing only two widgets per year, what areas would you need to measure to predict whether the number of firms will increase or decrease? 21. Suppose Americans can buy any number of birdcages on the world market at a 8–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. price P0 . American manufacturers have an upward-sloping supply curve that intersects the American demand curve at a price above P0 . a) At what price must American birdcages sell? Illustrate the gains to Amer- icans from the existence of the world market. b) Suppose the government imposes a quota, by which only Q0 birdcages per year can be imported from abroad, where Q0 is less than the number currently being imported. Show that there is exactly one price consistent with Americans being willing to import exactly Q0 birdcagees per year, and explain why the price will rise to that level. c) Who wins and who loses as a result of the quota? Use a graph to illustrate the deadweight loss. d) is the quota better or worse for Americans than a tariff that reduces the quantity of imported birdcages to Q0 ? 22. The following graph shows the American supply and demand curves for wid- gets. PRICE S $30 20 10 D 100 200 300 400 QUANTITY Answer the following questions: a) Suppose that foreign widget suppliers will provide any quantity of widgets at $10 apiece. How many widgets are imported? b) Suppose that foreign widget suppliers will provide any quantity of widgets at $10 apiece, and that the government wants to limit the number of imported widgets to 100. What size tariff can they impose to accomplish this goal? c) Suppose there are no foreign suppliers. Suppose also that the government distributes 100 ration tickets, and only the holders of ration tickets are permitted to buy widgets, so that only 100 widgets can be sold in total. Ration tickets can be freely bought and sold. What is the price of a ration ticket? 23. The American demand and supply curves for cars cross at a price of $15,000. However, foreign suppliers will provide any number of (identical) cars for $10,000 apiece. Suppose the government simultaneously: a) bans the importation of foreign cars 8–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) forbids American sellers to raise their prices above $10,000 and c) allows the President’s brother to buy all the cars that are produced in America and resell them to consumers at whatever price the consumers are willing to pay. Show the gains and losses to all relevant groups of Americans (including the President’s brother) and illustrate the deadweight loss. 24. Ordinarily, Americans import 7,000 cars a year from Japan. This year, to limit imports, the government has printed up 2,000 import licenses and distributed them at random. Only the holder of an import license can buy a Japanese car. An import license can only be used once, but before it is used, it can be freely bought and sold. Use a graph to illustrate the price of an import license. 25. In equilibrium, widgets sell for $8 apiece, and 1000 are sold. Now the govern- ment imposes a price ceiling of $3 per widget, but requires each producer to continue producing as many widgets as before. a) Assuming people’s time is worth $2 per hour, how long must you stand in line to buy a widget? b) Illustrate the new consumer and producer surpluses, and the deadweight loss. 26. (NOTE: THIS PROBLEM IS A NATURAL FOLLOWUP TO ADDITIONAL PROBLEM #57 IN CHAPTER 7 OF THIS INSTRUCTORS’ MANUAL.) Pogs are supplied by a constant cost industry in which each firm has fixed costs of $25. The industry-wide demand curve and the typical firm’s marginal cost curve are as follows: Industry-Wide Demand Firm’s Marginal Cost Curve Price Quantity Quantity Marginal Cost $5 480 1 $5 20 400 2 20 25 360 3 25 30 320 4 30 40 240 5 40 45 120 6 45 The government is deciding between two policies. Under Policy A, producers will pay an excise tax of $20 per pog. Under Policy B, each producer will be required to purchase a pog-selling license. Only 80 licenses wil be issued, and they will be sold to the highest bidders. Which policy creates the greater deadweight loss? 27. Suppose that any number of American computers can be sold abroad at the price P0 , which is higher than the price at which the supply curve of American producers crosses the demand curve of American consumers. a) What price will American consumers have to pay for American comput- ers? Why? Show on a graph the number of computers that Americans will buy. Show the number that American producers will sell. Show the number exported. Show the consumers’ and producers’ surplus gained by Americans. b) Let Q0 be the number of computers that would be sold in the United States if there were no foreign market. Suppose that legislation is enacted requiring American producers to sell at least Q0 computers in America be- fore selling any abroad. At what price would these computers sell? What quantity would producers now wish to export? Show the consumers’ 8–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. surplus, the producers’ surplus from domestic sales, and the producers’ surplus from foreign sales. c) Who gains and who loses from this legislation? What, if anything, is the deadweight loss? 28. The American supply and demand curves for bananas cross at a price of $5. Coincidentally $5 is also the world market price at which foreigners will sell any quantity Americans want to buy. A new law sets a price ceiling of $2 for bananas in America and requires American sellers to sell only to Americans. To eliminate waiting lines the government agrees to provide bananas (at $2 apiece) to any American who can’t find a willing seller. The government buys its bananas on the world market. Illustrate the gains and losses to all relevant groups of Americans and illustrate the deadweight loss. 29. Suppose that Americans can buy as much Columbian coffee as they want to at $10 per pound, but are prevented by law from selling any coffee to Colombians. However, American producers’ supply curve for coffee intersect the American demand curve for coffee at a price of $5 per pound. a) How much coffee will be imported from Colombia? Why? (Assume that coffee grown in the U.S. is identical to coffee grown in Colombia.) b) The U.S. government announces that it will supply coffee to any Amer- ican citizen who wants it at a price of $3 per pound. It will get this coffee by buying from Colombia. Show on a graph the new price of coffee in America, the quantity sold by American producers, and the quantity bought by American consumers. c) Show the gains and losses to all relevant parties from the program de- scribed in part b). What is the deadweight loss? 30. The following diagram shows the supply and demand for widgets. There is (and has always been) a price ceiling of $10 per widget. The government has recently instituted an excise subsidy: the government gives producers $5 for each widget they sell. Price A S $30 B C $25 D E F $15 G H J $10 K D 200 400 1000 Quantity a) Before and after the subsidy, how much do producers receive for each 8–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. widget they sell? (Your answer should consist of a “before” part and an “after” part.) b) Before and after the subsidy, how many widgets are supplied? c) How much does the subsidy change the producer surplus? d) Before and after the subsidy, how much do buyers feel like they are paying for widgets (including the value of their waiting time)? d) How much does the subsidy change the consumer surplus? e) How much does the subsidy cost the taxpayers? f) In order to determine whether the subsidy increases or decreases social gain, which three areas would you want to measure? Note: There is no need to shift the supply curve to solve this problem. 31. The American supply and demand curves for widgets cross at a price of $10, but foreigners will buy any quantity of American widgets at the world price of $15 each. One day the U.S. government imposes a price ceiling of $8 on widgets sold in the U.S. and requires sellers to let American consumers buy whatever quantity want at that price. (There is no price ceiling on widgets sold to foreigners.) American consumers are not permitted to resell widgets abroad. In terms of areas on the following graph, what is the deadweight loss due to the price ceiling? (Remember that you must justify your answer.) Price S $15 A D G F E B $8 C D Quantity 32. (NOTE: THIS PROBLEM IS VERY SIMILAR TO PROBLEM 32 IN THE TEXTBOOK.) Widgets are available on the world market, in any quantity, at $2 apiece. The American supply and demand curves cross at $5. American sellers produce 300 widgets and American buyers purchase 1000 widgets. Now the government distributes 500 ration tickets, which can be freely bought and sold. To buy a foreign-made widget, you must turn in a ration coupon. (An American made widget requires no coupon.) Use a graph to illustrate a) the new price of widgets, b) the price of a ration coupon, c) the gains and losses to all relevant groups of Americans, and d) the deadweight loss. 33. Suppose that the equilibrium price of peanut butter is $5 per pound. The U.S. government has agreed to sell peanut butter for $2 per pound, and to provide whatever quantity consumers want to purchase at that price. To acquire this quantity of peanut butter, the government is prepared to pay whatever price is necessary to get suppliers to provide it. All of the revenue that the government collects by selling peanut butter will be used to make welfare payments. a) Use a graph to illustrate the effects of this program on four groups of citizens: the consumers of peanut butter, the producers of peanut butter, 8–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. the recipients of welfare, and the taxpayers. b) Use your graph to illustrate the deadweight loss that this program creates. 34. Suppose that it is now between harvests, so that the number of oranges is in fixed supply. The demand curves for oranges are the same in Toronto and Montreal, but there are many more oranges in Toronto than in Montreal. a) On one graph, show the demand and supply curves for oranges in both cities. Show the market price of oranges in each city. b) Show the consumers’ and producers’ surpluses in each city. c) Now suppose that oranges can be costlessly transported. In light of the price difference between oranges in the two cities, what do you expect suppliers to do? How does this affect the supply curves in each city? When does the process stop? d) Do parts a) and b) over again, after the process described in part c) takes place. e) Are consumers made unambiguously better off by the transportation of oranges? Are producers? Is society? 35. In equilibrium, oranges sell for $5 apiece. According to the efficiency criterion, which is better: A sales tax that causes the price of oranges to fall to $4 apiece, or a price ceiling (that is, a legal maximum price) of $4 per orange? Why? 36. Suppose: • The American supply and demand curves for coffee cross at $5 a pound. • Foreigners are willing to sell coffee to Americans in any quantity for $9 a pound, but they are unwilling to buy coffee from Americans at any price. • The U.S. government sets a price ceiling of $3 a pound for coffee and agrees to provide as much coffee as necessary to prevent waiting lines from forming. The government gets its coffee by buying it from foreigners. • The revenue the government collects from selling coffee is all given away to the president’s brother. Use a graph to illustrate the effects of the government’s policy, showing the gains and losses to all relevant groups of Americans. Use your graph to illus- trate the deadweight loss. 37. The American demand and supply curves for oranges cross at a price of $8. All Americans are free to buy or sell on oranges on the world market at a price of $5 each. One day, the U.S. government announces that it is willing to pay $6 apiece for American oranges and to buy as many oranges as Americans want to sell at that price. The government then takes those oranges and resells them on the world market for $5 each. Use a graph to show how this plan affects all relevant groups of Americans, and to illutrate the deadweight loss. 38. Widgets are produced by a competitive constant-cost industry. In long-run equilibrium, widgets sell for $3 apiece. Suppose now that the government requires each widget manufacturer to pay an annual license fee of $100, whereupon the long-run equilibrium price of widgets rises to $5 apiece. a) Approximately how many widgets does each firm produce? b) Draw a diagram showing the industry-wide demand for widgets and the new short-run supply of widgets. On this diagram, identify an area equal to the sum of all license fees paid by all the firms. (Hint: Paying the license fee and selling at $5 must be exactly as attractive as not paying the license fee and selling at $3.) 8–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. c) Use your diagram to illustrate the deadweight loss from the license fee in the long run. (Hint: Remember that in the long run, producers earn zero profit with or without the license fee, so your calculation can ignore the producers.) 39. Broomsticks are manufactured by two firms which constitute a competitive in- dustry. Neither firm has any fixed costs. There are two consumers, W.W.West and W.W.East. The following charts show the marginal cost of producing var- ious quantities of broomsticks at each firm, and the marginal value of various quantities to each customer: Marginal Cost Marginal Value Quantity Firm A Firm B Quantity W.W.West W.W.East 1 $2 $4 1 $10 $9 2 3 5 2 8 8 3 4 6 3 6 7 4 5 7 4 4 6 a) What quantity of broomsticks are sold and at what price? How many are built by Firm A and how many by Firm B? How many are bought by W.W.West and how many are bought by W.W.East? b) How much producers’ surplus is gained in this market? How much con- sumers’ surplus? How much social gain? Your answers to all three ques- tions should be numbers. 40. “If it weren’t for secretaries, business would collapse. Therefore, secretaries should be paid as much as corporate executives.” Comment. 41. “In an efficiently run society, people who work equally hard would receive equal wages.” Comment. 42. A doctor wrote a letter to the Des Moines Register where he said, “Why should I get $50 for a procedure in Iowa and a physician in New York get twice as much? That does not seem equitable.” Comment. 8–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 8 1. a) From buying the widgets. b) A gadget. c) The shaded rectangle is subtracted from consumer surplus: Price A 10 B D 30 31 Quantity 2. Price False. Consumer surplus increases by C+D. ButC=$100, so consumer surplus increases by more than $100. P C D P minus $.10 D Quantity 1000 3. a-d are all preferred to e according to the efficiency criterion and c is preferred to e according to the Pareto criterion. 4. True, if the amount of land is really fixed. Since the amount of land can’t change, there is no possibility of deadweight loss. The figure below illustrates this. Price A B D C E D D' Quantity 8–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Without Tax With Tax Consumers’ Surplus A+B A+B Producers’ Surplus C+D+E E Tax Revenue - C+D Social Gain A+B+C+D+E A+B+C+D+E It should be noted, however, that this picture is unlikely to correspond to any important market in the real world. Generally, one is not interested in land per se, but rather in goods like “land suitable for farming” or “land suitable for ranching.” These goods are not in fixed supply. “Land suitable for farming” can be produced via such activities as the removal of boulders, irrigation and so forth. The supply curve for such land is therefore upward sloping, and a sales tax on such land does create deadweight loss. 5. False; you can never prove anything is bad (according to the efficiency criterion or any other sane criterion) by listing its costs. You must also consider the benefits (in this case the benefit to the consumers) and weigh the costs against the benefits. 6. Using the graph from Exhibit 8.12, you can first take C+D+E+F+G from the taxpayers (just as the subsidy program does) and then hand out F+G to the consumers and C+D to the producers (just as the subsidy program does). This leaves you with E, which you can distribute as you like, giving some (or all) to the consumers, some (or all) to the producers, some (or all) back to the taxpayers and some (or all) to your favorite uncle. 7. False. The line lengths adjust until the value of the waiting time is the same in both countries. 8. In Middle Slobbovia, the value of wasted time will be less than in either Upper or Lower Slobbovia, as those with relatively low time values can be hired to do some of the waiting. 9. True: Price A S S' B C No excise tax Excise Tax CS A+B+ C A F PS I+ J+K+L L D E H TaxRevenue I+ J G $2 I K DeadweightLoss C +K J L D The excise tax causes even fewer potatos to be supplied, hence creates a deadweight Quantity loss. 8–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 10. False: Price S B A No sales tax Sales Tax D CS A+B A+B C E PS H H F G TaxRevenue C +D $2 "DeadweightGain" C +D H D D' Quantity The point is simply that the sales tax makes people less willing to wait in line for the item and so saves society the cost of some line-standing. Instead of paying for the item with valuable time that is recovered by nobody, the consumers pay with cash that goes to the tax recipients. In fact, a sufficiently large sales tax can eliminate all line standing (though there is still a deadweight loss associated with the tax). Can you draw the corre- sponding picture? 11. Price S A S' B C D E G F H $10 J L K D Quantity a. The subsidy increases CS from A to A+B+C. It increases producer surplus from J to F+G+J. The cost to the taxpayers is F+G+H. b. Social gain increases by B+C-H To determine whether this is positive or negative, you'd need to measure the areas B+C and H. c. D+E+F+G+H 12. The Senator is proposing a price control. In terms of Exhibit 8-14 in the textbook, his plan will increase the deadweight loss from C + E to B + C + D + E. 13. True. The “price to demanders” in the wholesale market for wheat—that is, the price that bakers pay for wheat, inclusive of the value of their time—would rise. This price is part of the marginal cost of producing bread, so marginal costs rise in the bread market; hence prices rise as well. 8–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 14. Price S A pound of potatos sells for P0 (at any A Ahigher poundprice, sellers sells ofpotatos wouldfornotP0be(atable anytohigher sell their price, desired sellers wouldquantities, not be ableand price to sell their P 1 desired quantities would drop). Priceand price wouldmust to consumers drop).be Consumers must price, P1 (at any lower pay P1 (at any buyers lower would notprice, B D buyers be ablewould to buybetheir unable to buy desired their desired quantities and quantities and price would rise). Therefore price would rise). Therefore price of ration the price of a ration ticket must be P1-P0. P CSticket is A,must PS beis C,P1-P0. value ofCS is A,tickets ration PS is is C , 0 value of of ration tickets is price of ration ticket of C the price a ration ticket times the quantity D times quantity tickets or B. Thusof ration tickets, or deadweight B. isThus loss D. deadweight loss is D. 0 25 Quantity 15. Sellers can sell only 250 pounds, so they A must receive a price of only P0 (if they received P1 any more, they'd want to sell more potatos than they're able to and the price would be bid C down). Similarly buyers must pay P1. The D difference must be accounted for by the price of a ration ticket, so this means that a) the price of a potato is P0 and b) the price of a ration ticket is P1-P0. Thus c) the CS and PS P are given by areas A and B. d) The value of the 0 B ration tickets is equal to the price times the number of tickets which is area C. e) The deadweight loss is the "missing" social gain D. 250 16. Price S' S Initially the government collects A B C D+E+F+G+H in license fees. D E F After the excise tax is imposed, the G governnmentcollects G+H in license fees plus A+B+D+E in H excise tax. Total revenue could either rise or D fall, depending on whether F is less or more than A+B. Quantity 8–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 17. Price S A P Before the program, CS=A+B+ C and PS=D+E. B C With the program, the price of potatos rises to P. E Consumer surplus falls to A. Sellers are willing to D pay B+D for permits, and all of this goes to the government. Therefore total surplus is A+B+D. The deadweight loss is C+E. D Quantity 1000 2000 Price S 18. A P B C E D $2 F D 1000 Quantity a. In Upper Slobbovia, the price of a pair of shoes, plus the value of the time spent waiting in line, is P. In Lower Slobbovia the price of a pair of shoes is P. So consumers are equally happy in either country. b. In Upper Slobbovia, producers collect $2 for a pair of shoes. In Lower Slobbovia, they collect $(2+P) and pay $P for a permit, so they keep $2. So producers are equally happy in either country. c. The collectors of permit revenue are, of course, happier in Lower Slobbovia (where they collect B+C) than in Upper Slobbovia (where they collect nothing). 8–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 19. Price S is the supply curve for commercial toy S manufacturers. Santa causes the price of commercial toys A to drop to P. Commercial toy makers produce Q toys and consumers end up with Q+1,000,000. Producer surplus falls from B+E to E. B To compute consumer surplus: The value of C D all the toys is A+B+ C+D+E+F+G+H. Consumers pay P*Q=E+F. So consumer surplus rises from P A to A+B+ C+D+G+H. E F G H Social gain rises from A+B+E to D A+B+C+D+E+G+H. The "deadweight gain" is therefore C+D+G+H. Quantity Q Q+1,000,000 20. Price S A No price floor Price floor B D CS A+B+ C A C PS E+G B+ C +D+E+G E G Cost to taxpayers C +D+E+G+H F H SG A+B+ C +E+G A+B-H D DWL C +E+G+H { Quantity Q . purchased by govt. 21. Price S Consumers are always free to buy oranges at $5, so their consumer surplus (A+B+C +D+E+F) cannot be affected. A B Producers now get $6 instead of $5 for 6 oranges, so PS rises from G to C +G. C D E F 5 Govtbuys quantity Q and takes a loss of G D $1 per orange, so loss is C +D. Q Quantity DWLis D. 8–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 22. The triangle on the left reflects the fact that people purchase foreign cars that could have been produced more cheaply at home. The triangle on the right reflects the fact that people now buy fewer cars. Can you explain why? 23. Price S No tax Tax U.S. buyers pay 10000 10000 A U.S. sellers get 10000 8000 B CS A+B A+B 10000 PS C +D+I I C D H Tax Revenue C E F G 8000 I D DW Loss D Quantity 24. a) Sellers continue to sell if their Producer Surplus is positive. PS=B-C-D, so these are the areas D to measure. A b) CS=A+C, PS=B-C-D, so C Social Gain=A+B-D. DWLoss is D. 15 c B c) Area A+B is now the deadweight loss. 25. Price S No tax Tax U.S. buyers pay 10000 12000 A U.S. sellers get 10000 10000 B CS A+B+ C +D+E+F+G A+B 12000 PS I I C D H Tax Revenue C +D+E+F E F G 10000 DW Loss G I D Quantity 8–19 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 26. Americans can get cars for $8000, so they won’t pay more than $8000 for an American car. Therefore American producers sell exclusively abroad where they can get $10,000. The graph is as follows: Price S No subsidy Subsidy U.S. buyers pay 10000 8000 A U.S. sellers get 10000 10000 B CS A+B A+B+ C +D+E+F+G 10000 PS C +D+I C +D+ I C D H Cost to taxpayers C +D+E+ F+G+H E F G 8000 DW Loss H I D Quantity If American producers can’t sell abroad, they’ll have to accept $8000 per car and the graph becomes: Price S No subsidy Subsidy U.S. buyers pay 10000 8000 A U.S. sellers get 10000 8000 B CS A+B A+B+ C +D+E+F+G 10000 PS C +D+I I C D H Cost to taxpayers D+ E+ F+G+H E F G 8000 DW Loss D+H I D Quantity 27. Price S No subsidy Subsidy U.S. buyers pay 10000 10000 A U.S. sellers get 10000 12000 B CS A thru G A thru G 12000 PS I C +D+I C D H Cost to taxpayers C +D+E E F G 10000 DW Loss E I D Quantity 8–20 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 28. Price S No subsidy Subsidy U.S. buyers pay 10000 8000 A U.S. sellers get 10000 10000 B CS A+B A+B+ C +D+E+F+G 10000 PS C +D+I C +D+I C D H Cost to taxpayers C +D+E+F+G+H E F G 8000 DW Loss H I D Quantity 29. Price S A B 10000 D H C E F G 8000 J D Quantity Without subsidy With subsidy CS A+B A+B+C+D+E+F+G PS C+D+J C+D+J Taxpayers - (C+D+E+F+G+H) DWL H 8–21 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 30. With the taxes in place, Americans must pay $13000 for a foreign car. They will therefore pay $13000 for an American car. Of this $13000, $1000 goes to the govt, so the remaining $12000 goes to the seller. A Therefore: B 13000 NO TAXES TAXES C D E F 12000 CS ABCDEFGHJK AB G H J K 10000 PS L GL L TAX REV C+ DEJ SOCGAIN ABCDEFGHJKL ABCDEGJL DWLOSS F+H+K . Plan A is to retain a tariff. Plan B is not to retain any tax. The effect of a tariff is shown in Exhibit 8.17. As you can see in that exhibit, domestic car makers are better off with a tariff than without one. Starting with the tariff (Plan A) and using the notation from Exhibit 8.17, you could take G+H+I+J from the consumers (just as a tariff does), give G to the producers (just as a tariff does), give I to the tax recipients (just as a tariff does) and have H+J left over with which to make everyone happier. 31. Price S A NO SUBSIDY SUBSIDY D B C E CS A+B+ C A PS F+G+H+I B+ C+D+F+G+H+I I Taxpayers - -(C+D+E) H F G DWLoss C+E b) One example of a plan everyone would prefer: Take B+C/2 from consumers, take C/2+D+E/2 from taxpayers, and give B+ C+D+E/2 to producers. D There are many other correct answers to b). Quantity 1000 2000 32. In order for demanders to want exactly 500 foreign widgets, the price to demanders of a foreign widget must be $6. Of this, $2 goes to the foreign widget maker so $4 must be the price of the ration ticket. 8–22 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price 33. S A B $15 D C E F G $12 H I J K L $10 M D Quantity a. The program raises the price of a camera from $10 to $15 and therefore reduces consumer surplus by C+D+E+F+G+H+I+J+K+L. It allows American producers to sell at $12 instead of $10 and therefore increases their surplus by $H+I. The tariff revenue is $D+E+F+J+K$. The deadweight loss is therefore C+I+G+L. b. It requires $3 worth of waiting time to buy an American camera. Therefore the value of the time spent waiting in line is C. 34. Price A S P0 Farmers must cut back production D from Qsto Qd. This requires a B C payment of C +D+F. So consumers lose B+ C , farmers gain B+ C +D, F taxpayers lose C +D+F, and E deadweight loss is C +F. D Qd Qs Quantity 35. Price S Before the law, Americans earn $15 per hour. CS (earned by firms) is A+B+ C +D A and PS (earned by American workers) is F. E 25 After the law, firms hire Q0Americans B C at $25 per hour and Q1-Q0foreigners D at $15 per hour. CS is A+D and PS is 15 F B+F. Deadweight loss is C . D Q0 Q1 Quantity 8–23 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 36. Price MC PS must fall by the amount of the per-firm subsidy in order to maintain the zero-profit condition. If price falls by $1 (in diagram) then PS $1{ A B falls by A+B, so A+B=$8000. New quantity is Q so A= Q x $1 = $ Q . D Since A<A+B, we have Q <8000. Q Quantity Thus the govt pays more than $1 per widget produced. With an excise subsidy of $1 per widget, price would fall by the same amount, so consumers are indifferent between the two subsidies. Firms earn zero profit no matter what, so they are also indifferent. Govtpays $1 per widget under the excise subsidy, but more than $1 per widget under the per-firm subsidy. Thus the excise subsidy is more efficient. 37. True. The MC curve in Exhibit 8.18 becomes flat, so area B disappears and the social cost (A) is equal to the loss to the victim. 38. WIMPY 0 Blackened dot shows endowment point. Shaded area is region of mutual advantage. Darkened lines show contract curve. The only competitive equilibrium is at the bottom right corner of the box. 0 POPEYE 39. He will produce either all nuts or all berries depending on the relative price. 40. His own demand curve is not important for determining supply side decisions in a world with free trade and many differing producers. He simply takes market prices as given and chooses to produce where his production possibility frontier has slope equal to the relative prices in the economy. This allows him to obtain the budget line which is the farthest from the origin and thus the highest indifference curve. 8–24 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Nine: Knowledge and Information What’s New In This Edition I’ve updated several of the examples, most notably replacing a somewhat dated example about alternative energy sources with a more contemporary discussion of the local foods movement. Teaching Suggestions 1) In the study guide that accompanies this textbook, there is reprinted Hayek’s article on the use of knowledge in society. I always assign this article as required reading. It is one of very few pieces of economic writing that genuinely meets two criteria: it is completely accessible to students, and it is profound. In fact, the accessibility tends to mask the profundity: Students have the idea that nothing so easy to read could possibly be important. I assign it after I have covered the material of Section 9.1, so that students know what themes to watch for. 2) In the text, there are many examples of ways in which prices enable the market to make use of specialized information, even though that information is unavailable to any central planner: the fact that linseed oil is used to make the ink for books, that there are two ways to get chickens to lay more eggs, and so forth. It is worth emphasizing to students that when Hayek talks about the knowledge of the particular circumstances of time and place, he is referring also to information that is even more specialized. He is referring to the knowledge that one of the typists is bored this afternoon and would not mind being asked to help with some filing, or that if you stack things just right you can squeeze one additional odd-shaped parcel into the delivery van. The importance of such knowledge for economic planning, and the mechanism by which it is used under a price system, is Hayek’s great insight and the theme of this chapter. 3) I do not ordinarily cover the material of 9.2 and 9.3 in class. It is fun and interesting, but there is usually just no time. Occasionally I have had a little extra time at the end of the semester and used it to come back to this. 4) The material on efficient markets presents a paradox which an occasional bright student might notice. If the price of an asset contains all of the informa- tion relevant to that asset’s future performance, then nobody has any incentive to expend resources investigating more fundamental variables. But if nobody inves- tigates such variables, how can the information they contain become incorporated in the price of the asset? On the one occasion when a student asked me this, I commended him heartily for his insight, told him that many economists had been troubled by the same thing, made some noises about models with informed and non-informed agents, and referred him to the famous paper by Grossman and Stiglitz. I don’t know whether he looked it up. 5) As to the example on signaling in the animal kingdom, things are actually worse than described in the textbook. The text says that male birds signal their reproductive fitness to females by devoting resources to the production of extrav- agant tails. These resources are wasted from a social point of view, in that an agreement among all males to grow tails only half their present length would be a Pareto-improvement. But no such agreement is enforceable. That much is in the text. Here is what’s left out: Male birds with long tails are more likely than average to have had fathers with long tails. This is so because of 9–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. the laws of heredity. It follows that male birds with long tails are more likely than average to have had mothers who are particularly attracted to long tails; after all, their mothers did choose to mate with their fathers. Thus long- tailed males are likely to have received genes from their mothers that, if present in a female, cause attraction to long tails. When a long-tailed male mates, it is often to a female with an attraction to long tails. Thus any female offspring are likely to receive genes from both sides that incline her to choose long-tailed males. At the same time, a female with an attraction to long tails is likely to have had a mother with the same attraction, hence a father with a long tail, hence to be carrying genes that cause long tails in males. When she mates it is likely to be with a long-tailed male, so that the male offspring can receive genes from both sides that produce long tails. The upshot is that the traits of long tails in males and an attraction for long tails in females reinforce each other in a particularly strong way, and there can be explosive growth in tail length in a very short time. This is a famous example in bi- ology, due to R.A. Fisher, whose book on natural selection I recommend. A popular account is in Richard Dawkins’s The Blind Watchmaker, which I also recommend, subject to the caveat that the reader ignore the remarks about economists that are made in that book. Dawkins’s The Selfish Gene is a delightful book which looks at biology the way an economist would look at it. 6) For insightful commentary on executive compensation in general and the Jensen/ Murphy results cited in the textbook in particular, see K. McLaughlin, “Individual Compensation and Firm Performance: The Economics of Total Output Contracts,” preprint (1990). 9–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Citizens are chosen randomly to serve on juries, and are required to serve if chosen. True or False: Since the selection of jury members is random, nobody can alter his behavior to avoid it. Thus there is no social loss associated with the jury system. 2. Parking space is in short supply at MacAdam University. At a cost of $10,000, the University has just constructed a new parking lot containing 100 parking spaces. True or False: In order to insure that the spaces are allocated effi- ciently, the University should sell them at a price of $100 apiece. 3. True or False: The calculation of deadweight loss due to a price control is overly optimistic since it fails to take account of the costs of misallocation a la Hayek. Remark: If you assign problem 3, you should probably allow some time for class discussion, since the answer is subtle. If people are able to compete for the good by hiring line-standers, purchasing advertisements, etcetera, then there is a deadweight loss as in chapter 8, but no misallocation since goods still go to the highest bidders. Thus the answer is false. If there are no markets for such activities, so that people have to wait in line themselves, then if people all have the same value of time, the answer is still false, for the same reason. If goods are allocated via waiting lines, and there is no market for waiting services, and people have very different values of time, then goods could end up being allocated to people who value them little but value their time even less. This is a misallocation, though it seems debatable whether we should attribute it to the price control or to the lack of a line-standing market. Finally, if people are somehow effectively prohibited from any form of compe- tition other than price— and it is worth emphasizing to students that this is more unlikely than it might first sound—so that the goods are allocated essentially ran- domly to those consumers who happen to be right in the vicinity when the goods appear on the shelves—there is certainly a loss due to misallocation, but on the other hand, the losses due to line-standing disappear. 4. Suppose that land can be neither created nor destroyed, so that the supply curve for land is perfectly vertical. a) Suppose that a law is passed which sets a maximum allowable price for land, and that this price is below equilibrium. Show the deadweight loss. b) Suppose instead that a law is passed under which a national lottery will be held and the winners will be given free land, which they can not sell. Exactly enough winners are chosen to distribute all of the land in the country. Is there a deadweight loss associated with this plan? Explain. c) Give an example of a real social cost of the plan described in part b) that is not reflected in your measure of deadweight loss. How could the plan be modified to eliminate this cost? 5. Suppose that the supply curve for land is perfectly vertical, and that the price of land is legislated to be at some level below equilibrium. a) Show the deadweight loss. b) Suppose that people could somehow be prevented from engaging n costly activities in their attempts to acquire scarce land. Show that the dead- weight loss is now zero. 9–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. c) True or False: In the case of part (b), there is no social loss due to the price control. 6. Suppose that in equilibrium Americans consume 1000 fruitcakes per year. The government is considering two plans to increase fruitcake consumption. Under Plan A, fruitcake buyers receive a subsidy that causes consumption to rise to 3000 fruitcakes per year. Under Plan B, the government gives away enough fruitcakes to raise consumption to 3000 per year. True or False: Since in each case the number of fruitcakes is identical, it follows that the two plans are equally socially desirable. 7. No fruitcakes are produced in the United States. Americans can buy any num- ber of fruitcakes from abroad at a price of $10 each. At this price, Americans buy 1000 fruitcakes per year. 8. The U.S. government has decided to make fruitcakes available to American citizens at a price of $3 each. The government will provide as many fruitcakes as people want to buy at this price, and will get them by purchasing them from foreigners. a) Show the gains and losses to all relevant groups of Americans as a result of this program. Compute the deadweight loss. b) Suppose that the government modifies the program. It will continue to sell fruitcakes at $3, but it will provide only 1000 per year, choosing randomly those citizens who will be permitted to buy them. Compute the deadweight loss now. c) In part b), can you think of any real social costs of the program that are not taken into account by your analysis? 9. Suppose the equilibrium price of potatoes is $4 a pound. To gain the support of potato farmers, the government agrees to buy potatoes at $7 a pound, and to buy as many potatoes as farmers want to sell. Then the government resells the potatoes to demanders, at whatever price demanders are willing to pay for that quantity. a) Use a graph to illustrate how this program affects potato farmers, potato consumers, the taxpayers, and the recipients of the government’s revenue from potato sales. Illustrate the deadweight loss from this program. b) Suppose that instead of reselling the potatoes, the government gives them away for free to the same people who would otherwise have bought them. How does this affect your calculations in part a)? How does it affect the deadweight loss? c) If you heard that the government was buying potatoes and giving them away, would you consider your deadweight loss calculation an adequate measure of this program’s social cost? If so, why? If not, give an explicit example of something your calculation leaves out. 9–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 9 1. False, or at least not necessarily true. Although the elves want to be as helpful as possible, they have no way of knowing where their services are most valuable. As a result, they might end up spending a lot of time repairing old black and white television sets when they could be repairing the space shuttle. If humans are able to bid against each other for the elves’ services, the elves will be able to concentrate their efforts where they do the most good. This makes humans better off; on the other hand, the actual payments to the elves make them worse off. The net effect on humans could go either way. 2. None of the council members has the expertise to determine the extent of the risk from the chemical plant and none has the expertise (or information) to determine the extent of the benefits. It is reasonable to expect that the company owners and their insurers (who are experts in assessing risks) have access to more such information than the council has. Under the councilman’s proposal, they have the incentive to make use of such information. If the chemical company agrees to bear all of the costs of reimbursement, we may infer that it expects to earn enough from the plant to more than cover these costs. Similarly, if the insurance company is willing to bear the risk in exchange for a price that the chemical company is willing to pay, we may infer that it expects the amount of damage to the townspeople to be less than the gains to the chemical company. The councilman’s suggestion creates an incentive for those with easiest access to the relevant information to analyze that information and act on it in a socially desirable way. 3. a) If price gouging were prohibited, less ice would have been transported to the affected areas. b) But even if the effect in (a) could have been prevented, there would have been no incentive to allocate that ice to those who needed it the most. Social welfare would have been reduced. c) The pure altruist might know that ice is worth $50 a pound to some people and not want it to fall into the hands of those who value it at only $10 a pound. If he’s not sure who’s who, the only way to find out is to set a high price. Later, he can donate the $50 to general hurricane relief efforts. 4. False; there are many things that divisional managers know that central manage- ment does not and indeed can not know. These include general facts: John and Harry don’t get along, so putting them next to each other on the assembly line tends to slow things down; when you let Judy go five minutes over on her coffee break, she becomes much more productive for the rest of the afternoon; Fred the janitor is better at computer repairs than the computer repairman that the com- pany sends out. But even more importantly, the divisional managers are aware of very specific facts—knowledge of the particular circumstances of time and place— that can not possibly be communicated to central management in any systematic way: Judy is feeling bored this afternoon and would enjoy tackling a tough assign- ment; computer #7 is making strange noises, so perhaps we should be sure we have backups of all its data; Mary’s desktop is clear right now, so its a good place to set down some files while we sort through them. 9–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Can you imagine central management making decisions about where to set the files down? Central managers don’t know about Mary’s clear desktop, they don’t know how bulky the files are; they don’t know how long you’ll need to look at them, and they don’t know when Mary needs her desk back. John and Harry’s long-standing feud could perhaps in principle be explained to the management— but how is management to know that George and Helen just had a quarrel five minutes ago and shouldn’t be assigned to work together today? Countless decisions are made every day that require specific knowledge avail- able only to one or a few people. There is an advantage to having decisions made by those with access to this knowledge. 5. a) Under competition, price equals marginal cost equals $6 per sword. At this price, Aramis buys 2, Porthos buys 1, and Athos buys 2, for a total of 5 swords. b) In part a) the social gain is the total value of the swords ($10 + $8 + $7 + $9 + $6 = $40) minus the total cost of producing them (5 × $6 = $30), or $10. Now the total value of the swords is reduced to $7 + $5 + $4 + $3 + $9 = $28, and the social gain is reduced to $(-2). The planner’s decision leads to a social loss of $12. 6. Plans (c) and (d) are equivalent. Under Plan (c) a young person is told, “You must pay $100 in tax. You may also join the army if you wish, in which case you will receive a wage of $100.” Under Plan (4), the same young person is told, “You must enter the army, unless you hire someone else to take your place at a wage of $100.” (The market- clearing wage must be the same in each case, because the army is of the same size in each case.) Whichever way you word it, the young person’s choices come down to: sacrifice $100 or join the army. Under Plan (a), the army consists of exactly the same young people as under Plans (c) and (d): those with the lowest opportunity costs. Thus from a welfare point of view, plans (a), (c) and (d) are equally desirable. Of course young people prefer plan (a), under which the cost of the army is shared by all, and other citizens prefer plans (c) and (d), under which young people bear the entire cost. Plan (b) appears at first to be equivalent to plans (c) and (d), but it differs in one crucial respect: Under Plan (b), some young people with high opportunity costs will be drafted instead of others with lower opportunity costs. This can not be avoided unless the officers of the Selective Service system know every detail of every young person’s talents, ambitions, plans, and circumstances. Thus Plan (b) is inferior to the other plans on welfare grounds, despite the fact that a graphical analysis as in Chapter Eight would reveal no deadweight loss. The additional social costs are borne entirely by young people; young people as a group are worse off under Plan (b) than any of the others, whereas for other citizens Plan (b) is neither better nor worse than Plans (c) and (d). Incidentally, the equivalence of Plans (c) and (d) is a new way to see that a volunteer army is no more expensive than a draft in any meaningful sense. Soldiers are paid a market- clearing wage in (c) and no wage at all in (d), but each individual citizen is equally well off under either plan. One further remark: If the young people who are chosen to be taxed in Plan (c) are exactly the same as the young people who are drafted in Plan (d), then the plans really are equivalent from each individual person’s point of view. If only some young people are drafted in Plan (d), but all young people share the tax burden in Plan (c), then Plan (c) allows a more equal division of the burden, but the cost to young people as a group remains the same. 9–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7. a) In the simple case where there is a homogeneous product called land, the Fabians are correct. The idea is that even if the tax is 99 percent, owners will look for the highest possible bidder in the marketplace in order to maximize their rents (this of course presumes there are no costs to searching for such bidders). This ensures that the land will be distributed efficiently and there will be no social loss. The key idea here is that the quantity of land supplied will not be reduced in response to the distortionary taxation; thus there is no deadweight loss. Nevertheless, when land is differentiated by quality (i.e., well maintained vs. mismanaged land) the Fabians argument breaks down. In this case, the tax causes a reduction in the quality of land and thus a reduction in social welfare through a deadweight loss. b) If it were costly to locate high bidders, then a 99% tax could discourage such efforts and cause land to be misallocated. 8. P In the best case scenario, the shaded S area is the deadweight loss. This area $5 breaks up into rectangles, with each rectangle representing the marginal cost of providing a haircut minus the marginal value of that haircut. But this assumes that haircuts are given to the consumers who value them most. If instead some of the haircuts go to D consumers who value them less, the Q social loss will be greater. 9. Price S A P' T { P B C D Quantity a) Suppose that parking spots are sold at the artificially low price P . The “full” price must rise to P 0 in order to equilibrate supply and demand. Thus the price of a ticket must be T . Consumers’ surplus is A, producers’ surplus is C, and the total value of the tickets is T times the number of tickets, which is B. Comparing with the situation before the lottery we have Without Lottery With Lottery Consumers’ Surplus A A Producers’ Surplus B+C C Value of Tickets - B Social Gain A+B+C A+B+C Thus parkers are neither better nor worse off when the plan is instituted. The area B is transferred from the University to the winners of the lottery tickets. 9–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Warning: Do not become confused by the fact that some ticket winners are also parkers. Such people gain part of area A in their capacity as parkers and part of area B in their capacity as ticket winners. b) The effects are identical, since in either case all that happens is that some wealth is transferred from the University to randomly chosen students. The plan in part a) was actually proposed recently by a faculty member at the University of Rochester. He circulated petitions in its favor, which were signed by a large number of faculty, students, and staff. A rival petition, favoring the more straightforward approach of randomizing tuition (and, for faculty and staff, randomizing salaries) gathered considerably less support, for reasons that are not entirely clear. c) Now some of the tickets will end up in the hands of students who value them less than others do, creating social waste. The most extreme cases are those where a ticket ends up in the hands of a student who has no use for it whatsoever, because he has no car. But there are losses in other cases as well. If lottery winner Maxine wins a ticket that she values at $5, and lottery loser Saul would be willing to pay $15 for that ticket, then preventing the transaction creates a social loss of $10. 10. Price S A B C D Quantity In the graph, consumers gain area B + C, while producers lose the same area. (This does not, however, account for the value of the producers’ good feelings due to their burst of generosity.) This calculation presumes that all pizza will be delivered to consumers who like pizza. If instead large amounts of pizza are delivered to consumers who don’t like pizza then the net result could be to make consumers either better or worse off. 11. Price Santa causes the supply curve for toys S to shift rightward by 1,000,000. S' Consumers end up with Q2toys, of A which Q1come from commercial manufacturers and the remaining 1,000,000 come from Santa. B C Santa causes CS to rise from A to A+B+C +F+G and PS to fall from B+D D F to D. Net social gain from Santa Claus E G is C +F+G. D Q1 Q2 Quantity This presumes the toys go to the children who value them most. Otherwise, the true social value is less. 9–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 12. Price A a) Consumers gain B+ C . Taxpayers lose $10 B+C +D. Deadweight loss is D. D b) True. Area D consists of rectangles, B C each equal to the $10 cost of a pound of coffee minus the value of that coffee to a $3 consumer. c) Consumers gain B. Taxpayers lose B. D Deadweight loss is zero. 1000 Quantity d) Coffee might not go to those who value it the most. 13. Price a) New price is P. A b) Consumers gain B+ C +D. Producers lose E B+C +D+E+F+G+H+I. Recipients of free $40 widgets gain G+H+I. Deadweight loss is E+F. F B D c) Govt. does not know which firms can C produce widgets most cheaply, but the computation P G H I assumes that widgets are produced by the low D cost producers. 500 600 Quantity 14. In situation (a) college is not worth the cost and in situation (c) it fails to signal intelligence. But in situation (b) bright students can use college as a valuable signal. 15. Suppose that all applicants with incomes over $70,000 have revealed their incomes. Then if your income is $70,000, you can only gain by revealing it. The same is true at every income level. Thus all incomes are voluntarily revealed. 16. a) If the company had to charge the same rate, then only high risk persons would be insured in equilibrium. This occurs because the rate charged by the insurance company would have to be prohibitively high for low risk individuals if the insurance company desires non-negative profits. If the rate were set lower, the insurance company would go out of business as all the high risk individuals would purchase too much insurance. b) In this case the company could charge different rates to individuals who are in different risk categories. Thus the adverse selection problem would seem to be mitigated. But there is a hitch. Since there are people who would purchase in- surance with the prior knowledge that they have AIDS, the insurance companies are forced to price at a higher rate. One possible outcome: This rate drives out all the individuals who do not have AIDS and thus the only people who purchase insurance are those who have already contracted the disease. 9–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 17. It would promote social welfare in the sense that the law defines low quality versus high quality automobiles. Thus, a new market in which high quality used cars are traded has been opened due to the law. Prior to the law such a market did not exist because of the adverse selection problem. With the new market opened, buyers and sellers of high quality used cars can trade and thus welfare is increased. 18. In a large enough group the insurance company has a good idea of the number of risky versus non-risky individuals (i.e., it could extrapolate from the entire popu- lation). Thus, the company can charge an intermediate price for a fixed quantity of coverage to both low risk and high risk individuals. The high risk individuals will be subsidized by the low risk individuals but since the low risk individuals are typically given the insurance as a “fringe” benefit, they are essentially forced to subsidize these people. This works to combat the adverse selection problem and could be socially preferable in the presence of incomplete information. 19. The warranty implies the sellers are responsible for the quality of the automobile. This yields the desirable result that high quality automobiles will be sold with a more comprehensive warranty and thus are distinguishable from low quality cars. The ability to distinguish cars ends the adverse selection problem and increases social welfare. On the other hand, buyers would have less incentive to care for their cars (since they could always invoke the warranty if something went wrong), which is a moral hazard problem. 20. False. Although the percentage increase in existing claims would be minimal, the volume of future claims would increase due to moral hazard. Moral hazard arises here because persons care less about the well-being of their automobile when they are not responsible for any of the damages. The lack of caring causes an increase in auto thefts and accidents which yields a higher number of claims to the insurance company. Thus rates must increase. 9–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Ten: Monopoly General Discussion and Teaching Suggestions 1) Beyond what is covered in the text, there are many interesting topics in monopoly pricing that you can mention in class, use in constructing exam problems, or assign students to write short papers on. One is the all-or- nothing offer: If all consumers are identical, the monopolist computes the quantity that each consumer would buy at the competitive price, packages the good in boxes containing this quantity, and charges an amount equal to the full consumers’ surplus. (Since the monopolist collects the entire consumers’ and producers’ surpluses, he wants to maximize the sum of the two, hence the choice of the competitive quantity.) With all consumers truly identical, this is equivalent to a two-part tariff. With some heterogeneity among consumers it is not. You can ask students to think about the circumstances under which the monopolist might want to use all-or-nothing offers in preference to two-part tariffs or the ordinary forms of price discrimination. Of course, this will very quickly bring you into sophisticated research areas, where students can not be expected to have much insight. But some students are intrigued by hearing about the problems. 2) With regard to all-or-nothing offers, I report for the record that a student in a Principles(!) course recently approached me after class on the very day when I first defined consumers’ surplus, and suggested that if the producer packaged his goods in quantities equal to what the consumer was going to buy anyway, he could charge the full consumers’ surplus. Teaching has its rewards. 3) Another interesting monopoly pricing topic is the block booking of movies, wherein studios require theaters to purchase a package of movies as opposed to being able to pick and choose among them. (Diamonds at wholesale are sold in a similar way.) The layman’s (and apparently the Supreme Court’s) explanation, which makes no sense (see below), is that the studio, having monopoly control of a popular film, uses it to force theaters to book its less popular films as well. A debunking of this, and an alternative explanation, are to be found in Stigler’s “A Note on Block Booking” from The Supreme Court Review (1963) and reprinted in Stigler’s book The Organization of Industry. Students readily understand and enjoy this. I quote from Stigler: Consider the following simple example: . . . Gone With the Wind is worth $10,000 to the buyer, while . . . Getting Gertie’s Garter is worthless to him. The seller could sell the one for $10,000, and throw away the second, for no matter what its cost, bygones are forever bygones. Instead the seller compels the buyer to take both. But surely he can obtain no more than $10,000, since by hypothesis this is the value of both films to the buyer. Why not, in short, use his monopoly power directly on the desirable film? It seems no more sensible, on this logic, to block book the two films than it would be to compel the exhibitor to buy Gone With the Wind and seven Ouija boards, again for $10,000. The explanation of the practice must lie elsewhere. The simplest plausible explanation is that some buyers would prize one film much more relative to the other. Consider the two buyers: A would pay $8,000 for film X and $2,500 for film Y. 10–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. B would pay $7,000 for film X and $3,000 for film Y. If the seller were to price the two films separately, he would receive: 1. $5,000 for the sale of Y, at $2,500 per buyer. A higher price would exclude A and reduce receipts. 2. $14,000 for the sale of X, at $7,000 per buyer on the same logic. The total received is $19,000. But with block booking, a single price of $10,000 can be set for the pair of films, and $20,000 will be received. 10–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. True or False: Any producer, if he were in business at all, would choose to operate at a point where marginal cost equals marginal revenue. This is so regardless of whether the industry is competitive or monopolized. 2. True or False: The only way a monopolist can charge a higher than competi- tive price is by selling a lower than competitive quantity. 3. Suppose that a monopolist with a fixed marginal cost curve increases his out- put due to a shift in demand. True or False: We may be sure that the price of output will increase as well. 4. Suppose that a monopolist with a fixed marginal cost curve increases his price due to a shift in demand. True or False: We may be sure that the quantity of his output will increase as well. 5. Suppose that the demand for widgets undergoes a parallel shift upward. In which case does the price of widgets adjust further: When the widget industry is competitive or when it is monopolized? (This question is rather difficult for many students.) 6. What’s wrong with this picture? Price 10 MC 7 D 6 8 Quantity MR 7. There is only one doctor in the town of Llareggub. He pays $.50 apiece for disposable syringes and $100 per year to rent an X-ray machine. To show its appreciation for the doctor, the town council plans either to begin paying all of his syringe bills or all of his X-ray machine rental bills. Which plan will benefit the doctor’s patients more and why? 8. Broomsticks are manufactured by two firms which constitute a competitive in- dustry. Neither firm has any fixed costs. There are two consumers, W.W.West and W.W.East. The following charts show the marginal cost of producing var- ious quantities of broomsticks at each firm, and the marginal value of various quantities to each customer: Total Cost Total Value Quantity Firm A Firm B W.W.West W.W.East 1 $2 $10 $10 $37 2 3 19 7 5 3 4 26 6 4 4 5 32 2 1 a) What quantity of broomsticks are sold and at what price? How many are 10–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. built by Firm A and how many by Firm B? How many are bought by W.W.West and how many are bought by W.W.East? b) How much producers’ surplus is gained in this market? How much con- sumers’ surplus? How much social gain? Your answers to all three ques- tions should be numbers. c) Suppose now that Firms A and B band together and form a single (non- competitive) firm, and that this merger has no effect on the industry-wide marginal cost curve. Now how many broomsticks are sold and at what price? d) What is the size of the deadweight loss due to the formation of the monopoly? Your answer to this question should be a number . 9. True or False: If the customers of a monopolist could get together and bribe him to act like a competitor, then they could make both themselves and him better off. 10. Elmer is a monopolist in the carrot industry. His customers have formed an organization that proposes to rent the carrot patch from Elmer and operate it for the mutual good of the customers. Use a graph to illustrate the market for carrots. On your graph, show the lowest rental fee that Elmer will accept and the highest rental fee customers are willing to pay. Does the deal get struck? 11. Widgets are produced by a competitive industry and sold for $5 apiece. Each widget firm must have a license. The government sets the highest license fee that widget firms are willing to pay. If the widget industry were monopolized, widgets would sell for $8 apiece. The government is considering imposing an excise tax that would cause the price of widgets to rise to $8. Use a graph to illustrate the following: a) The size of the excise tax (i.e. the tax per widget). b) The government revenue from the excise tax. c) The amount by which license fees will have to change if the tax is imposed. d) The net gain to the government from imposing the excise tax (accounting for both the excise tax revenue and the license fees). Now answer the following: e) Does the excise tax lead to a net gain or a net loss in government revenue? f) Suppose that in addition to licensing sellers, the government also licenses buyers: Only licensed widget buyers can buy widgets, and the govern- ment charges the highest annual license fee buyers will pay. (You can assume buyers are all identical.) Under this new policy, does the excise tax increase or decrease government revenue? 12. True or False: A monopolist with a U-shaped marginal cost curve might choose to operate on the downward sloping portion of that curve. 10–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 13. The domestic hatpin industry is monopolized. The diagram below shows the U.S. demand curve for hatpins and the monopolist’s marginal cost curve. There is also a world market for hatpins, where the going price is $9. PRICE MC A B C D E 12 F G H I 9 J L M N O 4 K R T S P Q 2 D QUANTITY MR a) Suppose all Americans are free to buy and sell hatpins in the foreign market. What is the deadweight loss from the existence of the domestic monopoly? b) Suppose it is illegal for Americans to buy or sell hatpins in the foreign market. What is the deadweight loss from the existence of the domestic monopoly? c) Suppose it is illegal for Americans to sell hatpins to foreigners, but legal for Americans to buy hatpins from foreigners. What is the deadweight loss due to the domestic monopoly? d) Suppose it is illegal for Americans to buyhatpins from foreigners, but legal for Americans to sell hatpins to foreigners. What is the deadweight loss due to the domestic monopoly? e) Suppose the demand, marginal revenue and marginal cost curves are as in the picture above, but the world price is $1 instead of $9. Redraw the picture accordingly and answer questions a) through d) again. f) Suppose the demand, marginal revenue and marginal cost curves are as in the picture above, but the world price is $3 instead of $9. Redraw the picture accordingly and answer questions a) through d) again. g) Suppose the demand, marginal revenue and marginal cost curves are as in the picture above, but the world price is $12 instead of $9. Redraw the picture accordingly and answer questions a) through d) again. 14. In the town of Nwot there are many dentists but just one eye doctor. Are senior citizens more likely to be offered discount prices for dental exams or for eye exams? Justify your answer. 15. True or False: A monopolist is best off operating on the inelastic portion of the demand curve, where he can charge high prices without losing many customers. 16. Comment on the following reasoning: “The oil companies collude with each other to charge a monopoly price for gasoline. They are able to do this because gasoline is a virtual necessity for which demand is highly inelastic.”* * The delightful observation that economic theory reveals a contradiction between the two halves of this common argument is made in Browning and Browning’s textbook. 10–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 17. True or False: Because a monopolist is able to charge a higher price than competitors could, his marginal revenue is higher than what a competitor’s would be. 18. True or False: The calculation of deadweight loss due to monopoly may be overly optimistic, because it does not account for costs of misallocation a la Hayek. 19. True or False: The calculation of deadweight loss due to monopoly may be overly optimistic, because it does not account for resources spent in attempts to maintain the monopolist’s market position. 20. True or False: Devices like “50 cents off” coupons are used only under com- petition, since a monopolist can always require his customers to pay full price. 21. Copy centers usually give substantial discounts to customers with large orders. Do you think they are price discriminating? Why or why not? 22. True or False: If General Motors could require all GM car owners to buy all of their replacement parts directly from GM, it would charge monopoly prices for those replacement parts. 23. Consider a monopolist who produces his product in two different plants, each with its own marginal cost curve. Describe how he determines the quantity to produce at each plant and the price to charge for it. 24. Under what circumstances might the monopoly owner of a camera store want to offer discounts to his own employees? 25. (Note to instructor: This is a good problem to assign immediately after students have worked problem 25 in the textbook.) Snidely Whiplash owns all the houses in the Yukon Territory, where he charges the highest rent the citizens (who are all identical) are willing to pay. Snidely also owns all the grocery stores in town, where he sells groceries at a competitive price. True or False: If Snidely cuts the price of groceries below the competitive level (and provides all the groceries consumers demand at that price) he can raise the price of housing and come out ahead. 10–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 26. (Note to instructor: This is another good problem to assign immediately after students have worked problem 25 in the textbook.) In the Yukon Territory, both the housing market and the grocery market are competitive. The market for housing is shown on the left, where you can see that there are currently ten families in town. All ten families have the same demand for groceries. The graph on the right shows the grocery market (so that the demand curve is the sum of the ten families’ demand curves). Marginal cost is flat at the price PC , which is therefore the price residents pay for their groceries. Price ($/apartment) S Price 10 9 8 7 10 10 6 5 10 4 30 20 3 2 PC MC 1 D D 2 4 6 8 10 12 14 16 18 20 Quantity of Quantity of groceries apartments MR Snidely Whiplash has just purchased all the grocery stores in the Yukon Ter- ritory and plans to start charging a monopoly price. a) How many families will leave town? b) After they leave, how much producer surplus will Snidely earn? 27. The Little Red Violin School offers music lessons to children. Each student must buy a violin from the school and then pay for lessons. Many of the children continue their lessons for years; many others drop out after a few weeks. Should the Little Red Violin School charge a high or a low price for the violins? Should it charge a high or a low price for lessons? Why? 28. There are three stores at Eastview Mall. Each store has some monopoly power. Eastview charges customers an admission fee to the mall, and charges rent to the stores. All customers are identical. a) Illustrate how Eastview determines the admission fee to the mall. b) Suppose Eastview requires all stores in the mall to set competitive prices. How will this affect the admission fee to the mall? How will it affect the rent the stores are willing to pay? c) If Eastview wants to maximize profits, is it a good idea to require stores to set competitive prices? 29. The Westview Mall rents space to clothing stores and charges shoppers an entry fee to get into the mall. All clothing stores are identical and all shoppers are identical. Answer the following questions, using a graph that shows the supply and demand for clothing: a) If the mall rents space to several competitive clothing stores, how much can it collect it rent? How much can it collect in entry fees? How much can it collect altogether? b) If the mall rents space to a single monopoly clothing store, how much can it collect in rent? How much can it collect in entry fees? How much can 10–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. it collect altogether? c) Would you advise the Mall owner to rent to several competitive stores or to one monopoly? Why? 30. Widgets are sold competitively. One day, a monopolist takes over the entire widget industry and starts charging a monopoly price. However, widget con- sumers are required by law to continue buying the same number of widgets they bought under competition. Illustrate the new consumer surplus, the new producer surplus, and the deadweight loss. 31. Suppose the University of Rochester has 1000 identical students. One day, the University suddenly makes two simultaneous announcements: a) We’re raising prices in the dining halls by enough to increase the dining halls’ profits by $100,000 (that is, $100 per student) per year. b) We’re cutting tuition by $100 per student per year. Should students applaud or oppose this pair of policies? 32. A monopoly movie theater has two customers—Gene, who never buys popcorn but is willing to pay $(A+B+C+E+F+G) to see the movie, and Roger, who is willing to pay nothing at all to see the movie but just comes to buy popcorn. The accompanying graph shows Roger’s demand curve for popcorn and the marginal cost of providing that popcorn. Price MC A 60 D B C 50 E F G H 40 D Quantity Suppose you’re deciding whether to charge 40 cents a bag or 50 cents a bag for the popcorn (you’ve already ruled out all other options). Which four areas on the graph would you want to measure in order to make this decision? (You can assume that you always want to keep both customers.) 10–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 10 1. a) Fixed cost, no change. b) MC falls, price falls. c) Demand falls, MR falls, price falls. d) Demand falls, MR falls, price falls. e) Sunk cost, no effect. f) This is a rise in fixed costs if Gus has to choose between working at the factory and driving a cab; in this case he’ll either quit to work at the factory or nothing will change. It’s a rise in variable costs if Gus can moonlight; in this case, MC up, price up. g) Not relevant. h) Not relevant. i) Not relevant. j) Demand falls, MR falls, price falls. k) Not relevant. l) Rise in MC, price rises (or Gus quits). m)Either a rise in fixed costs (no effect) or Gus quits rather than pay. 2. False, because of the phrase “unlike competitors”. Anybody can charge any price he wants to for anything. However, there is only one profit-maximizing price to charge, and it is foolish to deviate from this price, whether you are a monopolist, a competitor, or anything in between. 3. Price PS rises by the area marked $10 MC MC' minus the area marked $9 D Quantity MR 4. It drops vertically a distance $1. 5. Refer to Exhbit 10-2 in the text. Customers will offer up to C + D + E and the monopolist will accept anything over C + D − H. Since C + D + E > C + D − H, a deal will be struck. Thus true. 6. From problem 4, we know that a $1 sale tax causes the M R curve to drop $1. We also know that an excise tax causes the M C curve to rise $1. Therefore the two taxes yield the same quantities, the same price to demanders (read off the old demand curve) and the same price to the monopolist. 7. False; it is more detrimental, since the monopolist produces less to begin with, so that the gap between marginal cost and marginal value of the last unit produced is greater for a monopolist than for a competitor. 10–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8. True, or at least often true. Suppose that the amount of land in existence is Q0 . The marginal cost curve lies along the horizontal axis between 0 and Q0 and becomes vertical at Q0 . In the left-hand panel below, a monopolist supplies the full quantity Q0 to the marketplace. However, in the right-hand panel, he supplies the smaller quantity Q1 , causing deadweight loss. P P D D MR Q Q Q0 Q1 Q0 MR 9. In the diagram below, Consumer surplus falls from A+B +C +D+E to A+B −F . Producer surplus increases from G + H + J to G + H + J + C + D + E + F . There is no change in social gain. MC A B F C D E H J G D MR 10–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 10. Price A B An excise tax of $ T improves the MC welfare of Americans: { T I C F D G H E PS Tax Revenue No excise tax F+G+H+I Excise tax of $ T I C +D+F+G (We know from the text that D C +D+F+G+I, which is the PS that MR would be earned by a monopolist, Quantity is greater than F+G+H+I.) 11. Keeping in mind that the demand curve is the marginal value curve, we can compute the entries in the following table (“Price” means the price corresponding to the given quantity on the demand curve.) Quantity Price TR MR TC MC 1 $10 $10 $10 $2 2 $9 $18 $8 $4 $2 3 $7 $21 $3 $5 $3 4 $6 $24 $3 $11 $4 5 $5 $25 $1 $15 $4 6 $4 $24 $(-1) $19 $4 7 $2 $14 $(-10) $24 $5 8 $1 $8 $(-6) $29 $5 A competitive industry produces at the intersection of the supply (marginal cost) and demand curves, at a quantity of 6 and a price of $4. A monopolist produces only as long as marginal revenue exceeds marginal cost, which is to say that he produces 3 items and sells them at $7. The deadweight loss under monopoly arises from the monopolist’s failure to produce items 4, 5 and 6 on which the excess of marginal value over marginal cost is $2, $1 and $0 respectively, so the deadweight loss comes to $2 + $1 + $0 = $3. (Alternative calculation: Under competition, social gain is T V − T C = $41 − $19 = $22, wherease under monopoly, social gain is T V − T C = $26 − $7 = $19; the $3 difference is the deadweight loss.) 12. You need to know which is bigger: A + B + C + D + F + G + I + J (the gain under monopoly) or A + B + C + D + E + F + G + H (the gain under competition). Equivalently, you need to know which is bigger: I + J or E + H. So measure areas I, J, E and H. 10–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 13. True. No price control can make a natural monopolist behave like a competitor. In the diagram below, any price ceiling below P will drive the monopolist out of business altogether, since at any lower price he is unable to cover the average cost of production. When the price is P, the monopolist produces quantity Q, which is more than the ordinary monopoly quantity but still less than the competitive quantity. Only through a subsidy can the monopolist be induced to produce more than Q. Price MC AC P D MR Quantity Q 14. False; the exact opposite is true. The two panels of Exhibit 10–5 in the textbook show quantities produced under zero-profit regulation (QZ ) as compared with the optimal quantities QC . In Panel B, the natural monopolist produces less than is optimal, while in Panel A, the non- natural monopolist produces more than is optimal. There is no other way to draw the pictures, given that MC crosses AC at AC’s minimum and that AC is downward sloping when it crosses demand for a natural monopolist; upward sloping otherwise. 15. True, if regulation takes the form of a restriction on profit, or on the excess of price over average cost. Since discrimination is costly (by definition, it requires not always hiring the best person for the job), an unregulated profit-maximizing firm has an incentive to avoid it. However, a firm which is able, but not permitted, to earn high profits can choose to discriminate without losing anything. 16. Total sweaters = 7; total men’s sweaters = 4; price of men’s sweater = $7; total women’s sweaters = 3; price of women’s sweater = $12. 17. False; under heavy competition there is no price discrimination. 18. To observe that this is price discrimination is a good partial answer. A complete answer requires explaining why families with children have a higher elasticity of demand for hotel rooms than other travelers. One answer might be that families with children are far less likely to be on business trips than other travelers, and hence more apt to change their travel plans if they find the hotels are too expensive. Another is that families traveling with children tend to have more expenses (because they have children) and/or to be less well off (because they can’t afford to leave the children home with a sitter), and are consequently more sensitive to price than other travelers. 10–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 19. This appears to be price discrimination in favor of U.S. tourists. To support this view, one would need to explain why U.S. tourists have a higher elasticity of demand for meals at certain restaurants than the natives do. But it seems that this is the exact opposite of the truth: tourists, if they are to eat at all, must eat in restaurants, whereas natives have the option of eating at home. Also, natives are more likely than tourists to know of other, more out-of-the-way restaurants. Perhaps, then, we should look for an explanation that does not involve price discrimination. This means looking for ways in which meals served to Americans are not the same goods (from the restaurants’ viewpoint) as meals served to Cana- dians. One possibility (and this is just a guess) is that Americans are better tippers, so that they actually pay more (inclusive of tip) for their meals than Canadians do. Of course, this keeps the staff happy and enables the management to pay lower wages. Thus, it is effectively less expensive to serve Americans than it is Canadians. We repeat that this explanation is a guess. If you have a better one, please send it to the author in care of Cengage. 20. To support a diagnosis of price discrimination, we must ask why riders with traveling companions have a more elastic demand for cab rides than riders who are alone. Walter Oi suggests that it is because three riders who know each other can decide to rent a car and split the cost three ways, whereas riders who are alone must pay the entire cost of a rental car. In the same spirit, it seems reasonable that people traveling in groups of three are more willing to get on buses and subways, which take longer than cabs, since they have friends to pass the time with and can protect each other from getting lost. 21. a) The $5 fee is offered to those customers who are not as excited about visiting there and don’t value the experience highly. Those people who are especially interested are those who want to take pictures to enjoy in the future, so they are probably willing to pay more to enter the community. This pricing schedule is to lure the elastic demanders (non camera users) into the market. b) It may be more costly to admit camera users as the “photographers” may impose on the inhabitants of the community by being distractive and noisy. The extra five dollars compensates the Indians for the added irritation. Or perhaps people with cameras create competition for postcards manufactured by the Indians themselves. c) This is left for the reader to decide. Some additional information may include discussions with the inhabitants to whether the cameras disturb their lifestyle. 22. This seems to be an example of a two part tariff. The marginal cost of providing a subscriber with an additional cable channel is zero. Thus subscribers are charged zero per channel, but also pay an entry fee. If all subscribers are identical, the entry fee is equal to the total value of all the channels. Typically, “premium” channels such as HBO and Cinemax are priced sepa- rately. Why do you suppose this is? 23. False; in terms of Exhibit 10-11, Fredonians lose C + D + E in consumer surplus and get back only C + D − H in payments from the electric company. 24. True that consumers would be better off (the admission fee allows Wegman’s to capture all their surplus, so they’re surely better off without it); false that social gain would increase (Wegman’s would now charge a monopoly price, causing a deadweight loss). 10–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 25. The market for groceries can be represented by Exhibit 10-11 in the text. When he raises the price of groceries, Snidely will have to cut the rent on houses by C+D+E. Because his consumer surplus at the grocery store rises by only C + D − H, this is not a good idea for Snidely. 26. Price A B a) F+G+H MC b)C +D+F+G D c) tuition receipts fall by C +D+E C E d) going with the monopolist means G H collecting an additional C +D-H in F rent but losing C +D+E in tuition. The loss exceeds the gain so going with the monopolist is a bad idea. MR D Quantity 27. a) Without an admission charge, the bookstore sets a monopoly price and earns C + D + F + G. If it can charge admission, the bookstore sets a competitive price and earns a total surplus (on book sales plus admission charges) of A + B + C + D + E + F + G + H. Therefore the bookstore will pay up to A + B + E + H for the right to charge admission. b) Students will lose their entire surplus of A + B, so tuition must be cut by this amount. c) The university is surely willing to sacrifice A + B in tuition in order to receive a payment of A + B + E + H, so yes, the bookstore will get permission. 28. Price MC a) Department store merchandise is priced competitively at P. The monopoly parking lot owner charges the maximum A B consumers will pay for a space, which is A+B+ C+D+E. P' b) The monopoly department store charges P'. The C D competitive parking lots charge marginal cost, which is E P zero. G H c) Consumers are better off with a monopoly store and F competitive parking lots, which leaves them a surplus of A+B (as opposed to zero in the opposite situation). Store owners getC+D+F+G, for a social gain of A+B+ C+D+F+G. In the opposite situation, store owners get F+G+H and the parking monopolist gets A+B+ C+D+E for D a higher social gain. Quantity (Dept store merchandise) MR 10–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 29. a) In the diagram below, the owner initially collects D+E +F in rent. After imposing the tax, he collects B + D in tax revenue and F in rent. Thus the question is: Can B + D + F be bigger than D + E + F ? We know the answer to this question is yes, because B + D + F would be the monopoly producer surplus if the dashed curve happened to be the industry MR curve. MC A B C E D F D b) Now the owner collects the full social gain, so the tax can’t be a good idea. 30. Part a) is true, part b) is false. If Hughes attempts to prevent competitors from resharpening, it is presumably charging over $100 per resharpening and so must have a diverse base of customers. 31. a) You charge the monopoly price of $12 and earn C + D per customer. b) The price per bag is set equal to the value of that bag to the customer, which is A + B + C + D + F . You earn A + B + C + D per customer. c) The price per bag is equal to the value of the second bag, or E + G + H. You earn E per bag, or 2E per customer. d) You charge A + B + C + D + E + F + G + H per bag and earn A + B + C + D + E per customer. f) The strategy in part d) maximizes your profit. Notice that E < C + D, so 2E < C + D + E < A + B + C + D + E, which is why strategy d) beats strategy c). 32. Strategy 1: Charge 50 cents a bag for popcorn and charge A + B + C to enter the theater. Thelma won’t come, and you’ll earn A + B + C from Louise. Strategy 2: Charge 50 cents a bag for popcorn and charge A to enter the theater. They both come and you earn 2A. Strategy 3: Charge 40 cents a bag for popcorn and charge A + B + C to enter the theater. They both come, but you lose B + C + D at the popcorn stand, so your total gain is 2(A + B + C) − (B + C + D) = 2A + B + C − D. Strategy 3 is best if and only if 2A+B+C−D > A+B+C and 2A+B+C−D > 2A; that is A > D and B + C > D. So you need to measure areas A, D, and B + C. 10–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 33. Strategy 1: Charge $60. Maximal admission fee is $300 (otherwise Eve balks). You earn $400 profit selling 40 widgets to Adam, $300 profit selling 30 widgets to Eve, and $600 in admission fees. Total gain: $1300. Strategy 2: Charge $50. Admission fee is $675. Profit from selling widgets is zero. Total gain: $1350. Strategy 3: Charge $40. Admission fee is $1200. Loss from selling 60 widgets to Adam and 60 to Eve is $1200. Total gain: $1200. Conclusion: Charge $50. 34. a) If you want both Gene and Roger to see the movie, you must charge $4 for admission; in that case you can charge 60 cents for popcorn and earn $2 in producer surplus from Roger at the popcorn stand. Your total is $4 + $4 + $2 = $10. But a better solution is to charge 50 cents for popcorn and $18 for admission. Then only Roger will attend, but you earn $18. b) If you are willing to drive Gene away, you can charge Roger $18 for admission and sell popcorn for 50 cents. Your gain is $18. But a better solution is to charge $9 for admission and 60 cents for popcorn. Then you earn $2 producers’ surplus at the popcorn stand for a total of $9 + $9 + $2 = $20. c) If you are willing to drive Roger away, you can charge Gene $25. But a better solution is to charge $23 admission and sell popcorn for 40 cents. You lose $6 at the popcorn stand, so your total gain is $23 + $23 − $6 = $40. 10–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1. For the quantity Q, the demand price is given by P = (a − Q)/b. Thus total revenue is given by Q · P = (aQ − Q2 )/b. Now marginal revenue is aQ − Q2 a(Q − 1) − (Q − 1)2 a − 2Q + 1 − = b b b a − 2Q ≈ b when 1 unit is small. N2.a) From the answer to N1, we see that marginal revenue in markets A and B is given by 100 − 2QA QA M RA = = 10 − 10 5 8 − 2QB M RB = = 4 − QB . 2 For any given positive Q, we have Q 10 − >4−Q 5 so that M RA (Q) > M RB (Q), which implies that elasticity is greater in market A than in market B. b) The monopolist sets M RA (QA ) = M RB (QB ) = 0. In view of the formulas for marginal revenue in N2a), this gives QA = 50, QB = 4. Getting price from the demand curves, we find that PA = 5, PB = 2. c) We must solve the equations QA QA + QB 10 − = = 4 − QB . 5 21 The solution is QA = 40, QB = 2. The prices are given by PA = 6, PB = 3. d) While it is true that for any given quantity, demand is more elastic in market A, it is also true that demand in market A at the quantity 40 is less elastic than the demand in market B at the quantity 2 . Thus in part c), the higher price is found in market A. The explanation of part b) is more subtle. Here the elasticity in each market is equal to 1 at the quantity being sold. Since the elasticities in both markets are equal, you might expect the prices in both markets to be equal. Indeed, this expectation is correct for any elasticity other than 1. However, for elasticity 1, the argument on pages 351–352 of the text breaks down (can you see why?) and leaves us with the possibility of different prices in the two markets. 10–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. e) If we equate the marginal cost of QA + QB with the marginal revenues of QA in market A and QB in market B, using the formulas for marginal revenue from part a), we write QA QA + QB 10 − = = 4 − QB 5 3 which gives QA = 20, QB = −2! Obviously, this makes no sense, so let us reconsider the situation. The picture is as shown below (this is the analogue of Exhibit 10–10): P 10 MC 25/4 MR 4 MRB MR A Q 4 75/4 50 54 (The scales on the axes have been distorted so that everything fits.) Now we see the problem: At the price where MC crosses MR, there is no corresponding quantity on the M RB curve. The monopolist produces 75/4 units and sells them all in market A at a price of 65/8. N3.a) If either were less than 1, the monopolist could simultaneously increase revenue and decrease cost by decreasing his quantity. b) Since 1 1 30 1 − = 10 1 − , |ηA | |ηC | 3|ηC | we have |ηA | = . 2|ηC | + 1 3 c) . 2 10–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Eleven: Market Power, Collusion and Oligopoly What’s New In This Edition I’ve replaced some aging examples with new ones featuring more recent an- titrust actions, including Apple v. Amazon. Teaching Suggestions 1) It is worth pointing out that concentration is not the same as oligopoly, and the relationship between them is at least controversial. 2) One way in which a firm can attempt to develop a degree of market power is through a reputation for the quality of its products and services. There are several points in this chapter where it is natural to introduce this topic. The discussion of the repeated prisoner’s dilemma suggests that firms would never gain from costly attempts to maintain such a reputation. Suppose that I operate a firm for my entire lifetime, which is three years. In any given year I can produce either a low-quality product, or, at greater expense to myself, a high-quality product. Consumers do not discover the quality of the product until after they have owned it for a year. Then it seems plausible that I would produce high-quality products in year 1 in order to develop a reputation that increases the demand for my products in year 2. But this is not the case. In year 3, I have no incentive to produce high-quality products (since it is my last year in business). Because everyone knows this, nothing I do in year 2 can help my reputation. Thus I have no incentive to produce high- quality products in year 2. Because everybody knows this, nothing I do in year 1 can help my reputation. Thus I might as well produce low quality products in year 1. On the other hand, firms clearly do produce products that are of higher quality than consumers are able to verify at the time of purchase. You might point this out to your students and ask in what important way the real world fails to fit the assumptions of our model. (Two candidates for the culprit: uncertain lifetimes and continuous time.) Perhaps firms need infinite lifetimes to avoid the paradox, which explains why stores like Sears are set up to outlive their founders. The topic arises again in the discussion of monopolistic competition. The text contains a few inadequate words about the welfare consequences of imperfect competition and mentions the social loss arising from advertising that just moves customers from one firm to another. Counterbalancing this is the possibility that advertising, and the use of brand names, is a device for disseminating information about reputation, and thus provides firms with an incentive to produce high-quality items. 3) The chapter offers some examples of creative responses to regulation, and the ensuing unexpected consequences. I have been told of a wonderful example, whose historical accuracy I have not been able to verify. In renaissance Europe, regulations forbade unlicensed actors to speak on stage. The result was the advent of modern pantomime. 4) Examples of unexpected consequences tend to make students perk up. Some other striking ones: Certain pesticides are banned because of potential health haz- ards. This raises the cost of growing fruits and vegetables, increases their price, and lowers the quantity demanded. The fall in fruit and vegetable consumption can be more damaging to health than the pesticides were. (This example is suggested 11–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. by the biologist Bruce Ames.) 5) Another unexpected consequence: Airlines must now require infants to have their own seats, since this is safer than allowing them to sit on parent’s laps. But it also greatly increases the cost of air travel for families (who must pay for the additional seats), and consequently many travel by car instead of by air. Since car travel is much more hazardous than air travel, the safety regulations lead to an increase in infant deaths. (See the January/February 1991 issue of The Margin for data supporting this scenario.) 6) If you want to stir things up, you can suggest another possible unexpected consequence, though this one is entirely speculative (i.e., aside from anecdotes, I know of no evidence on the magnitude of this effect). Legislation that forbids discrimination in hiring increases the cost of hiring even for non-discriminators, since they may be forced to defend against a lawsuit without merit. One result is that employers choose to hire fewer people, the equilibrium wage falls, and even the groups that are discriminated against can be made worse off. 11–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. The following passage by Professor William Shepherd of the University of Michigan appeared in the Antitrust Bulletin in the Spring of 1986. Analyze it critically, with particular attention to the appropriateness of the analogy from sports. The need is to provide a reasonable degree of competitive parity, so that effective competition can occur among comparable rivals. The imbalance between dominant and small firms usually applies only “soft” or ineffective competition to the dominant firm, while putting the small firms under severe pressure or threats. This problem can be seen clearly with an analogy from sports. Consider football “competition” between a large university and a small college. The university could finance a 100- player squad, with platoons and specialists at all positions, while the small college might manage to assemble just 30 players, most of whom would have to play both offense and defense. Such a gross imbalance would prevent the game from involving any meaningful competition. The university team would have an easy time, while the small college team would merely be punished. Severe mismatches like this are usually carefully prevented, by sepa- rating athletes and teams by their sizes, ages, sex, professional–amateur status, and so forth. Heavyweight boxers are not permitted to fight fly- weights, etc. Even within equalized subgroups, a variety of rules and limits must usually be applied, in order to protect competitive parity. Indeed, in all competition (sporting and other), the need to equalize the weapons and chances is regarded as crucial. 2. Suppose that the industry supply curve for gizmos is a straight line through the origin, and that the demand curve is a straight line whose slope has the same absolute value as the supply curve. If all of the gizmo manufacturers could merge into a single firm, they could produce at zero marginal cost. By the efficiency criterion, should they be allowed to merge? 3. At a recent party where there were several simultaneous conversations, every- body ended up shouting to be heard over everybody else. But they could all have been heard better (and saved wear and tear on their vocal cords) if they had all spoken more quietly. True or False: Therefore, all of the shouting was irrational. (The above makes a good problem for Chapter 12, where students are thinking about ill-defined property rights, or for the present chapter, where students are thinking about the unenforceability of cartels.) 4. Suppose that in a certain industry there are exactly two identical firms, with linear upward sloping marginal cost curves. If these firms act as Cournot oligopolists, will industry output be more or less than 2/3 of the output under competition? How do you know? 5. Consider an industry in which there are exactly two firms with identical flat marginal cost curves. Price and output in the industry are determined as follows: first firm 1 announces how much it will produce; then firm 2 decides how much to produce; then production takes place and all output is sold at a price read off the demand curve. 11–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. a) Will the industry output be greater or less than it would be under Cournot behavior? b) Which firm is better off: firm 1 or firm 2? 6. True or False: In the long run, a monopolistic competitor will operate at the lowest possible average cost. 7. Many bars have afternoon “Happy Hours” where drinks are sold at a reduced price. True or False: Because bar owners voluntarily engage in this prac- tice, we may infer that a law banning Happy Hours would make bar owners unhappy. 11–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 11 1. Yes. The merger will not change the price or quantity of output and thus will not change consumer surplus, but it will lower costs so producer surplus will be higher. 2. Conceivably a vertical merger could be used to prevent resales. Suppose that a monopoly steel manufacturer wants to sell cheaply to auto makers and expensively to construction firms. The steel firm worries that auto makers can buy cheaply and resell to construction firms. But if the steel firm acquires an auto maker as a subsidiary, it can sell cheaply to the auto maker while ordering it not to engage in resales. 3. This appears to form of resale price maintenance but there is no apparent mo- tivation as retail stores don’t usually compete in the candy market by providing expertise on the product. Therefore, we don’t know the answer! 4. It would increase. It would decrease. 5. Salesmen provide services to their customers in the form of education about the product, assistance when something goes wrong, and so forth. Customers value these services and are willing to pay for them, but will of course prefer to get them for free. With more than one salesman in the territory, customers can get services from one salesman and patronize another. This removes the incentive for any salesman to offer services, which significantly lowers the value of the product. Thus salesman are granted exclusive territories, so that those customers they make happy are certain to buy from them. This theory predicts that exclusive territories will be found in markets for products where salesmen offer a significant amount of service before the product is purchased. 6. Price MC2 MC1 A D B D2 C D1 Q1 Q Quantity PM Since only a few customers value the additional services, the demand curve may not shift a constant distance right at every price, but may twist somewhat as in the above graph. In this case, social welfare can decrease. Before the price maintenance at PM , consumer plus producer surplus is A + B + C. After imposing PM , the marginal cost curve shifts to M C2 and demand moves to D2 (with the addition of extra services). Now QP M is produced, and consumer plus producer surplus is A + B + D, perhaps less than before. 11–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7. a) Price A P M B C Pc D Quantity Consumers’ surplus = A; Producers’ surplus = B; deadweight loss=C. b) The marginal cost curve will rise to PM as firms incur cost to produce more extras. If anything less is produced in the way of extras, then the airline could compete and attract additional customers. The airlines will compete all economic profits away. c) Price X A P M B C Pc D D' Quantity Demand shifts upward as the services have extra value to customers. New consumers’ surplus = A + X; new producers’ surplus=0. d) Services whose marginal value exceeds their marginal cost would have been offered under competition. Therefore X < B and the regulation reduces net social gain. 11–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8. False. The opposite is true. The value of dealer services must exceed the cost of producing them at the margin or the wholesaler would lower the maintained price. If the marginal value of dealer services falls off rapidly, Exhibit 11–4 would be replaced by the following exhibit, in which the gain from retail price maintenance (B 0 − C) is greater than in 11–4. (Here the marginal value of dealer services at the quantity provided is P1 − P2 .) Price B' A P MC' 1 C P MC 0 P2 D' D Quantity 9. One frequently cited alternative theory is that the manufacturer is acting as an enforcer for a cartel among the dealers. Under what circumstances do you find this theory either more or less plausible than the theory that is elaborated in the textbook? 10. One possibility: When a new product is introduced, the manufacturer might want to keep sales volume up even at the expense of profits, in order to gain visibility for the product. Retailers won’t share this incentive, since the profits they sacrifice now are compensated for by future sales that go mostly not to themselves but to other retailers. 11. False. Even if all firms would benefit, a cartel is unlikely to be enforceable. 12. False, because of the Prisoner’s Dilemma. Each worker can rationally calculate that his own voluntary contribution is unlikely to be critical in determining the success of the union, and therefore chooses not to join. It is important to notice that workers will elect not to join regardless of whether or not they believe that others are joining. It is possible that all workers could benefit from an outside enforcer who requires them to unionize. 13. False. Under perfect competition every firm charges the same price. 14. Though the new firm faces a reduced marginal cost curve, it won’t exercise any monopoly power because new firms could enter and charge the lower competitive price and attract all of the customers. Therefore, price will equal marginal cost and no firms will enter. The threat of new firms entering is enough to force the merged firm to price competitively, where the new marginal cost curve intersects the demand curve. 15. The industry output is equal to N/(N + 1) times the output of a competitive industry. When N is large, the Cournot industry’s output and the competitive industry’s output are approximately equal. 11–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 16. Refer to Exhibit 11–9 in the text. Suppose that firm A believes that the other N −1 firms together produce quantity QB . Then firm A’s marginal revenue curve is M RA and it produces the monopoly quantity QA = (1/2) · (QC − QB ). Since all firms are identical, each produces the same quantity; thus we have QB = (N − 1) · QA . Combining the two equations gives 1 QA = · QC N +1 so that industry-wide output is N n · QA = · QC . N +1 As the number of firms gets large, this quickly approaches the competitive quantity QC . 17. There is no equilibrium with three vendors. The leftmost vendor will always want to move right until he shares his spot with another vendor. Likewise for the rightmost vendor. Thus in equilibrium, all three vendors would have to occupy the same location, and each would get 1/3 of the market. But by moving slightly away from that location, either vendor could secure more than 1/3 of the market for himself (because the distance from that location to one of the two endpoints must exceed 1/3). Therefore there’s no equilibrium. 18. With four vendors, there’s an equilibrium in which two vendors occupy the location 1/4 of the way from the left endpoint and the other two occupy the location 1/4 of the way from the right endpoint. Everyone gets 1/4 of the market, and nobody can do better by moving. With five vendors, there is an equilibrium with two at the 1/6 mark, one in the middle, and two at the 5/6 mark. 19. a) Any location at all is an equilibrium. Regardless of how the vendors are located, anyone who moves will lose as many customers on one side as he gains on the other. b) They can’t be all on one semicircle. If, for example, B were located between A and C within a semicircle as shown, then B could do better by leaping to any point on the opposite semicircle. However, as long as they are not on the same semicircle, any distribution is an equilibrium. (Try proving this! All you need to show is that if B moves to any other point on the chord AC, he fails to improve his situation, and if he moves to any point on the other side of the chord AC, he also fails to improve his situation. Thus B has no incentive to move, and by the same argument neither does A or C.) 11–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1.a) 50 − Psteel /2. b) Qsteel = 50 − Psteel /2. c) Quantity of steel = 25 tons. Price of steel = $50 per ton. Quantity of cars = 25. Price of cars = $75 per car. d) Quantity of cars = 50. Price of cars = $50 per car. N2.a) A browser and an operating system sell for $33.33 each; the price of the package is $66.66. b) An operating system sells for $50 and a browser sells for $25; the price of the packate is $75. c) The price of the package is $50. N3.a) Dr. Miles sells 50 bottles of medicine at $25 per bottle. Consumers’ surplus is $625. Producer’s surplus is $1250. b) To get the optimal quantity, maximize benefits minus costs. That is, maximize 5 · C − C 2 − C, to get C = 2. The optimal amount of service costs retailers $2 per bottle to provide, and is worth $(5 · 2 − 22 ) = $6 per bottle to consumers. c) If C is less than P1 − P0 , retailers make a positive profit on each bottle, so it is worth increasing C to lure competitors’ customers away. Thus C rises to P1 − P0 . The socially optimal value for C, by part b), is $2 per bottle. d) At a wholesale price of P0 dollars per bottle, the retail price will be P0 + C dollars per bottle. However, consumers, who receive $V worth of services, feel as though they are paying P0 + C − V = P0 − 4 · C + C 2 dollars per bottle. At this price they purchase Q = 100 − 2 · (P0 − 4 · C + C 2 ) bottles. Thus demand is given by Q = 100 + 8 · C − 2 · C 2 − 2 · P0 . In order to maximize Q for any given P0 , Dr. Miles sets C = $2 per bottle. That is, he requires retailers to sell for $2 per bottle over wholesale. e) The demand curve facing Dr. Miles is now Q = 108 − 2 · P0 . To maximize profit, Dr. Miles sells 54 bottles to retailers at a wholesale price of $27 per bottle. These 54 bottles sell on the retail market at $29 apiece. The retail demand curve is Q = 112 − 2 · P1 . The area under this demand curve, down to a price of $29 and out to a quantity of 54 is the new consumers’ surplus. That is, consumers’ surplus is $729. Producer’s surplus is $1458. Notice that there is a net gain in social surplus of $312. (That is, ($729- $625)+($1458-$1250).) Where does this come from? First, on each of the 54 bottles sold there are dealer services with a value of $6 per bottle. These services are produced at a cost of $2 per bottle, for a net social gain of $4 per bottle, or $216 altogether. Second, the number of bottles sold has increased from 50 to 54, and the total value of those bottles to consumers is $96. Since they are produced at zero marginal cost, this $96 is pure social gain. These two gains add up to give the increase in social surplus: $216 + $96 = $312. 11–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. N4.a) Profit = P (100 − P ) is maximized at P = 50, so this is what he charges. b) The two monopolists charge price P1 and P2 . The cost to consumers of crossing the bridge is P = P1 + P2 . So Q = 100 − P = 100 − P1 − P2 travelers cross the bridge. The first monopolist earns P1 Q = P1 (100 − P1 − P2 ) Maximizing with respect to P1 (and treating P2 as a constant, we find that the maximum occurs at 100 − P2 P1 = 2 and similarly 100 − P1 P2 = 2 Solving the last two equations simultaneously gives P1 = P2 = $33.33 c) Consumers are better off with one monopolist charging $50 than with two monop- olists charging a total of $66.67. An analogous argument shows that consumers will pay less for their operating systems plus software if the operating system and the software are provided by a single monopolist. 11–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Twelve: Game Theory Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 12 1. I. (Right, Down). II. (Right, Up), (Left, Down), and (Right, Down). III. (Right, Up). IV. (Right, Down). V. None. VI. (Left, Up) and (Right, Down). VII. (Left, Up) and (Right, Down). VIII. (Left, Up). 2. I. (Right, Up), (Left, Down), and (Right, Down). II. (Right, Up), (Left, Down), and (Right, Down). III. (Right, Up). IV. (Right, Up), (Left, Down), and (Right, Down). V. (Left, Down) and (Right, Down). VI. (Right, Down). VII. (Left, Up) and (Right, Down). VIII. (Left, Down) and (Right, Down). 3. I. Yes. Yes. II. No. No. III. Yes. No. IV. Yes. Yes. V. No. No. VI. No. No. VII. No. No. VIII. Yes. No. 4. I. (Right, Down). II. (Left, Down). III. (Right, Up). IV. (Right, Down). V. (Right, Down). VI. (Right, Down). VII. (Right, Down). VIII. (Right, Down). 5. I. (Right, Down). II. (Right, Up). III. (Right, Up). IV. (Right, Down). V. (Left, Down). VI. (Right, Down). VII. (Left, Up). VIII. (Left, Up). 7. 16 14 21 21 14 16 20 15 10 10 15 20 12 9 9 12 5 5 8. a) V. b) VIII, or the prisoner’s dilemma. d) II or VII. e) VI. 9. No. 10. In 12.1, if the strong pig goes first we get (Left, Down); if the weak pig goes first we still get (Left, Down). In 12.2, we get (Left, Up) no matter who goes first. In 12.3, if Fred goes first we get (Left, Up) but if Ethel goes first we get (Right, Down). In 12.4, if Dot goes first, we get either (Left, Up) or (Right, Down), but if Ditto goes first, we get either (Right, Up) or (Left, Down). 11. True. 12. False. 12–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Thirteen: External Costs and Benefits General Discussion 1) Coase’s seminal article is easy to find on the Web. In the absence of guid- ance, students find it difficult, partly because several different ideas are developed simultaneously and it is sometimes hard to tell what the examples are supposed to illustrate. But with a bit of preliminary background—consisting, say, of class- room coverage of this chapter—the article is quite accessible. The examples are entertaining, and students like the fact that they are derived from real litigation. 2) In formulating the Coase Theorem, the text emphasizes the (short-run) equivalence of property rights and liability rules. It will come as a surprise to many professors of economics that liability rules are not equivalent to property rights in the long run. After considerable confusion in the literature, this issue was completely clarified by H. E. Frech in the paper cited in the text. In the presence of potential entry, a liability rule (say, all polluting steel factories must reimburse neighboring laundromats for damage done to their business; or, alternatively, laun- dromats must bear the full cost of pollution from steel factories) does not convey a well-defined property right, because the right to use the contested resource changes hands at the time of entry or exit. Thus a liability rule favoring laundromats is not the same thing as awarding laundromat owners property rights to the air, both because the laundromat owner who closes his business must sacrifice his control over the use of the air, and because anyone who opens a laundromat can use the air for free. Another way to say this is that a change in property rights is a lump sum transfer, whereas a change in liability rules taxes one activity and subsidizes an- other. Thus property rights have no allocational consequences in either the short run or the long run, but in the long run liability rules matter. For a starker example, consider the liability rule at a crosswalk. For simplicity, suppose that either 1) drivers are liable for all injuries to pedestrians or 2) pedes- trians are liable for all injuries to themselves. Many—I dare say most—economists would be comfortable saying that in case 1), the pedestrians have been awarded property rights to the intersection, while in case 2) drivers have been awarded those same property rights. From this they conclude that if there were no transactions costs between drivers and pedestrians, the rule of liability would not matter. Both beliefs are wrong. It is not correct that liability rule 1) is equivalent to awarding property rights to pedestrians. One reason is that while, in principle, a pedestrian in the intersection can charge drivers for the right to enter, he can not under this liability rule charge another pedestrian for the right to enter. Another reason is that his rights disappear once he steps up onto the opposite sidewalk. Moreover the rule of liability matters: under rule 1), there will be more pedestrians in the intersection; under rule 2) there will be more drivers. Neither outcome is efficient. It is possible to argue that in a world with literally zero transactions costs, where every potential pedestrian could be a party to a single negotiation, the rule of liability would not matter. But there is this crucial distinction: when there is a well-defined property right, the optimal allocation of resources can be achieved in a negotiation involving only a finite number of participants. If somebody owns the intersection, only he and the users who value it most must be parties to the 13–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. negotiation; all others are then excluded from the intersection by fiat. But under the pro- pedestrian liability rule, every potential pedestrian—in principle an infinite number of parties—must be included in the negotiation. Anyone who is excluded can costlessly enter the intersection and muck up the agreement. I would like to propose what seems to me to be a useful terminology for all this (although, because it is non- standard, this terminology is not used in the textbook). Let us define a property right to be any right of control over a resource that meets this condition: when there are no transactions costs among finite collections of agents, the transfer of the property right from one firm to another has no effect on the allocation of resources. (The restriction to firms is to avoid getting tangled up in income effects.) Then part of Coase’s theorem becomes: In the short run, liability rules are property rights. All of this comes down to a subtle collection of issues perhaps best not aired in the classroom, unless you plan to devote a lot of time to law and economics. But for those students who want to think more deeply about such things, there is further discussion in the text, plus as much of the above as you care to share with them. 3) There are two additional important qualifications of the Coase Theorem that seem to be missing from Coase’s paper. One is the need to take account of income effects. This seems to be widely understood among economists, and I believe that the discussion of free agency in the text will make it widely understood among students. The second is a less widely known observation, clearly exposited in a paper of Ralph Turvey (who references Buchanan and Stubblebine): As an example in the text shows, a Pigou tax in the partial absence of transactions costs can be worse than no tax at all, and also worse than the same Pigou tax in the presence of full transactions costs that preclude all negotiations. 4) The text surveys a variety of sources of transactions costs. Many of these come down, in one way or another, to the fact that some contracts are unenforceable (for example, when one party’s behavior can not be observed). That is, they come down to principal–agent problems. An interesting feature of such problems, which is not emphasized in the book, but which your students might want to hear about, is that agents can be made better off if they are able to constrain their own behavior. For example: A one-time borrower would like to default on his debt when it comes due. Because lenders know this, they will not lend to him. If the borrower can somehow pre-commit himself to paying, he can secure a loan. Thus, even though he prefers default once the loan is obtained, he is better off in a world with- out that option than in a world with it. This is an example of time-inconsistency, which occurs when an agent can make himself better off by guaranteeing at time A that he will not do the thing that he most wants to do at the later time B. Time-inconsistency comes up in an important way in macroeconomics. Governments benefit from unexpected inflation, and lose when inflation is less than expected. (See Section 9.3 in the textbook for one reason why.) Thus they would like to engage in continual unexpected inflation, which is unfortunately not possible (just as the borrower can not secure loans that he has no incentive to repay). If the government could credibly promise not to inflate, inflationary expectations would vanish, yielding an outcome that is preferable to the one where government is unconstrained. (See various papers of Robert Barro and David Gordon for more on this.) 5) For another example: consider a firm owned and operated by several part- ners, each of whom has an incentive to shirk. Shirkers can not be detected. Thus 13–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. in order to prevent shirking, the partners agree that when output falls, indicating the presence of a shirker, everyone will be punished so severely that all shirking is deterred. If implemented, such an agreement improves everyone’s welfare. Unfortu- nately, each potential shirker knows that the agreement will never be implemented: When the time comes to mete out the punishment, there will be a unanimous vote to change the rules. Thus all partners are better off if they can bind themselves to really carry out the punishment. (This harks back to the “Chinese bargemen” example of Chapter Eleven.) Perhaps one way in which they do this is by giving ownership of the firm to some outside party with the power to fire them all. The partners become managers, and the outside party is called a stockholder. Maybe this is an important reason for the separation of ownership from control. The preceding paragraph suggests that the separation of ownership from con- trol evolves as a solution to a principal– agent problem. It is also, however, the source of a new principal–agent problem. Will a salaried manager work as hard as one whose income is directly tied to the performance of the company? Yes, if the owners can completely monitor his performance, but no otherwise. Thus managers, and in particular corporate officers, are often encouraged or required to hold large amounts of corporate stock, to give them an appropriate interest in the company’s performance. Separating management from ownership solves one principal– agent problem only to create a new one. Large equity positions for corporate officers solve the new problem, but create yet another one: Since the outside owners of the corporation hold diversified portfolios, they want the corporation to maximize expected returns without regard to risk; but at the same time, the officers, much of whose wealth is tied up in a single company, will want that company to behave in a way that is risk-averse. Again, if owners can completely monitor officers’ behavior, there is no problem, but in the absence of perfect monitoring a problem arises. Ken Judd once suggested to me that this makes it desirable for corporate officers to have a great deal of personal wealth, since there is reason to believe that behavior becomes more nearly risk-neutral as wealth increases. This theory is developed in Chapter 18 of this textbook. 6) For yet another example: Publishers bring out new editions of textbooks every three years, partly to combat the used market. In the absence of this motive, they might bring out new editions only every five years. When a student buys a new book in the first year of an edition, he pays the present value of its use to himself plus what he will receive at resale; that is, he pays the present value of its use to him and to the two students who will use it after him. If new editions were spaced every five years, resale prices would be higher, students would be willing to pay more for new books and the publisher would save on production costs. (Ultimately, this leads to entry and a fall in the cost of textbooks.) Thus a publisher who promised credibly to space new editions farther apart could benefit both himself and his customers. Unfortunately, no such promise is enforceable. The publisher always wants to bring out a “surprise” new edition, rendering obsolete books that have been sold under false pretenses. In summary, publishers and students can both gain from a bargain in which students pay more for the books and publishers agree not to bring out new editions. But because publishers have every incentive to renege on their promises, the deal can not be struck to begin with. If publishers could find a way to constrain their own future freedom, they would want to do so. 13–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7) At the risk of belaboring this point, I would like to present one additional set of time-inconsistency examples, taken from the paper of Lott and Roberts that is cited in the text. Suppose that under a regime of rent control, a landlord and a prospective tenant want to contract for a rental fee in excess of the legal maximum. At the legal maximum, the landlord would not be willing to rent to this tenant; thus both gain if the deal is struck. The law discourages this in a clever way: it specifies that the tenant can report the agreement after he has lived in the apartment, and can sue to retrieve his “overpayments.” The law also makes it impossible for the tenant to waive this right. The landlord, knowing this, and knowing that the tenant has no incentive to forego such behavior, will not rent to him. If the tenant could somehow constrain his own future behavior, he would be better off. Another example is that of a firm and a prospective employee who want to contract for a salary that is below the legal minimum wage. Here again, if the employee can sue for back wages ex post, then there can be no employment. But here Lott and Roberts suggest a solution. Suppose that the potential employee has committed some crime that would surely come to light in the process of collecting back wages; suppose in particular that the employee is an illegal alien. This guar- antees that he will not exercise his “rights” in this matter and makes it possible for him to be hired. It follows that a general amnesty for illegal aliens would make many illegal aliens worse off! 8) There is much more to be said on the subject of law and economics, and much of it can be found in the references in the text. One particularly interesting example, due to Posner, concerns the award of punitive damages. By and large, punitive damages are not permitted in negligence cases. Posner argues that this is consistent with the hypothesis that the common law fosters efficiency, since it is appropriate for tortfeasors to pay for the social costs of their actions and not more. He also makes a related point which is particularly appropriate here: Punishment for negligence would close an important safety valve in the negligence system. A standard of care is necessarily a crude approx- imation to optimality. Allowing enterprises a choice whether to comply or pay the social costs of violation may permit a closer approximation. Suppose there is a rule that a dam owner is responsible for flood dam- age unless his dam is at least 16 feet high. Presumably the rule reflects a judgment that the cost of raising the dam is less than the cost of the floods that a lower dam would fail to contain. One owner thinks the rule is incorrect. He estimates that the only flood likely to occur is one that would swamp a 16-foot dam and therefore that he can save money by violating the rule. Courts are not infallible and we give maximum play to individual judgment if we let the dam owner act on his estimate. If he is wrong he will have to pay a judgment, but if he is correct an unnecessary expenditure on dam building will have been saved.* Pedagogically, this is a nice topic to cover because it ties in the present material with the material on knowledge in society from Chapter Nine. Those who own dams are likely to have better information about local conditions than those who make laws, and we want this information taken into account when dams are or are not built. Punitive damages constitute an artificial incentive to ignore such information and are therefore contraindicated. * Posner, A Theory of Negligence. 13–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 9) If you cover the material on the Good Samaritan Rule, you might want to mention the “last clear chance doctrine.” In the Ploof case, the court held that the owner of a dock can not deny its use to a ship in trouble if the ship has no alternative means to rescue itself. By denying the use of the dock, its owner becomes liable for damage to the ship. The logic here seems contrary to that of the Good Samaritan Rule, and bolsters the claim that the Good Samaritan Rule is an isolated aberration in its apparent tolerance of inefficiency. 10) If you have the luxury of being able to spend a significant amount of time on law and economics, there are a host of issues you can raise regarding both the meaning and the desirability of an efficiency standard. Steven Margolis in the Journal of Legal Studies (approximately 1985) poses the following conundrum: A and B live on adjoining properties. B wants to build a wall along the property line, and values such a wall at $50 more than the cost of building it. A is a student who knows that he will have a high future income, but can not borrow against this because of imperfect capital markets. If A could borrow against his future income, he would be willing to pay $100 to prevent the wall from going up, but given his current budget constraint he is only willing to pay $10. Under an efficiency standard, should B be allowed to build the wall? One common formulation of the efficiency standard is that courts should seek to achieve that allocation of resources that would come about in a world with no transactions costs. According to this formulation, the wall should be prohibited, since in a world without transactions costs, capital markets would be perfect and A would bribe B not to build the wall. But, as Margolis points out, this is probably not the outcome that is intended by those who formulate the standard in this way. The fact of the matter is that capital markets are imperfect and it is not within the court’s power to change that fact. Taking this as given, the efficient outcome is for B to build the wall. There is room for much argument on either side of this issue. I imagine that with the right class—one where the students are bright, interested in the law, and intellectually curious—you could generate a quite lively discussion on this topic. I have done so successfully with graduate students, but have never tried it with undergraduates. 11) Continuing to explore the efficiency standard, there is another conundrum that seems to come up repeatedly in these discussions. I am not sure of its source (though I believe that it is referenced in Landes and Posner’s book on tort law, which I do not have in front of me as I write this). Consider a man who would like to have sexual intercourse with a particular woman and would be willing to pay $100,000 to do so; she would be willing to pay $50,000 to prevent him. Should he then be allowed to commit rape? This is too easy: there is no need to allow coercion here because the efficient outcome will be reached through voluntary transactions. But now what if coercion is essential to the man’s enjoyment? The act is worthless to him unless he knows that the woman is not being compensated. Here the efficiency standard seems to mandate sanctioning the rape, which is a conclusion that most people find distasteful. I believe that Posner has tried to dispense with this one by claiming that for $100,000 the man should certainly be able to find a woman who will put on a convincing show of being forced, but this really evades the question. We can hypothesize that the man requires actual coercion for his pleasure and that nothing else will do. Is there a way out of this? I don’t know. I have never tried raising this issue or anything like it in class, and I would not do so unless I had budgeted several 13–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. weeks for law and economics. This rules out bringing it up in any standard micro course, but for more specialized courses I think it is an appropriate example. 12) Steve Cheung’s article on tenant farming in the Journal of Political Econ- omy is another good source of examples for the material in this chapter. 13–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Explain the reason for the following phenomenon: At parties in which several conversations are simultaneously in progress, it is common for everybody to be shouting to be heard over everybody else, whereas they would all be heard better (and save wear and tear on their vocal chords) if they all spoke in normal tones of voice. 2. True or False: A profit-maximizing monopolist whose firm was a source of negative externalities might produce exactly the socially optimal level of out- put. 3. Consider a competitive industry in which there is an upward-sloping long run industry supply curve due to a factor price effect. Explain why the private marginal cost curve of the firms in the industry lies above the social marginal cost curve. Which of these marginal cost curves coincides with the long run industry supply curve? The next twelve problems (#4 through #15) have multiple parts that can be assigned independently of each other. Thus each of these problems is really three or four different problems. Problems 4a, 4b, and 4c are essentially identical to problems 12, 13 and 14 in the textbook; Problem 7a is essentially identical to problem 15 in the textbook. 4. Suppose Japanese cars and American cars are identical from their owners’ point of view, but Japanese cars cause harmful pollution while American cars do not. Each American owner of a Japanese car imposes $1,000 worth of pollution costs on his neighbors. Suppose the U.S. supply and demand curves cross at a price of $10,000, but Americans can buy as many cars as they want to from Japan at $7,000 apiece. a) Suppose the U.S. government imposes a tariff of $1,000 apiece on all Japanese cars sold in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in the United States, both foreign and domestic. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? c) Suppose the U.S. government offers a subsidy of $1,000 per car to all American car makers. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 5. Suppose Japanese cars and American cars are identical in every way. The production of American cars creates pollution costs of $1,000 per car. There are no pollution costs associated with driving cars or with the manufacture of Japanese cars. The U.S. supply and demand curves cross at a price of $10,000, but Americans can buy as many cars as they want to from Japan at $7,000 each. a) Suppose the U.S. government imposes an excise tax of $1,000 on every car manufactured in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? 13–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in the United States, both foreign and domestic. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American car buyers a subsidy of $1,000 for each imported car they buy. (There is no subsidy for domestic cars.) Suppose also that American car manufacturers are forbidden to sell cars to foreigners. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 6. Suppose Japanese cars and American cars are identical in every way. Each American who owns a car (regardless of whether that car is Japanese or Amer- ican) imposes $1,000 worth of pollution costs on his neighbors. Suppose the U.S. supply and demand curves cross at a price of $10,000, but Americans can buy as many cars as they want to from Japan at $7,000 apiece. a) Suppose the U.S. government imposes a tariff of $1,000 apiece on all Japanese cars sold in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government imposes an excise tax of $1,000 on every car manufactured in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? c) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in the United States, both foreign and domestic. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? 7. There are two mange cures on the market: Mange-Away, which is made in the United States and sold by producers who have an upward-sloping supply curve, and Look-Ma-No-Mange, which is made in Mexico and available in any quantity at $5 a dose. The supply curve for American Mange-Away crosses the (U.S.) demand curve for mange cures at a price of $8 per dose. To the individual mange sufferer, Mange-Away and Look-Ma-No-Mange are interchangeable products. But although American Mange-Away cures the dis- ease, it also leaves the patient contagious to others. Mexican Look-Ma-No- Mange both cures the disease and renders the patient noncontagious; thus, every user of Look-Ma-No-Mange confers $1 worth of external benefits on his neighbors. a) Suppose the U.S. government imposes an excise tax of $1 on every dose of Mange-Away produced in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? b) Suppose the U.S. government offers American mange sufferers a subsidy of $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There is no subsidy for American Mange-Away.) Suppose also that the makers of Mange-Away are free to sell their products to foreigners at the going world price. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American mange sufferers a subsidy of $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There is 13–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. no subsidy for American mange-away.) Suppose also that the makers of Mange-Away are forbidden to sell their product to foreigners. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? d) Suppose the U.S. government offers American mange sufferers a subsidy of $1,000 for every dose of mange cure they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 8. There are two mange cures available: Mange-Away, which is made in the United States and sold by producers who have an upward-sloping supply curve, and Look-Ma-No-Mange, which is made in Mexico and available in any quan- tity at $5 a dose. The supply curve for American Mange-Away crosses the (U.S.) demand curve for mange cures at a price of $8 per dose. To the individual mange sufferer, Mange-Away and Look-Ma-No-Mange are in- terchangeable products. But although Mexican Look-Ma-No-Mange cures the disease, it also leaves the patient contagious to others. American Mange-Away both cures the disease and renders the patient noncontagious; thus, every user of Mange-Away confers $1 worth of external benefits on his neighbors. a) Suppose the U.S. government imposes a tariff of $1 per dose on all Mexican Look-Ma-No-Mange in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government offers a subsidy of $1 per dose to the Amer- ican manufacturers of Mange-Away. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American mange sufferers a subsidy of $1,000 for every dose of mange cure they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 9. Two mange cures are available: Mange-Away, which is made in the United States and sold by producers who have an upward-sloping supply curve, and Look-Ma-No-Mange, which is made in Mexico and available in any quantity at $5 a dose. The supply curve for American Mange-Away crosses the (U.S.) demand curve for mange cures at a price of $8 per dose. Mange-Away and Look-Ma-No-Mange are interchangeable products in every way. Both products not only the cure the disease; they also render the patient non- contagious. Thus any user of either mange cure confers $1 worth of external benefits on his neighbors. a) Suppose the U.S. government offers American mange sufferers a subsidy of $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There is no subsidy for American Mange-Away.) Suppose also that the makers of Mange-Away are free to sell their products to foreigners at the going world price. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? b) Suppose the U.S. government offers American mange sufferers a subsidy of $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There is no subsidy for American mange-away.) Suppose also that the makers of Mange-Away are forbidden to sell their product to foreigners. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy 13–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. increase or decrease social welfare? By how much? c) Suppose the U.S. government offers a subsidy of $1 per dose to the Amer- ican manufacturers of Mange-Away. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? d) Suppose the U.S. government offers American mange sufferers a subsidy of $1,000 for every dose of mange cure they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 10. Suppose the price at which American car makers’ supply curve crosses the American demand curve is $10,000 per car. However, manufacturers can sell as many cars as they want to in the world market at a price of $15,000 per car. Every time a car is produced in the United States, the factory creates $2,000 worth of pollution. a) Suppose the U.S. government imposes an export tax of $2,000 on all cars that are shipped abroad. Illustrate the gains and losses to all relevant groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government imposes an excise tax of $2,000 on every car manufactured in the United States, regardless of where that car is sold. Suppose also that U.S. citizens are free to buy cars on the world market if they want to. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? c) Suppose the U.S. government imposes an excise tax of $2,000 on every car manufactured in the United States, regardless of where that car is sold. Suppose also that U.S. citizens are prohibited from buying foreign cars. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? d) Suppose the U.S. government imposes a sales tax of $2,000 on all cars sold in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? 11. Suppose the price at which American car makers’ supply curve crosses the American demand curve is $10,000 per car. However, manufacturers can sell as many cars as they want to in the world market at a price of $15,000 per car. Every American who drives a car imposes $2,000 worth of pollution costs on his neighbors. a) Suppose the U.S. government imposes an excise tax of $2,000 on every car manufactured in the United States, regardless of where that car is sold. Suppose also that U.S. citizens are prohibited from buying foreign cars. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? b) Suppose the U.S. government imposes a sales tax of $2,000 on all cars sold in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American car makers a subsidy of $2,000 for each car they export. (There is no subsidy for cars sold in the U.S.) Illustrate the gains and losses to all relevant groups of Americans. 13–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Does the subsidy increase or decrease social welfare? By how much? 12. Suppose the price at which American car makers’ supply curve crosses the American demand curve is $10,000 per car. However, manufacturers can sell as many cars as they want to in the world market at a price of $15,000 per car. There are no external costs associated with either car production or driving. However, whenever cars are exported they are sent via ships that pollute United States coastal waters, causing pollution damage that amounts to $2,000 per exported car. a) Suppose the U.S. government imposes an export tax of $2,000 on all cars that are shipped abroad. Illustrate the gains and losses to all relevant groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government imposes an excise tax of $1 on every dose of Mange-Away produced in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the excise tax increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American car buyers a subsidy of $2,000 for every car they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 13. Suppose that cookies are produced in the United States and sold both do- mestically and abroad. American consumers will buy only American cookies. Cookie production creates pleasant aromas, so that every time a box of cookies is produced in the U.S., those who live near the factores enjoy $2 worth of ben- efit. The benefit is the same regardless of whether the cookies are ultimately sold in the U.S. or abroad. The price at which the cookie manufacturers’ supply curve crosses Americans’ demand curve is $5 per box. Manufacturers can sell as many cookies as they want to in the world market at a price of $10 per box. a) Suppose the U.S. government offers American cookie makers a subsidy of $2 for each box of cookies they export. (There is no subsidy for cars sold in the U.S.) Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? b) Suppose the U.S. government offers American cookie makers makers a subsidy of $2 for each box of cookies they produce. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American cookie buyers a subsidy of $2 for every box of cookies they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 14. Suppose each stick of deodorant that is consumed in the U.S. creates $3 worth of positive externalities to Americans. Deodorant used abroad does not confer positive externalities on Americans. The price at which the American deodorant supply curve crosses Americans’ demand curve is $5 per stick. Manufacturers can sell as much deodorant as they want to in the world market at a price of $10 per stick. a) Suppose the U.S. government imposes an export tax of $3 on every stick of deodorant shipped abroad. Illustrate the gains and losses to all relevant 13–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. groups of Americans. Does the tariff increase or decrease social welfare? By how much? b) Suppose the U.S. government offers American deodorant manufacturers a subsidy of $3 for every stick of deodorant they produce, regardless of where that stick is sold. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? c) Suppose the U.S. government offers American consumers a subsidy of $3 for every stick of deodorant they buy. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? 15. The price at which Americans’ demand curve for blue jeans crosses the man- ufacturers’ supply curve is $10. Manufacturers can sell as many blue jeans as they want to in the world market at a price of $15. There are no externalities involved in the production or wearing of blue jeans, but there is an externality when American blue jeans are are shipped abroad: Blue jeans create good will toward Americans and allow us to reduce our defense expenditures. Each pair of American blue jeans sold abroad reduces the U.S. defense budget by $2. a) Suppose the U.S. government offers American clothing manufacturers a subsidy of of $2 for each pair of blue jeans they produce. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? b) Suppose the U.S. government offers American clothing manufacturers a subsidy of of $2 for each pair of blue jeans they export. Illustrate the gains and losses to all relevant groups of Americans. Does the subsidy increase or decrease social welfare? By how much? c) Suppose the U.S. government imposes a sales tax of $2 a pair on all blue jeans sold in the United States. Illustrate the gains and losses to all relevant groups of Americans. Does the tax increase or decrease social welfare? By how much? d) Suppose the U.S. government passes a law requiring all American con- sumers to buy their blue jeans from abroad. Illustrate the gains and losses to all relevant groups of Americans. Does the law increase or de- crease social welfare? By how much? 16. Snidely Whiplash owns a competitive factory that produces widgets for sale on the world market. He also owns several houses near the factory, which he rents to identical tenants. The factory pollutes the air. The following diagram shows the world price of widgets and the social and private marginal cost curves at Snidely’s factory. 13–12 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. MCS MC P P D world price of widgets A C B Q Q0 Q1 a) Is it more profitable for Snidely to produce Q0 widgets or Q1 widgets? (Be sure to account both for the producer surplus at the widget factory and the amount he’ll be able to charge for housing.) b) How and why might your answer change if the residents are not all iden- tical? 17. The widget industry is competitive. Widget factories pollute the neighbor- hoods where they are located. The attached diagram shows the demand, private and social marginal cost curves for the industry. The cost of moving the neighbors elsewhere is B + C + (1/2)D. P MCS MCP A D C B D Q Q Q1 0 a) Suppose widget firms face no penalty for polluting. How many widgets are produced? Do the neighbors move away? Why or why not? What is the social gain? b) Suppose widget firms are subject to a Pigou tax. How many widgets are produced? Do the neighbors move away? Why or why not? What is the social gain? c) According to the efficiency criterion, is the Pigou tax a good policy? 18. Whenever you purchase a stereo, you bid the price of stereos up, which has negative consequences for all other purchasers of stereos. Does it follow that the social cost of purchasing a stereo is greater than your private cost? Is this an argument for taxing the purchase of stereos? 19. “According to the Coase Theorem, freed slaves will continue to do the same work that they did under slavery.” a) Explain the argument underlying this assertion. b) What important factors does the argument overlook? 13–13 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. c) In what general circumstances would you expect the quoted statement to be true? To be false? 20. A set of railroad tracks runs through the town of Nwot, and long freight trains often block the flow of traffic. The town government has gone to court to request the right to regulate the passage of the trains. Under various assump- tions, discuss the senses in which the judge’s decision matters and the senses in which it might not. What factors should the judge take into account in rendering his decision? 21. Courts have recently been called upon to decide whether surrogate motherhood contracts should be enforced. Under these contracts, a couple hires another woman to bear a child which the couple adopts as soon as it is born. Often the contract contains a clause forbidding the biological mother to have any contact with the child once it is adopted. Sometimes the biological mother changes her mind after the child is born and attempts to acquire the right to visit the child, or even raise it as her own. The court must decide whether surrogate motherhood contracts should be enforceable as written, or whether the biological mother should have the right to change her mind. What effect does the court’s decision have on the number of surrogate motherhood contracts that get written? What effect does it have on the number of surrogate mothers who eventually get to visit or raise their biological children? Who benefits from a decision in favor of enforcing the contracts and who benefits from the opposite decision? If you were the judge, what would you decide and why? 22. Bakers produce cookies at a private marginal cost of 5, but a social marginal cost of only 3, since each cookie being baked creates 2 worth of pleasant aromas for passersby to enjoy. Assuming a competitive market for cookies, use a graph to show all of the social gains from the existence of the cookie industry. Now suppose that bakers are offered a subsidy of 2 per cookie baked and recompute the social gains. Is the subsidy a social improvement? 23. Discuss the pros and cons of the following statement: “Entry to decreasing cost industries should be subsidized by the government.” 13–14 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 24. The following graph depicts the demand for widgets and the social and private marginal costs of producing widgets. The externalities are in the form of pollution which is breathed by people who live near widget factories. Price MCsocial MCprivate D A C B Demand Quantity Suppose the government imposes a rule that says widget firms must pay a penalty equal to the pollution costs that are imposed on the neighbors (firms that have no neighbors pay no penalties). The penalties are used to make welfare payments to people who do not live near widget firms. Assume also that all neighbors are identical. Then fill in the blanks in the following sentences: a) The neighbors will choose to move if the cost of moving is less than . b) According to the efficiency criterion, the neighbors should move if the cost of moving is less than . c) According to the efficiency criterion, it would be better to have no penalty at all for polluting if the cost of moving is between and . 25. A competitive firm pollutes the air. Consider three possible legal rules: A. The firm can pollute as much as it wants to with no penalty. B. The firm must pay a fine equal to the amount of damage it causes; this fine is paid to the mayor’s brother. C. The firm must compensate the neighbors for all the damage it causes. Suppose it is extremely expensive for the neighbors to move away or to protect themselves from the pollution in any way. Then which of the three legal rules above leads to an efficient outcome? Answer in each of the following four scenarios, and justify your answers: a) Very high transactions costs all around. b) Zero transactions costs between the firm and the neighbors; very high transactions costs between the firm and the mayor’s brother. c) Very high transactions costs between the firm and the mayor’s brother; zero transactions costs between the firm and the neighbors. d) Zero transactions costs all around. e) Repeat parts a) through d) on the assumption that it is almost (but not quite) costless for the neighbors to move away. 13–15 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 26. A competitive firm creates negative externalities by polluting the air. Trans- actions costs are high, so there is no possibility of negotiation between the firm and the affected neighbors. Price MCsocial MCprivate B Demand D C Quantity Three policies are being considered: A. The firm is given the legal right to pollute all its wants to, with no penalty. B. The firm is subject to a Pigou tax (i.e. an excise tax equal to the exter- nality); the proceeds from the Pigou tax are used to provide benefits to people 3,000 miles away. C. The immediate neighbors are entitled to compensation from the firm for all damage caused by pollution. In each of the following circumstances, determine which of the three policies lead to efficient outcomes and which lead to inefficient outcomes. a) The neighbors’ cost of moving is less than C b) The neighbors’ cost of moving is between C and C + D. c) The neighbors’ cost of moving is between C + D and B + C + D. d) The neighbors’ cost of moving is greater than B + C + D. (Hint: In each case figure out what the efficient outcome is- –should the neigh- bors move or shouldn’t they?—and then figure out which of the policies will yield that outcome and which won’t.) 27. A competitive firm pollutes the air. The following graph shows the demand for the firm’s product and the private and social marginal cost curves. The numbers in the graph indicate areas. a) Suppose: • there is no legal penalty for polluting • there are no transactions costs, and • it is impossible for the neighbors to move. 13–16 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. What quantity does the firm produce? Give a concrete description of a deal that might be struck between the firm and the neighbors (including the exact amount of money that changes hands). What is the social gain (your answer to this should be a number ). b) Suppose: • the firm is required to reimburse the neighbors for pollution damage • there are no transactions costs, and • it is impossible for the neighbors to move. What quantity does the firm produce and why? c) Suppose: • the firm is required to pay a Pigou tax for pollution damage • there are no transactions costs between the firm and the neighbors who breathe the pollution; however, it is impossible for the firm or the neigh- bors to negotiate with the recipients of the tax revenue. • it is impossible for the neighbors to move. What can you say about the quantity produced by the firm? What can you say about the social gain in this situation compared to part a)? d) Suppose: • transactions costs are so high that negotiation is impossible • it would cost the neighbors $6 to move. • there is no legal penalty for pollution. Do the neighbors move? Why or why not? What is the social gain? e) Suppose: • transactions costs are so high negotiation is impossible • it would cost the neighbors $6 to move • the firm is legally required to reimburse the neighbors for all pollution damage. Do the neighbors move? Why or why not? What is the social gain? 28. Baseball games attract more fans when there is suspense regarding the out- come. They also attract more fans when the team has been winning. Thus a team’s revenues depend in complicated ways on the qualities of other teams in the league: If the other teams are either much better or much worse than the home team, there is no suspense, and if they are all just a bit better, the home team loses more often than it wins. Thus whenever a team improves its performance, the revenues of all other teams are affected in complicated ways. Assume that teams can improve their quality through costly invest- ments. What determines a teams’ optimal investment in quality from the point of view of the league as a whole? How does this optimal investment differ from the investment that teams would choose if they maximized only their own revenues? Suppose that it is costly for teams to negotiate among themselves whenever one team wants to take action to improve itself, but that it is costless for teams to lay down some general ground rules. What sorts of ground rules might you expect to observe? Sometimes two teams can both improve themselves through a mutually beneficial trade. What sorts of restrictions on trading might you expect to observe? This is intended as a “thought problem,” and I do not have any specific answers in mind. I suspect that the problem is very difficult. 13–17 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 13–18 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 13 1. Price MCprivate a) He produces Qe. His PS is A; the MCsocial gain to the orchard owners is B. D b) A subsidy leading him to produce Qowould increase social gain by C . $5 PS is A+B+C , gain to orchard owners A C is B+ C +D, cost to taxpayers is B+ C +D. B c) In the sense that Qowill be the quantity produced with or without the subsidy, because the orchard owners Quantity will pay the beekeeper to raise more Qe Qo bees if necessary.. 2. True, since students would have a reduced incentive to take precautions like sticking to well-lighted paths, staying alert to their surroundings, and learning self-defense techniques. If there were no transactions costs between the university and the students, the answer would be false, since the university would offer to pay students enough to induce them to take exactly the same amount of care that students take when the university is not liable. However, the key transactions cost here is the unobservability of the students’ behavior. Unless the university constantly monitors the students, they will agree to the deal, accept the money, and still behave recklessly. This transactions cost prevents the deal from being struck in the first place. 3. False. Married couples split the housework in the way that minimizes joint costs and then subsidize each other through side payments. There might be an exception for couples who are already married when the law comes into effect, because those husbands experience a negative income effect and so might end up choosing less leisure and more housework. But for couples who are not yet married and still negotiating the terms of their relationship, there should be no effect. 4. One could as easily assert that Farmer Smith should bear the costs of the damage, since it is caused by the lettuce. Removing the lettuce would solve the problem as well as removing the rabbits would. 5. It is impossible to tell. If the neighbors remain in the area and do nothing to protect themselves from the noise, then the social cost of the expansion is $350 ($50 to the taxpayers and $10 × 30 = $300 to the neighbors), while the social benefit is only $300. That’s a reduction in social welfare. But perhaps the neighbors will either soundproof their houses or move to a different area at a cost substantially less than $10 per neighbor. In that case, the expansion could improve social welfare. 6. True, in the sense that every monopolist would produce the competitive quantity. This is the quantity that maximizes social surplus, so there is always a deal that can be struck between the monopolist and his customers whereby both benefit from this behavior. 13–19 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7. Assume first that there are no transactions costs between the beekeeper and the car dealer. In that case, your decision does not matter in the sense that it has no effect on the number of bees that are kept, the procedures used to contain the bees, the number of cars sold, the investment in tents by the car dealer, whether the car dealer will move away, and so forth. It matters in the sense that the beekeeper prefers one decision and the car dealer another. Alternatively, if there are transactions costs, then all of the things that were left unaffected in the preceding paragraph can indeed be affected. A ruling for the car dealer could induce the beekeeper to rein in his bees (say with better netting) or to scale back his operation, while a ruling for the beekeeper could induce the car dealer to erect a tent or to move. Since there are only two parties and they are in close proximity, the assumption of no transactions costs seems the more reasonable. If a large collection of motorists is involved, the transactions costs can become considerable. It is difficult for the motorists to collectively negotiate with the beekeeper, particularly if different motorists are affected on different days. Many motorists might not even recognize the source of the problem. In this case, some factors relevant to the decision are: How much would it cost the beekeeper to prevent his bees from flying over the roadway, either by containing them or moving elsewhere? What alternatives are available to motorists? Can they easily take a different route or would it be very costly to do so? How much damage to the bees actually do to the cars, and how much does it cost motorists to cope with this damage, either by having it repaired or by deciding to tolerate it? 8. False. Monopolies underproduce; firms that create externalities overproduce. It makes no sense to complain that a firm is simultaneously producing too little and too much. In fact, these problems tend to cancel each other. 9. a) Only (iii) and (iv) are affected. b) It would be a mistake to rule against the laundromat if the steel factory could easily install filters in its smokestacks to prevent soot from falling on the laundromat. It would be a mistake to rule for the laundromat if the laundromat could easily erect an awning to protect against soot. 10. a) If there are low costs of transacting, the rules don’t affect whether your roommate decides to play his stereo. They do affect who might have to bribe whom. b) In this case it would most likely be difficult to make arrangements (or contracts) with a large number of people in your dormitory. Thus, transactions would at least as high as in part a. and the rules are more likely to effect the outcome. c) Some considerations are: Would it be easy for you to study elsewhere, or to wear earplugs? Could your roommate find some other location or activity that he would enjoy almost as much? And how much does it really matter whether you pass economics? 11. a) If there are no transactions costs between the employees and the firm, then the court’s ruling has no effect on the number of children the employees will have, the extent of the safety equipment installed by the company, or the ultimate number of birth defects. The assumption of no transactions costs contains the assumption that the workers are as aware of the problem as the company is, and that all contracts between the workers and the company are enforceable. b) Yes, because this introduces a large transactions cost. As long as the workers are not entitled to compensation from the company, there is no problem, because workers can “bribe” the company to install safety equipment and can verify that the equipment has been installed. However, if the company is liable for birth 13–20 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. defects, it might want to “bribe” employees to forego having children in the future. Since such a contract is unenforceable, the optimal balance of safety equipment and foregone reproduction might not be achieved. c) This remedies the potential problem in part b), since it once again makes the relevant contracts enforceable. This puts us back into the situation of part (a). Without transactions costs, the contracts will only be signed if the cost to employees of signing them is less than the cost to the firm of preventing the radiation exposure. The fact that the contracts are possible insures that the court’s decision will not matter. d) Now we are once again in the realm of transactions costs. In this case, there is a case to be made for absolving the company of liability. If the company is not liable for birth defects, it still has every incentive to install safety equipment, since the workers can still pay bribes. However, if the company were fully liable, workers would have no incentive to practice restraint in reproduction, and the number of birth defects could be more than is optimal. In short, a reasonable expectation is that there will be an optimal number of birth defects unless both the firm is liable for damage and the sterilization require- ment is disallowed. If the law adopts both these positions, then the number of birth defects could go up. 12. Price A B $8000 D F H C E G $7000 Quantity No Tariff Tariff CS A+B+C+D+E+F+G A+B PS I C+D+I Externality D+E+F+G+H F Tariff Revenue — F A+B+C+I-H A+B+C+D+I The tariff creates a net gain of D + H. 13. Refer to the graph for problem 12. With the tax, CS = A + B, P S = I, the externality is D + E + F , and the tax revenue is C + D + E + F , for a total of A+B +C +I. The tax creates a net social gain of H, and so is better that nothing, but not as good as the tariff of problem 3. 14. Refer to the graph for problem 12. With the subsidy, Americans will still pay $7,000 for cars, but American carmakers will charge a price of $8,000. Thus CS = A + B + C + D + E + F + G, P S = C + D + I, the externality is F + G + H, and the cost of the subsidy is C + D + E, for a total of A + B + C + D + −I − H, which amounts to a net social gain of D. 13–21 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 15. Price S A B $5 D F H C E G $4 D Quantity No Sales Tax Sales Tax CS A+B A+B PS C+D+I I Externality F D+E+F Tax Revenue — C A+B+C+D+F+IA+B+C+D+E+F+I The sales tax creates a net gain of E. 16. Under monopoly, social gain is A + B + C + D + F + G. Under competition, social gain is A + B + C + D + E + F + G + H − M . So the breakup adds E + H − M to social gain; in order to determine whether this increment is positive, it suffices to know the values of E, H and M . 17. Neighbors would offer up to C + D. The firm would accept anything over C. The deal goes through because C + D > C. 18. a) The firm produces quantity 70. The neighbors could pay the firm anywhere be- tween $5 and $12 to decrease its output from 80 to 70. Social gain is $8. b) If the neighbors stay, they are subjected to $24 in pollution costs; therefore they will leave. Social gain is $25 in PS minus $6 in moving costs, i.e. $19. c) Now there is no incentive to move. Social gain is reduced to $8. 19. a) Currently residents earn A + B in surplus and suffer C + D in externalities. If Snidely lowers the price of electricity, consumer surplus increases to A + B + C + D + E while externalities increase to C + D + E + F . Thus the value of living in the Yukon is increased by C + D + E on one account and lowered by E + F on the other. The net increase is (C + D + E) − (E + F ) = C + D − F , and this is the amount by which Snidely can increase the price of housing. b) If he lowers the price of electricity, Snidely’s producer surplus falls from C + D to zero. He gains back C + D − F in the housing market. Since C + D − F < C + D, this plan is a bad idea for Snidely. c) Social gain is currently A + B (A + B in consumer surplus, plus C + D in producer surplus minus C +D in externalities. Because we are already operating at the point where demand crosses M Csocial , no greater social gain is possible. Therefore the deadweight loss is zero. 13–22 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 20. If the firm is subject to a Pigou tax, it chooses quantity Q0 , where social gain is $25. Externalities are $15, which is less than $30, so the neighbors remain and this is the final outcome. If the firm is not subject to a Pigou tax, it chooses quantity Q1 . Here ex- ternalities are $33, which is more than $30, so the neighbors leave and the externality vanishes. Social gain is now $50 minus the $30 cost of moving, or $20. $25 beats $20, so the Pigou tax is efficient. 21. a) People were willing to stick around when externalities were C + G. They move when externalities go to C + G + D + H + E. Therefore the cost of moving must be between C + G and C + G + D + H + E. b) Social gain is currently A+B+F −E. With a Pigou Tax spent entirely on worthless projects, social gain is A + B + F − C − G. To determine which is bigger, must compare E with C + G. 22. a) When the price of gasoline rises from P0 to P1 , consumers’ surplus falls by $200. But at the same time, $160 worth of pollution externalities are eliminated. Thus total willingness-to-pay to live in the Territory falls by $40. The total cost of housing falls by this amount, so each of the five houses now rents for $92 a month instead of $100 a month. b) As shown in part a), Snidley’s profit in the housing market falls by $40 a month. His producer’s surplus in the gas market rises by $120 a month. c) Yes, as shown in part b). 23. a) With the tax in place, the firm earns B + F . Without the tax, the firm could earn F + G + H. So the firm is willing to pay up to G + H − B to make the neighbors move. The neighbors currently tolerate externalities of C + G. If they move, they eliminate these costs and replace them with the cost of moving, which is X. So the neighbors will agree to move for any payment of at least X − C − G. Thus the deal can be struck if and only if G+H −B >X −C −G (This assumes the Pigou tax is paid to a third party. If the Pigou tax is paid to the neighbors, then the inequality becomes G + H − B > X.) b) Moving creates an additional social gain of C + D + G + H in the widget market, so moving is efficient if and only if C +D+G+H >X 13–23 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 24. In the diagram below, you can initially charge firms the amount F − C − D − E from each firm. After you impose the new pricing system, you collect B + F . So the new pricing system is better for you. It’s also socially more efficient, as social gain increases by E. The losers are the consumers, whose surplus falls from A + B + C + D to A. Price MC (social) MC(private) A E B CD H F G Demand Quantity 25. a) Drivers gain A + B + C and pedestrians lose B + C + D so the social gain is A − D. b) Drivers gain A and pedestrians neither gain nor lose so the social gain is now A; that is, social gain increases by D. c) Because now pedestrians will have no incentive to avoid accidents. d) Without air bags, drivers medical costs are G + H + L + M + Q + R. With air bags, their medical costs are Q + R + S + T . So you’d want to compare G + H + L + M with S + T . e) Without air bags, the social gain (computed in part a)) is A − D. With air bags, the social gain is A + B + C + G + H + I − P . So air bags improve social gain if and only if B + C + D + G + H + I > P . f) Drivers would be willing to pay G + H + I + L + M + N + O for airbags. g) Drivers will now be willing to pay G + H + I + L + M + N + O − X, where X is the amount of the tax. Thus they will buy airbags if and only if G+H +I +L+M +N + O − X > Y where Y is the cost of an airbag. On the other hand, the social benefits of air bags exceed their costs if and only if B +C +D +G+H +I −P > Y . To make sure that drivers buy air bags if and only if their social benefits exceed their costs, we want G + H + I + L + M + N + O − X = B + C + D + G + H + I − P ; equivalently X = L + M + N + O − B − C − D + P . This can be simplified further if you notice that L = B and M = C +D; thus the optimal tax is X = N +O +P . A more direct route to the same conclusion is this: Airbags increase the externality from reckless driving by N +O+P (from B+C +D to L+M +N +O+P = B+C +D+N +O+P ); to get drivers to internalize that additional externality, we have to charge them an equivalent amount. 26. True. Suppose that driving carefully to the drug store creates an expected accident loss of $10 to someone else (because even careful drivers sometimes have accidents) but the value to you of the trip is only $5. The trip is inefficient. But if you are a careful driver, the negligence standard protects you from liability, so you go anyway. 13–24 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 27. The advantage is that everyone in the vicinity of the accident has a full incentive to take any cost-justified measure that would avert the collision. The disadvantage is that people will stay away from areas where accidents are common, which may be inefficient. 28. a) A. C − B + A. b) C − D. c) A < C − D. C − B + A < C − D. d) Social gain from completion < social gain from breach, or D − B + A < 0. e) Expectation damages, since the inequality in part d) is equivalent to the second inequality in part c) 29. It does not follow that expectation damages are the appropriate standard. Al- though expectation damages lead to efficient breaches of contract, they might not lead to an efficient number of contracts being signed in the first place. A full anal- ysis of the problem must account for the fact that the number of contracts signed will vary depending on the legal standard that is in force. Such a full analysis is provided by David Friedman in “An Economic Analysis of Alternative Damage Rules for Breach of Contract,” Journal of Law and Economics 23 (1989). Fried- man establishes that either expectation or reliance damages could be more efficient, depending on circumstances. 13–25 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Fourteen: Common Property and Public Goods General Discussion 1) Ken McLaughlin has given me the solution to the check-splitting problem in this chapter. (The problem concerns a group of ten diners who are not able to get separate checks for their meals. Thus the private cost of ordering a $10 dessert is only $1, and the number of desserts ordered is greater than optimal.) The solution: Each diner pays the entire check! Now a diner will order a $10 dessert if and only if it is worth at least $10 to him. Why should diners agree to such a scheme? Since every dish that gets bought is paid for 10 times, the restaurant will be willing to pay the diners a large lump sum in exchange for their eating there. A similar principle applies in labor economics. Since no employee of General Motors can be monitored perfectly, he will sometimes work less hard than is optimal from the firm’s point of view. A profit-sharing plan is a very poor solution: if the firm has 10,000 employees then a given worker will put forth $1 worth of extra effort only if it increases profits by $10,000. The solution: Each employee should receive in salary an amount equal to the corporation’s entire profits. Now the opportunity to increase profits by anything more than $1 will elicit that $1 worth of extra effort. Where does all the money come from to pay these enormous salaries? Each employee pays a large lump sum to General Motors in order to “purchase” his job. Unfortunately these schemes only work if all diners (or all workers) are iden- tical, so that the same lump sum payment is appropriate for each. 2) The check-splitting solution may not be stable. Once the diners have come to the restaurant, a diner can say to the manager: “I value that $10 dessert at $3. If you give it to me for $2, you will collect $20 and make a clear $10 profit. Otherwise I won’t buy it.” If the diner is credible, the manager will agree, and the outcome is still inefficient. Of course, foreseeing such bargaining, the restaurant is unwilling to pay large lump sums to attract diners. It seems that we need some mechanism to rule such bargains out. Likewise at GM, management could bribe individual workers to do a bad job! 3) A potential solution to the public goods problem is for one agent to privatize the public good by acquiring all of the assets whose values are affected by it. For example, suppose that a streetlamp will raise the value of each of the 20 houses on the street by $10 apiece. The streetlamp costs $100 to build. For the usual reasons, no individual finds it in his interest to contribute. In this case there is a profit opportunity: one entrepreneur buys all of the houses on the street, builds the streetlamp, and resells the houses for a total of $200 more than he paid for them. The market provides the public good in the optimal quantity with no need for collective action. Likewise, when a group of retail stores are located near each other, security and clean-up for the surrounding area are public goods. In principle, the public good problem can be solved by a single entrepreneur buying all of the property, providing the desired services, and leasing the property back to the original tenants (at a rental rate that reflects the value of the services being provided). You can point out to your students that shopping malls are a striking example of precisely this principle in action. 4) For an interesting historical account of some partial private solutions to the 14–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. public goods problem, put your students onto Coase’s paper on “The Lighthouse in Economics.” It is reprinted in his book “The Firm, the Market and the Law.” 5) The public goods discussion focuses, as is traditional, on non-rivalrous and non-excludable consumption goods. For an interesting continuation of this line of thought, you can tell your students about Paul Romer’s discussion of non-rivalrous and non-excludable production goods, in the May 1990 American Economic Re- view . 14–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. The residents of Alphaville and Betaville are identical in their tastes and op- portunities, except that those in Alphaville hate crowds quite intensely while those in Betaville consider crowding to be only a mild annoyance. Each town has a free aquarium. True or False: Crowding at the Betaville aquarium has a lower social cost than crowding at the Alphaville aquarium. 2. At the Marketplace Mall water fountain, there is always a line to get a drink. a) What determines the length of the line? If all mallgoers have an equal demand for water, what is the social value of the water fountain? b) The mall management has decided to try an experiment: From now on, the newest arrival at the water fountain will be allowed to go directly to the front of the line instead of the back. Is this a social improvement? 3. Suppose you have invented a delicious new soup, but you are worried that if you try to market it, Campbell’s, Lipton and the other major soup manufacturers will copy your idea. What can you do to protect yourself? (The problem above is based on an idea of Jack Hirshleifer. The solution is to buy stock in Campbell’s and Lipton and then give them your soup idea for free. I include this here because it illustrates the same general principle that is involved when a private entrepreneur purchases a collection of neighboring properties, provides a public good, and then resells the properties at their new, higher value. The public good here is the soup recipe, and the neighboring properties are the soup company stocks.) 14–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 14–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 14 1. a) 8. 56. 0. b) 4 or 5. 40 c) 8 or 10 fish per day. 2. a) With free entry, 2 miners work in Mine A and 5 in Mine B. (Miners must allocate themselves so that they are indifferent between the two mines.) The social optimum consists of 3 miners in Mine A and 4 in Mine B, for a total output of 132 nuggets per day. An entry fee of 5 nuggets per day in Mine B achieves this optimum; alternatively, so does an entry fee of 1 nugget per day in Mine A and 6 in Mine B, or 2 in Mine A and 7 in Mine B, etc. The wicked queen charges 16 nuggets per day to enter Mine A and 21 to enter Mine B, thereby achieving the social optimum (and grabbing all the surplus for herself). 3. a) If the narrow road is more pleasant than the wide road, drivers on the wide road will switch to the narrow road, making the narrow road less pleasant; this continues until the two roads are equally desirable. If the narrow road is less pleasant than the wide road, drivers on the narrow road will switch to the wide road, making the narrow road more pleasant; again this continues until both roads are equally pleasant to drive on. b) When one driver is added to the narrow road, the private marginal benefit (to the new driver) is the same as when one driver is added to the wide road. This is because we already know that both roads are equally pleasant to drive on. However, the marginal social benefit from adding a driver to the narrow road is equal to his marginal private benefit minus the costs he imposes on all other drivers by making the road less pleasant. Thus the marginal social benefit from a driver on the narrow road is less than from a driver on the wide road. c) A planner could move one car from the narrow road to the wide road. Since the marginal social benefit is greater on the wide road than on the narrow one, total social benefit must increase. Another way to see this is that the driver who is moved was already indifferent about which road to be on, so he neither gains nor loses, but all of the other drivers on the narrow road gain from his departure. d) The planner continues until the marginal social benefit from adding a driver is the same on both roads. If drivers entering the narrow road had to pay an entry fee equal to the ex- ternality that they impose on other drivers, they would completely internalize the externality. Drivers would voluntarily stop entering the narrow road as soon as the marginal social benefit from adding a driver is the same on both roads. If the narrow road were owned, the owner would set exactly the optimal entry fee. This is so for the same reason that the giant who owns the forest sets the optimal entry fee. Make sure that you can reproduce the argument in the context of the present question. 14–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 4. a) Apples per dwarf F { Cost of entry A Q Q0 Dwarfs 1 B The line A denotes apples picked per dwarf and the line B denotes the marginal contribution to the apple harvest. The reason the latter lies below the former is because of the crowding effect. This effect causes the marginal contribution of each new dwarf to be smaller then the actual size of his harvest because he has a negative effect on the dwarfs who are currently picking apples. b) Prior to the giant, Q0 enter. The giant sets a fee of F so that Q1 enter. c) Apples per dwarf opportunity cost T { C D E F A Q Dwarfs 1 Q0 B The area C + D + E + F is the producer surplus and the number of dwarfs which enter without any fee is Q0 . d) In the graph for part (c), Q1 is the optimal number of dwarfs and T is the optimal fee. e) Not unless the revenues from the giant are redistributed in some way back to the dwarfs. Otherwise their producers’ surplus falls to F . With the giant’s welfare taken into consideration the society is made better off. (It is also possible that the giant would voluntarily undertake improvements to the forest that could increase both his own welfare and the dwarfs’; this would be reflected by an outward shift of the A curve.) 14–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. f) Suppose that when X dwarfs enter the forest, they pick a total of A − BX apples and the marginal dwarf has an opportunity cost of CX (where A, B, and C are positive constants). In the following diagram, the giant sets an entry fee of T to maximize the area F + G = T X0 , whereas under free entry the number of dwarfs entering is X1 : Apples per dwarf CX { T F G H I A-BX X X Dwarfs 0 1 A A We can compute X0 = 2(B+C) and X1 = B+C . With a monopoly giant, 2 A A2 C the giant gains area F + G = 4(B+C) and the dwarfs gain area I = 8(B+C) 2. A2 C With free entry, the dwarfs gain area G + H + I = 2(B+C)2 . Thus the giant is welfare-improving if and only if A2 A2 C A2 C + 2 > 4(B + C) 8(B + C) 2(B + C)2 or equivalently 2B > C. Since 2B is the absolute slope of the “marginal apple harvest” curve (not shown in the picture) and C is the absolute slope of the dwarfs’ marginal cost curve, the result is proved. 5. False. Any social gain must result from differences among fishermen. If they are identical, then there is no social gain regardless of their ability. 6. True. If the total population is Q and everyone there visits the aquarium, the value of a visit still exceeds the cost of entry. The shaded area C + D + E is undissipated rent. Note however that if only Q0 visitors came to the aquarium, the rents (A + B + C + D) would be greater. $/visitor A B C DE Value of a visit Crowd size Q' Q Social Marginal Value 14–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 7. True. Competition maximizes social gain, whereas a monopolist maximizes his private gain. But with all consumers identical, all rents go to the owner. Therefore the two conditions are equivalent. 8. a) For anyone with a T.V. this is non-excludable and non-rivalrous. b) Excludable and Non-rivalrous. c) Neither since it cannot be consumed by more than one person and it is costly to obtain. d) Both non-excludable and non-rivalrous as long as the crowds are not excessive and the park is free. e) Non-excludable when there are no crowds and rivalrous since one person drinking implies another cannot. 9. Acting in your own self interest leads you to become a free rider. It is in your best interest to let others pay for the programming and then watch it for “free.” Actually giving money to the station implies some altruistic behavior. 10. False. The new subway makes the north side more attractive to many individuals and presumably the rents for apartments will be bid up. 11. a) If the price were larger everyone would move to Cleantown and if the price were less everyone would move from Cleantown to Grimytown. The demand curve is as follows: Price per S apartment $200 D Apartments Q0 Q 1 where QT = QC + QG is the total number of apartments in Grimytown plus those in Cleantown and the shaded area is the producer surplus. There is no consumer surplus because the demand curve is flat. b) The shaded area is the increase in producer surplus as well as the increase in social gain. There is still no consumer surplus. Only the apartment owners gain. Price per S apartment $300 D' $200 D Apartments Q0 Q 1 14–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 12. a) Price per S apartment CS $200 PS D Apartments QG QT The demand curve for Grimytown apartments is downward sloping since those who value the pollution at less than $100 are willing to pay more for the apartment and thus gain consumer surplus. The area CS is consumer surplus and the area PS is producer surplus. b) Price per S apartment A B C D $200 E Apartments The movement to the flatter demand curve is the result of the clean air stan- dards. Consumer surplus changes from A+C to A+B; this could be an increase or a decrease. Producer surplus increases from E to C + D + E. Social gain increases by B + D. If we were to assume an upward sloping supply curve these results may be altered although there would still be a social gain. 13. Yes. Every bidder submits a truthful bid. Suppose you are a bidder who values the car at $100. You can reason thus: If the second highest bid is less than $100, then I want to win this auction, because I will get the car for less than $100. If the second highest bid is over $100, then I want to lose this auction, because then the car would cost me more than $100. So: I want to win if the second highest bid is less than $100; I want to lose if the second highest bid is more than $100. How do I insure that I get what I want? Answer: Bid $100.” Incidentally, this auction mechanism is essentially equivalent to the traditional English auction in which buyers call out successively higher bids until only one remains. The final bidder will be the one who values the item most, and the amount he pays for it will be just a hair over the second highest bid. 14. The Bob/Carol/Dale example from the text works here too. Replace “streetlamp” with “pollution control” and use the same mechanism. 14–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Answers to Numerical Exercises N1.a) N · (300 − N 2 ) − T C where TC is the total cost of the bridge. b) 17. 187 (The social gain is non-zero only because it is not possible for a fractional number of people to cross the bridge.) c) 10 1 d) N = (300 − T ) 2 or the lowest integer closest to N . e) T = 200 (this maximizes N · T where N is determined as in part d). The benefit of $2000 per day go to whoever collects the tolls. N2. When the last dwarf enters the forest, he reduces the number of apples picked by each other dwarf by some amount ∆A. Each of the Q dwarfs already in the forest experiences this loss, so the full external cost of the dwarf’s entering is given by Q · ∆A. Since exactly one dwarf has entered, we can write ∆Q = 1, allowing us to write the external cost as Q · ∆A . ∆Q But this last expression is the same as A/η. 14–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Fifteen: The Demand for Factors of Production Teaching Suggestions 1) Students find this material considerably more difficult than anything that has come before. It helps to stress that there are only a few major points: the relationship between demand and marginal product, the construction of the long run demand curve, and the fact that the sum of factor payments precisely exhausts the firm’s income. Unless your students are very strong, I would stay away from such esoterica as regressive factors and the impossibility of Giffen factors (though the latter is essentially proved in Exhibit 15–9 for those who want it). 2) In covering the topic of monopsony, the NCAA is a favorite example. Here we have a cartel of buyers, paying monopsony wages for athletes. The monopsony wage, as illustrated in Exhibit 15–10, is lower than the competitive wage, and there is no doubt that college athletes are paid less than they would be if colleges were free to bid for their services. Just as the members of a sellers’ cartel have an incentive to cheat by offering lower prices, so the members of a buyers’ cartel have an incentive to cheat by offering higher wages. As with a buyer’s cartel, there needs to be a mechanism for punishing cheaters, and the vast majority of your students will be familiar with some of the mechanisms available to the NCAA. 3) In covering monopsony, you might want to mention the possibility of bilat- eral monopoly, where the rents available to a particular buyer–seller combination are greater than to any other combination. Example: a specialized scientist whose research meshes perfectly with the work in progress at one particular university, or a sports player whose particular skills are especially needed by a particular team. Here (despite the considerable amount of research effort that has gone into bar- gaining models in the past several years) all we can really say is that the wage will be at some level that divides the excess rents between buyer and seller, and that we can’t predict exactly what the division will be. 4) If you want an example of a company town, the best one I know is Pullman, Illinois (now incorporated into Chicago), built and completely managed by the Pullman railroad car company and populated by its employees. 5) For students who are using the calculus appendix, you have an opportunity to illustrate how economic theory can be used to reveal a truly remarkable and non-intuitive fact about the behavior of firms. Let L(PL , PK ) and K(PL , PK ) be the quantities of labor and capital that the firm employs when the wage rates of labor and capital are PL and PK . Then ∂K ∂L = . ∂PL ∂PK That is, the change in capital employment that results from a rise in the wage rate of labor is equal in magnitude to the change in labor employment that results from a rise in the rental rate on capital. It is by no means clear to the untrained intuition that these quantities should have the same sign, let alone that they should be equal . Depending on whether you are using calculus in class, this is a fit topic either for a lecture or for a challenging homework assignment. Either way, I would stress to students how remarkable it is that such a thing could fall out of our theory. 15–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. If you assign it for homework, you might or might not want to give the following extremely helpful hint: first prove that ∂K/∂PL = ∂ 2 π/∂PL ∂PK , where π(PL , PK ) is the profit earned by the firm. 15–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Suppose that in the short run skilled labor is a fixed factor and unskilled labor is a variable factor. A minimum wage law is passed which sets the minimum legal wage at a level above what unskilled workers now earn but below what skilled workers now earn. What is the effect on the wages of skilled workers? Does your answer depend on whether skilled and unskilled labor are substitutes or complements? 2. True or False: A rise in the wage need not lead to any reduction in employment if producers are able to pass the increase on completely to their customers. 3. True or False: If firms earn zero profits, then the long run labor demand curve is always more elastic than the short run labor demand curve. Remark: This problem is hard and should not be assigned lightly. Students who have solved problems 11 and 2 in the textbook can combine their solutions to obtain the (affirmative) solution to this one. But few students will be so successful. 4. Suppose that capital and labor are substitutes. True or False: In the short run, a firm that has a lot of machinery will employ more workers than a firm that has less machinery. 5. True or False: In a competitive industry with a factor price effect, the in- dustry’s upward-sloping long-run supply curve is also the social marginal cost curve. But if the firms in the industry are able to act as a monopsony in the labor market (while remaining competitive in the output market) then the industry supply curve lies above the social marginal cost curve. 6. Suppose that the government undertakes a successful campaign to deport all illegal aliens who are holding jobs in the U.S. Use a graph to show the gains or losses to American workers, American owners of capital, and Americans as a whole. 7. Most of the people living on the north side of Boomtown are apartment dwellers who commute into the center of town every day to go to work. The city is considering building a new subway line between the north side and the center of town. True or False: Since the landlords all live on the south side of town, and the employers are all in the center of town, all of the benefits from the new subway will go to the working people on the north side of town. 15–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 15–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 15 1. If the wages of apple pickers are measured in “apples per hour”, this is true. But if the wages of apple pickers are measured in “dollars per hour” where dollars represent goods other than apples, then this is false. The rise in demand raises the marginal revenue product of labor as in Exhibit 15-3a. 2. True in the short run; false in the long run. Since the demand curve is vertical, the quantity produced won’t change. Thus in the short run, employment of labor won’t change. In the long run, however, it is possible to produce the same quantity of output with a different combination of capital and labor, and the firm will do so. For example, if the demand curve is vertical at a quantity of 3, and if the wage rate increases from PL to PL0 , then the firm moves from point A to point B in the following diagram, reducing its employment of labor from LA to LB . Capital Slope = P' /P' L K B A Slope = P /P L K LB LA Labor 3. True. A fall in the wage rate from W to W 0 increases employment from L to 0 L in the short run. Since capital and labor are complements in production, this increase makes capital more productive at the margin, so the demand for capital 0 shifts out from DK to DK in the second panel. This causes employment of capital 0 to rise from K to K , which increases the marginal productivity of labor, giving 0 the new short run labor demand curve DL in the first panel, and employment rises 00 further to L . Since employment rises more in the long run than in the short run, the long run labor demand curve must be more elastic than the short run labor demand curve. $/unit $/unit w R w' D' L D' K DL D K Labor Capital L L' L'' 15–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 4. Wage Rental Rate rate MRP w L 1 LongRun Labor Demand R0 w 0 MRP' L MRP K Labor K K K Capital L L L L 3 2 1 0 0 1 2 Initially, the wage rate of labor is W0 and the rental rate on capital is R0 . The firm hires L0 units of labor and K0 units of capital. Now the wage rate rises to W1 . In the short run, the firm reduces its employ- ment to L1 . Assuming that capital and labor are substitutes in production, this causes the M RPK curve to rise to the level of the middle curve in Panel B. The firm increases its capital employment to K1 . The increased capital employment lowers the M RPL curve to the level of the dashed curve in Panel A, causing labor employment to fall to L2 . This raises the M RPK curve still further, causing capital employment to rise to K2 , and the process repeats. Eventually, the M RPL curve settles at the new level M RPL0 . Here the firm hires L3 units of labor. Thus the long run labor demand curve (through (W0 , L0 ) and (W1 , L3 )) is more elastic than the short run demand curve M RPL . 5. a) The argument in Exhibit 14–9 shows that M RPL0 must lie to the left of M RPL . (The higher wage rate reduces labor employment, which pushes M RPK leftward, which pushes M RPL leftward.) Thus when the wage rate goes up, the new long- run quantity of labor employed, being read off M RPL0 , must be less than the old quantity of labor employed. That is, long run labor demand slopes downward. b) The argument in problem 3 shows that M RPL0 must lie to the left of M RPL . (The higher wage rate reduces labor employment, which pushes M RPK rightward, which pushes M RPL leftward.) Thus when the wage rate goes up, the new long- run quantity of labor employed, being read off M RPL0 , must be less than the old quantity of labor employed. That is, long run labor demand slopes downward. 6. True. When the wage rate goes up, firms employ less labor than before. Since labor is a regressive factor, this shifts their marginal cost curves downward, leading to a rightward shift in industry supply. This in turn leads to a fall in the price of output, which is an additional reason for firms to reduce their quantities supplied and consequently their employment of labor. For this reason, the industry supply curve incorporates a greater scale effect than the sum of the individual firms’ supply curves, and this makes it more elastic. 7. True. The reason why isocosts are straight lines is that their equations are given by PK · K + PL · L = C where PK , PL and C are constants. For a monopsonist in the labor market, PL is not constant: It varies with his employment of labor. Thus the isocosts are not straight lines. 15–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 8. Wage rate MCL A S C B F D E G H MRP L L Lc Labor Competitive Labor Market Monopsony Consumer’s Surplus (to firm) A+B+C A+B+D+E Producers’ Surplus (to workers) D+E+F+G+H G+H Social Gain A+B+C+D+E+F+G+H A+B+D+E+G+H Deadweight Loss C+F 9. True. In the art for problem 8, suppose that a minimum wage is set at WC . Then M CL essentially becomes flat at WC , and the optimal amount for the firm to hire is LC . This is analogous to the fact that a price control on a good sold by a monopolist can increase his output. 10. a) Wage rate A B MRP L L Labor The firm’s total revenue is A+B, of which B goes to labor. Thus (assuming firms earn zero profits), A goes to capital. A is the revenue earned by capital, but if capital is supplied perfectly inelastically, then all of its revenue is producers’ surplus. Thus the producers’ surplus earned by capital is area A. 15–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. b) Wage rate Ls L's C w D E w' F G MRP L Labor The labor supply increases from LS to L0S . The wage rate falls from W to W 0 . American workers lose D, American owners of capital gain D+E, and South Korean workers gain G. (That is, the producers’ surplus ofAmerican workers falls from D+F to F, the producers’ surplus of American owners of capital rises from C to C+D+E—this uses the result of part a)—and, since the total surplus to all workers is F+G with Americans getting F, South Koreans must get G instead of nothing.) c) Since workers lose only D while capital owners gain D+E, it unambiguously helps. 11. True. As the graph shows, a rise in the wage from W to W 0 causes the revenue earned by capital to fall from A to A+B. MPL A w' B w MPL Labor 12. True. Suppose that labor and capital were substitutes in production. Then an increase in the wage rate would cause an increase in the marginal product of capital 0 from M PK to M PK in the following graph. The revenue earned by capital would increase from D to D+F+G. But we already saw in Problem 10 that the revenue earned by capital goes down, not up. Thus capital and labor cannot be substitutes in production. 15–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. MPK E C F D G MP' K MPK Capital 13. The minimum wage law will eliminate much unskilled labor from the market. Apparently the union believes that this will increase the demand for skilled labor; thus skilled and unskilled labor must be substitutes in production. Temporarily divide inputs into “unskilled labor” and “all other inputs,” where “all other inputs” comprises both capital and unskilled labor. Arguing exactly as in problem 11, we see that unskilled labor and all other inputs must be complements. That is, a fall in the employment of unskilled labor increases the demand for all other inputs on average. On the other hand, a fall in the employment of unskilled labor increases the demand for skilled labor. Thus a fall in the employment of unskilled labor must decrease the demand for capital. In other words, unskilled labor and capital must be complements. It follows that the owners of capital will oppose the minimum wage. 14. The gains go to the factors that are in fixed supply. The one factor that is most clearly in fixed supply is land in the no-tax zones. (Although even this is less clear than it seems—if it is possible to build upward, then the amount of “land” available for use in the area can be increased without limit). Firms can come and go, customers can come and go, producers of machinery and workers can come and go, so in the long run they gain very little from the policy. Answers to Numerical Exercises N1.a) The slope of an isocost is −W/R. In long run equilibrium, the slope of the isocost is equal to the slope of the isoquant, so that W K − =− . R L Thus we can write W ·L K= , R R·K L= . W b) r R L=Q· , W r W K =Q· . R c) √ W ·L+R·K =2·Q· W · R. 15–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. √ d) The long run marginal cost √ is flat at 2 · W · R. e) Price = marginal cost = 2 · W · R. It is possible to answer this question without any information about demand √ only because the firm’s marginal cost curve is flat. f) Labor receives W · L = Q · R · W . √ Capital receives R · K = Q · R · W . √ The firm’s total revenue is 2 · Q · R · W , which exactly covers the cost of hiring labor and capital. N2.a) Suppose that each firm produces q units of q output using qk units of capital and l units of labor. As in N1b, we get l = q · W , k = q · W R R . Adding up over all firms in the industry we get r R L=Q· , W r W K =Q· . R b) r R Q· = W, W r W Q· = 4 · R. R Dividing one equation by the other and solving, we get W = 2. R c) Since each firm must be on its own supply curve, N1e) tells us that √ P =2· W · R. Substituting the expressions for the factor supply curves, we get p √ P = 2 · L · K/4 = L · K. p Combining √ the results of N2a) and N2b), we can replace L by Q · 1/2 and K by Q · 2 to get P = Q. The latter is the equation for the long run industry supply curve. d) Combining the demand curve with the supply curve just derived, and using the other results that were obtained alont the way, we get Q = 750 P = 750 p L = 750 · 1/2 √ K = 750 · 2 p W = 750 · 1/2 √ R = 750 · 2/4. 15–10 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. e) Producers’ surplus in the output market is the triangle bounded by the price axis, the line P = 750, and the supply curve Q = P , or 281250. p Producers’ surplus to labor is bounded by the wage axis, the line W = 750 · 1/2 and the labor supply curve L = W , or 140625. Producers’ √ surplus to capital is bounded by the rental rate axis, the line R = 750 · 2/4, and the capital supply curve K = 4 · R, or 140625. All of the firms’ surplus is paid out to factors. Firms earn zero profit, as we already knew from N1f). 15–11 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Sixteen: The Market for Labor General Discussion 1) I had originally intended to include a section on unemployment, but became convinced that the topic was too complex—and perhaps also too “macro”—to be dealt with here. However, if you cover labor markets, the subject may come up in class. It is important to distinguish between voluntary unemployment (people choos- ing not to work because the going wage is insufficiently high to attract them) and involuntary unemployment (people who can not find a job at the going wage). The distinction is subtle, both empirically and theoretically. Putting aside the difficult empirical questions, it is already hard just to pin down the definition of involuntary unemployment. Chuck Whiteman once told me that he was involuntarily unemployed as a quarterback for the Los Angeles Rams, in the sense that, given the going wage for that position, he preferred to supply more hours than he was able to. Clearly we must control for abilities. It has been suggested that you are involuntarily unemployed when you are identical to your neighbor in every way, except that he’s working, you’re not working, and he’s happier than you are. This seems a reasonable start. The next problem is to explain why there should ever be involuntary unemploy- ment, since our most basic models predict that competitive markets in general, and labor markets in particular, should achieve a price at which the quantity supplied and the quantity demanded are equal. Here we enter the realm of macroeconomics, and I think it is fair to tell students that they have now stepped beyond the bounds of the present course and will just have to wait a semester before they can find out what happens next. But there remain a few interesting tidbits we can throw out. One is that we really don’t know how much unemployment is voluntary, and that for all anybody really knows, it might all be voluntary. Half your students will have “involuntarily unemployed” relatives to hold up as counterexamples. Without getting into the unsavory details of their family lives, you can tell them that “all” does not mean literally every single case, but rather that models in which all unemployment is assumed to be voluntary fit the observed facts within reasonable statistical limits. The model of unemployment in section 9.2 is an example (in fact the archetypal example) of an attempt at such a model. An alternative you can mention is efficiency wage theory, which also appears in Chapter 9: Employees can not be monitored at all times, and are sometimes able to shirk or to otherwise steal from their employers. In order to discourage such behavior, the employer must be able to threaten a substantial punishment if the employee is caught. Since the harshest available punishment is to fire the employee, the only way to have a reasonable deterrent is to make employees feel that they have a lot to lose if they are fired. This requires paying them a wage higher than the one that clears the market. Since the wage that gets paid is above equilibrium, there must be some workers who can not find work. Another topic you can mention is the role of unemployment insurance and the system of experience ratings. An employer’s experience rating determines the percentage that he must contribute to the payment of his former employees’ un- employment compensation. It is usually an increasing function of the frequency with which the employer has terminated workers in the past. The fact that the employer does not pay the full compensation invites fraud: I, an employer, hire 16–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. you, my friend who really doesn’t want a job, fire you, and we split that portion of your unemployment check that comes from the government. The potential for such scheming has been put forth as an argument for 100% experience ratings. If you find yourself discussing problems of measurement, students are amused by the following observation: If you take a random sample of unemployed people and ask them how long they have been unemployed, the average response will usually be a gross overestimate of the average time that people spend unemployed. Reason: people who are unemployed for very short times are quite unlikely to happen to be unemployed at the particular moment when you are taking your survey. Thus they get undercounted. Finally, to shake your students up a bit, point out to them that unemployment is of course ceteris paribus a good thing. If we could all have our present incomes without working, we would be much happier. Bastiat exploits this in a number of essays (all of which make delightful reading assignments): Robinson Crusoe works 12 hours a day to make a fishing net, until one day some netting in perfect condition washes up on shore. Robinson is thrilled at first, but then realizes that if he uses this netting he will be unemployed; therefore he throws it back. That sort of thing. 16–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Dick and Jane each recently received substantial inheritances when their aunt passed away. In response, Dick started working fewer hours but Jane started working more. Next week, Dick and Jane’s wage rate is going to fall. a) Can you say for sure what will happen to the number of hours Dick works? Illustrate your answer with indifference curves. b) Can you say for sure what will happen to the number of hours Jane works? Illustrate your answer with indifference curves. 16–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 16–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 16 1. True. This change corresponds to a parallel shift in the budget line that relates consumption to labor, and so there is only an income effect. Assuming that con- sumption and leisure are both normal goods, the individual will choose to have more of each. 2. Jack’s budget line has a “kink” at eight hours, and we know that he choose point A, on the steeper part of the budget line. Jill’s budget intersects the vertical axis at the same place where Jack’s does (she has the same assets as Jack), has slope W 00 , and is tangent to the same indifference curve on which point A lies (she has the same tastes as Jack and is equally happy). The only way to draw such a picture is as shown below, with W 00 larger than W but smaller than W 0 , and with Jill choosing point B, where she works fewer than 10 hours. Consumption A slope w'' B slope w' 8 10 Labor slope w 3. Before going to college, everyone has the budget line labeled N (for “non- graduate”) in the diagram below. They choose point A. Anyone who attends college gets a new budget line G (for “graduate”). The slope of G is determined by the wage available to college graduates. The level of G is determined by the requirement that everyone be indifferent to attending or not attending college. The reason for this is that if, for example, everyone preferred to attend college, people would begin enrolling, bidding up the price of tuition until everyone was indifferent again. Thus G must be tangent to the indifference curve containing A. The tuition cost is the amount of consumption that one sacrifices in order to attend college, which is the distance T in the diagram. We can see from the diagram that college graduates, who choose point B must work more hours than non-graduates. Thus the answer to part b) is false. 16–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. G Consumption N B A { T Labor 4. Dick’s non-labor income increased. Since we know he works more, he must view leisure as an inferior good. Therefore, the wage rate increase leads to an income effect of working more hours and the substitution effect of working more hours. Since these effects move in the same direction, Dick works more. 5. Unlike Dick in problem 4, Jane views both consumption and leisure as normal goods. Therefore an increase in her wage has an ambiguous effect on hours worked. See Exhibit 15–5 for a graphical explanation. As the text mentions, if the wage was very low to begin with, an increase in the wage leads to an increase in labor supplied. 6. a) Just like Exhibit 16-5A in the text, except that point Q is to the right of Q0 . b) No; Q is to the right of Q0 so it must be to the right of P . Therefore Horace’s labor supply curve must slope up. 7. a) In the diagram below, Hortense’s initial budget line is the line through O and P . Her new budget line consists of the segment OP and the halfline beginning at P and continuing through Q. 16–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Consumption Q P Labor O 35 (Hrs/Week) b) False. She now chooses point Q and works more hours. 8. a) Car wash attendants must be indifferent between washing cars and the next best occupation. Therefore the basic wage rate must drop. The new budget line is shal- lower than the old one out to 40 hours, then becomes steeper. The new optimum could occur either to the right or left of the original, so the answer to part b) is false. 9. False; the opposite is true. When the wage increases, both men tend to work more hours in response to the substitution effect. However, the man who earns most of his income in wages also feels an income effect, leading him to work fewer hours in opposition to the substitution effect. The man whose income is mostly from other sources feels very little of this moderating income effect. 10. False. If workers come to enjoy their jobs, the supply curve of labor shifts out, the quantity supplied increases, and therefore the marginal product of labor decreases. So workers who enjoy their jobs more are less productive at the margin than those who enjoy them less. 11. The wage rate falls, less labor is supplied to the marketplace, and a given indi- vidual might supply either more or less labor than before. 12. a) The demand for labor will decrease since there aren’t many factories left who will employ. b) The workers’ non-labor income falls through low returns on their stock due to damage. Consequently, the workers will want to work more hours, implying an increase in the supply of labor. c) Assuming case (b) above holds, wage falls due to a demand decrease and supply increase. The amount of labor supplied to the marketplace in equilibrium can go either direction; it depends on whether the demand curve or supply curve shifted more. Likewise the amount of labor supplied by any individual can go either direction. 13. The wage rate rises, less labor is supplied to the marketplace, and a given (sur- viving) individual supplies more labor than before. 14. First, labor supply is reduced as only a half of the workers are available. However, there is also a less demand for the good as only half of the demanders are alive. Therefore, demand for labor also falls. The effect on the wage rate depends on the magnitude of the demand and supply curve movements. The amount of labor supplied to the marketplace falls. The change in labor supplied by any individual could go either way as we do not know what happened to the wage rate. For example, a wage increase could imply more hours worked. 15. False; capital could either gain or lose. The fact that the level of output is 16–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. fixed means that for some reason society must operate on the single horizontal line illustrated below. The rise in the marginal productivity of labor raises the total product curve from T P to T P 0 , and the value of capital changes from A to B. In the illustration, B is greater than A (so that capital benefits) but it is possible to draw the picture so that A is greater than B (make T P 0 much steeper), in which case capital would lose. Output TP' TP B A Labor 16. This has no effect on the demand for labor, but increases the supply as in problem 1. Thus the wage rate drops and the amount of labor employed increases. 17. The demand for labor falls equally in both cases. The supply of labor could decrease dramatically as a result of intertemporal substitution in case (a), while it certainly increases as a result of the income effect in case (b). In case (a), output and employment are down, while in (b) employment could be up (though output is certainly down since choose less consumption when they are poorer.) The wage rate is down in (b) by more that in (a). 18. In either case the supply of labor shifts leftward due to the income tax. On the other hand, if we assume that people feel poorer when they are taxed (because they value whatever the government buys for them less than they value what they would have bought for themselves), then there is an income effect that shifts the supply of labor rightward, by a small amount in the case of a temporary tax and by a large amount in the case of a permanent one. In the temporary case, there is also leftward pressure due to intertemporal substitution. We can conclude that labor supply shifts leftward quite far in response to a temporary tax, less far in response to a permanent tax. The temporary tax leads to a large rise in (pre-tax) wages and a large fall in employment and output. The permanent tax has smaller effects in the same directions. 19. True, because education is a form of investment in capital. Since the tax break ap- plies to other forms of investment but not to education, investors tend to substitute towards those other forms of investment. 16–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Seventeen: Allocating Goods Over Time General Discussion Sections 17.1 and 17.2 develop the student’s intuition for the meanings of in- terest rates and present values, separate from any discussion of how those variables are determined in equilibrium. I think that these two sections will be popular with business students. They can be used at almost any point in the course. Section 17.3 turns to markets and equilibrium, developing the interest rate as the price of current consumption. Demand is derived from indifference curves, giving additional reinforcement to the basic ideas of consumer theory. In this section, I take supply to be exogenous, making the model as simple as possible. The student is then invited to try a variety of exercises in comparative statics (a la Exhibits 17-8 and 17-9), reinforcing yet another set of important skills. In section 17.4, investment is introduced to the model, leading to a more sophisticated model of the supply curve and another set of exercises in comparative statics. I have chosen to cover the topic of government debt and its effect on market interest rates. Although government finance is widely perceived as a ”macro” topic, the basic issues are all really micro issues, and it is a subject that grabs student attention. The Ricardian Equivalence Theorem – that government debt, in certain cir- cumstances, has no real effects – is broken down into two separate propositions. The first is that if government debt does not affect interest rates, then government debt is a matter of no consequence. This, I think, will be entirely non-controversial among economists, although it surprises students, and the simplicity of the argu- ment pleases them. The second is that government debt does not in fact affect interest rates; here there is of course much controversy and both sides of the argu- ment are presented. The pro-Ricardian case comes first because it is the simplest; then the other side receives its due. The two Ricardian propositions are physically separated. The first spans pp. 603–604 in Section 2, where it appears as a straightforward application of the con- cept of present value. (The relevant discussion really begins on p. 602, under the heading ”Should You Pay With Cash or Credit?”) The deeper and more contro- versial issues, which involve market equilibrium, are postponed to pp. 622–625. 17–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. True or False: If you can afford to, it is a good idea to pay off your debts as quickly as possible, so that the interest charges don’t get too high. 2. Herman has an income of 2thisyearandwillhaveanincomeof 3 next year. At the current interest rate he chooses neither to borrow nor to lend. True or False: If the interest rate goes up, Herman will become a lender and be better off. 3. Use an indifference curve diagram to show why an economics student who expects to get a good job when he graduates will spend more than a philoso- phy student who expects to be unemployed, even though both have the same current income. 4. Herman has a choice between two jobs. One pays very little now, but promises high raises in the future. The other has a higher starting salary, but less potential for future raises. True or False: Herman’s choice should depend on his tastes. It’s all a matter of whether he’d rather consume a lot when he’s young or a lot when he’s old. 5. In The New Republic (6/17/89) James K. Glassman explained that housing has been a less good investment than stocks: ”If you bought a $200,000 house in Foggy Bottom in 1979, it would be worth $316,000 today. But if you bought $200,000 worth of stock in 1979, it would be worth $556,000 today – and you’d have another $68,000 in dividend income.” In words that James K. Glassman might understand, explain what’s wrong with his calculation. 6. In The New Republic (6/17/89) James K. Glassman writes that ”stocks ap- preciate faster than real estate; they always have, and they always will. The reason is that a share of stock is a piece of a company in which minds are producing value. Real estate just sits there.” Comment. Remark: The above problem has a rather nice twist, since the reason that stocks appreciate faster than real estate is precisely that real estate does not ”just sit there” — it returns a stream of dividends in the form of housing services. (This is the missing term in the equation in the preceding problem also.) 7. To compute your income tax, you first add up your income from all sources. You then subtract deductions to get ”taxable income,” and your tax bill de- pends on your taxable income. One allowable deduction is mortgage interest: Every dollar that you pay in mortgage interest can be subtracted from your taxable income. True or False: Therefore, if you have a choice between paying cash for your house or taking out a mortgage, the tax law makes it a good idea to take the mortgage. 8. True or False: When income tax rates fall, the value of the mortgage interest deduction falls, making housing less desirable and reducing the market price of housing. 9. The Wall Street Journal (9/19/91) printed a letter from Richard C. Leone, the chairman of the Port Authority of New York and New Jersey, opposing the privatization of New York’s airports. He asserts that the airports are worth well in excess of the Journal ’s $2.2 billion estimate, but that even at that price a purchaser would find it impossible to earn back his investment. Comment, using words that Mr. Leone could understand. 17–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 10. The makers of the insecticide Roach-Prufe advertise that their product is so effective it can only be bought by mail; grocery stores will not carry it for fear that their customers will eliminate all of their roaches and never have to buy an insecticide again. Do you believe them? Why or why not? 11. Because of a reduction in world tensions, the U.S. will be able to reduce its military expenditures by $100,000,000 this year. Senator Smith says that we should take this opportunity to cut taxes by $100,000,000. Senator Jones says that instead of cutting taxes, we should apply the $100,000,000 to reducing the deficit. Use a simple model to compare and contrast the effects of the Smith and Jones plans. Your answer should include a careful discussion of how people’s current consumption decisions are affected by the two plans. 12. Upper and Lower Slobbovia are identical countries in which there is n such thing as productive investment; all income is from endowment. The govern- ments of both countries have decided to impose an income tax and spend the proceeds wastefully. The only difference is that in Upper Slobbovia, the tax-and-spend plan is in effect for this year only, whereas in Lower Slobbovia the plan is permanent and will be repeated every year. In both countries, this year’s taxes have been collected and wasted. Compare the two countries’ interest rates, and compare their current consumption levels. 13. In 1981, the personal computer was introduced, creating a whole range of new opportunities for productive investment. Shortly thereafter, interest rates rose dramatically. Give a full explanation of how the new computers might have contributed to the rise in interest rates. If you draw a graph and shift curves, be sure to explain why the curves shift as they do. 14. Suppose that the interest rate is 10%. The Government wants to build a post office at a cost of $100,000. It can pay for the post office either by a) a tax on jelly beans that raises $100,000 this year; b) borrowing the funds and imposing a tax on jelly beans that raises $110,000 next year; or (c) any combination of a (a) and b) (such as rasing $50,000 in tax revenue this year and $55,000 next year). The government would like to minimize the present value of deadweight loss in the jelly bean industry. What policy should it follow? 17–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 17–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 17 1. False. This confuses a change in demand with a change in quantity demanded!! 2. The interest rate and the price of bonds cannot move in the same direction. A movement in the interest rate in one direction is always accompanied by a move- ment in the bond price in the opposite direction by definition. 3. False; it cost him three years worth of interest on the cost of the refrigerator. 4. A perpetuity which pays $1 forever is worth $10 when the interest rate is 0.10. An annuity for 17 years which pays a dollar each year is worth about $8.02. Thus the statement is true. 5. a) You would have to value it at least at $P r(1 + r). b) Doubling P doubles the cost of the punishment. Halving r more than doubles the cost of the punishment. Halving r is the greater deterrent. 6. Rent costs $18,000/year, therefore with a market interest rate of 10 percent and constant rent the cost of renting forever is $180,000. The discrepancy suggests that the market must be anticipating a rise in rents, so the statement is likely to be true. There is another possibility, however, and that is that the market anticipates a fall in the interest rate, which would raise the present value of a constant stream of rents. 7. False. The California house sells for less than the New York house and returns the same stream of dividends. Thus the rate of return is higher on the California house, and this compensates the owner for the risk. As long as the relative desirability of the two houses remains constant, the relative price of one in terms of the other can not change. 8. a) $20 + $20/1.1 + $20/(1.1)2 = $54.71. b) $200. c) Never issue new editions. The present value of the publisher’s revenue is equal to the present value of the stream of dividends that the book returns to students. New editions do not affect this stream, but they do raise costs. d) If students expect a new edition every three years, the price of a book falls to $54.71 and publishers must issue new editions to capture the full stream of dividends. e) True. Book price would rise from $54.71 to $200, present value of revenues would remain fixed, and costs would fall. 9. False. In present value terms the charges would be constant. 10. What Mr. Will overlooks is that the ”average American” gets something in return for those interest payments, namely the opportunity to defer taxes and earn interest. 11. Exactly what is wrong with it is the following: If the government buys me a suit of clothes with borrowed money, then I avoid having to buy the clothes myself. That 17–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. means that I have more money in the bank earning interest, and my grandchildren have a bigger inheritance. Suppose that the government borrows $1 to buy me the clothes, that the interest rate is 10%, and that I die after one year. My extra $1 in the bank will have grown to $1.10. The debt that my grandchildren must be taxed to pay will also have grown to $1.10. The larger inheritance exactly cancels out the debt burden. 12. a) Jeeter can spend $1000 today to buy a bond. He can put the bond in a desk drawer and forget that he owns it. In 5 years, when the loan comes due, he can hand the bond over to the bank. Since the bond grows in value at exactly the same rate that Jeeter’s debt to the bank grows, the bond will exactly cover his debt. This strategy “feels” exactly like paying the loan off for $1000 today and being done with it. b) Jeeter can spend $10,000 to buy Treasury Bills. The interest rate on these bills is exactly equal to the rate at which the government debt is growing, since selling Treasury Bills is precisely the way in which the government borrows. When- ever the government gets around to taxing Jeeter, he can turn over his treasury Bills, which are guaranteed to be equal in value to his share of the national debt. This strategy “feels” to Jeeter exactly like paying off his share of the debt now and never being charged any interest. 13. How about something like: DEAR ANN LANDERS: You really blew it in your reply to Ladder Legs of Lina, Ohio. If Wanda Worker spends $100 a year replacing nylons, Wanda Worker would be willing to pay up to $100 for a single pair of nylons that last a year without running or stretching. In fact, she’d be willing to pay considerably more than $100, since she’d avoid all of that aggravation and time spent running to the drug store. It shouldn’t have taken a call to a hosiery manufacturer to clue you in to the fact that they just don’t know how to make these miracle nylons. What kind of a conspiracy of self- interest would refuse to manufacture nylons that they could sell at $100 a pair? Three lashes with a wet noodle for this one, Ann. —Econ Whiz 14. False; they will have paid for medallions whose value is now zero. If the medal- lions were originally issued free of charge, then only the original medallion owners received any benefit from them; whenever a medallion changed hands it sold for the entire present value of the all of the monopoly profits that it was expected to convey. If the abolition comes as a surprise, then anybody who ever purchased one of these medallions will have paid more than it was worth. 15. False. The exact opposite is true. The monopolist wants his marginal revenue to grow at the rate of interest. (Be sure you see why this is so: How could he make himself better off if marginal revenue were growing either more or less slowly?) Because the marginal revenue curve is steeper than the demand curve, a given rise in marginal revenue corresponds to a smaller rise in price. Because price starts out higher than marginal revenue and increases by less than does marginal revenue, the percentage change in price must be less than the percentage change in marginal revenue. Thus the monopolist controls availability so that price rises more slowly 17–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. than the rate of interest. 16. False because of the word ”always.” At higher interest rates the consumer may become a net borrower and thus be made better off. 17. True. Herman’s original budget line is tangent to an indifference curve at (2, 3). His new budget line also passes through (2, 3). The geometry forces the new tan- gency to be northwest of the old one and on a higher indifference curve. 18. Both reduce the supply of current consumption. In case (a) demand falls a little and in (b) it falls a lot. The interest rate is higher in case (a). 19. In case (a) the demand for current consumption falls a little and in (b) it falls a lot. The effects on supply of current consumption are the same in both cases, unless labor supply decisions are important. They supply might fall much further in case (a) than in case (b), due to intertemporal substitution as studied in Chapter 16. 20. False. The representative agent is poorer now, and has a lower demand curve for current consumption. If his current consumption quantity is Q, then (Q − 1000) corresponds to 20% on the old demand curve. It must correspond to something less than 20% on the new demand curve. 21. Future Consumption A E $1.10 { D { Current $1 Consumption Terry starts with an endowment of A, faces an interest rate of 10%, and there- fore has the pictured budget line with slope −1.10. If the government taxes him $1 and then provides him with $1 worth of current consumption, his endowment point remains A (nothing has really changed). If the government borrows $1 to provide Terry with $1 worth of current consumption, it then taxes him $1.10 in the future to repay the debt. Terry’s endowment point shifts to D (with $1 more in present consumption and $1.10 less in future consumption). Because Terry’s new endowment point is on his original budget line, his optimum consumption basket does not change. Each plan leads to the same demand for current consumption and so to the same equilibrium interest rate. 22. The super-productive government taxes a dollar and gives back two dollars worth of consumption moving the agent from point A to point B. Or the government borrows a dollar, turns it into two dollars worth of consumption and increases future taxes by $1.10. This is the movement from A to C. The new budget line still has slope 1.1 and thus the interest rate remains unchanged. 17–7 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Future Consumption A B C Current { { Consumption $1 $1 23. False. The quantity of government spending matters (as well as how it is spent); it is the method of financing that does not matter. 24. Here are a few observations: First, Mr. Rohatyn asserts that borrowing will convert a 130billionlossintoa500 billion drain over 20 or 30 years. In other words, he treats a dollar paid 20 years from now as equal in value to a dollar paid today. If he is really com- mitted to such reasoning, Mr. Rohatyn should be happy to offer you a loan of 200billiontodayinexchangef orapaybackof 300 billion in 20 years. Try writing to him and see if he agrees. Second, he asserts that one should not borrow to finance losses that have already occurred, and elevates this dictum to ***”a basic economic principle.” On the contrary, people generally prefer to spread their consumption out evenly over their lifetimes rather than having some years of feast and some of famine. (This is why we tend to think of the Great Depression as a bad thing.) It follows that a one-shot unexpected large expense is precisely the sort of thing that ought to be financed by borrowing. Your indifference curve analysis in part (b) should confirm this assertion. Third, he is wrong in thinking that a short-term tax surcharge would necessar- ily limit the costs of the bailout to the immediate future. Precisely because people like to smooth out their consumption, they would borrow more (or, equivalently, save less) in the present to get through the temporary period of high taxes. The result would be the same as if the government had done the borrowing. But not quite. For a variety of reasons, individuals must usually borrow at higher rates than the government does. Therefore, Mr. Rohatyn’s proposal comes down to this: Let people attempt to borrow for themselves at high interest rates, rather than let the government borrow for them at lower rates. Finally, some economists would argue that people are insufficiently sophisti- cated to borrow their way through the higher tax years (that is, some would argue that people fail to move to the optimum point in the indifference curve diagram). If those economists are right, then Mr. Rohatyn is even farther off the mark, since these taxpayers in their naivete will fail to smooth out their consumption streams unless the government leads the way by borrowing for them. 25. False. A rise in the interest rate raises the cost of investment and makes investment less desirable. Of course the interest rate change itself must have a cause and one possible cause is that investment has become more desirable for 17–8 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. some other reason. 26. To the shoemaker, the hammer is capital. From the numbers given, we can deduce that the marginal product of capital is 15% per year. But the marginal product of capital must be equal to the market rate of interest. Thus the market rate of interest is 15% per year. Since the house provides $10,000 worth of service per year forever, its value is the value of an annuity that pays $10,000 per year forever; that is, $10, 000/.15 ≈ $66, 667. 27. The demand for current consumption increases because people are richer, and the supply decreases because investment is more productive. For both reasons, the interest rate rises. 28. People want to borrow therefore the interest rate increases. 29. People feel much poorer and may demand ***less current consumption than before. Therefore the interest rate could fall. (On the other hand, the effects described in problem 28 still work in the direction of pushing the interest rate upward.) 30. The answer is contained in Exhibit 17-13b. 17–9 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Eighteen: Risk and Uncertainty Additional Problems 1. What are some of the consequences of prohibiting insurance companies from charging higher rates to people who are in high risk groups for AIDS? What are some of the consequences of prohibiting insurance companies from requiring AIDS tests as a precondition for coverage? 18–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 18–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 17 1. It depends on the possible outcomes of the uncertainty, and it depends on the odds. Had the doctor been given the opportunity to sacrifice a certain shilling in exchange for a mere 99% chance at a million pounds, he might have reconsidered his position. Indeed, to forego suicide is to sacrifice the certainty of death for the uncertainties of life, buy most of us make this “unwise” choice. 2. False. Even if nothing is worth the certainty of death, it does not follow that nothing is worth (say) a 50% chance of death. 3. False. A risk-averse person will always accept one side or the other of an unfair bet, provided he is permitted to wager a sufficiently small amount. The diagram below shows why. John starts at point A and is offered the unfair odds budget line. If he is allowed to bet on state 1, and if he is allowed to bet an amount that will move him to a point- between A and B, then he will do so. State 2 45 o A B Unfair Odds Fair Odds State 1 4. Tails 45 o Slope = -1 Heads 5. False. The risk-preferring person pictured below, given the opportunity to bet on state 1 at the unfair odds that are indicated, would prefer not to bet. If the unfair odds were a bit less unfair, so that the line intersected the horizontal axis 18–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. outside rather than inside the illustrated indifference curve, then he would choose to bet. State 2 45 o Fair Odds Unfair Odds State 1 6. Suppose that the Cowboys are favored to beat the Rams. The “Rams” state of the world occurs if the Rams beat the spread and the “Cowboys” state occurs otherwise. This makes the fair odds budget line the line with slope -1 through the bettor’s endowment. The kinked boldfaced line is the budget line that the bettor is offered. He remains at his endowment, by refusing to bet. Suppose, however, that this bettor has a different view of the odds than others in the marketplace, and believes that the Rams are very unlikely to beat the spread. Then his indifference curve will be much steeper at the endowment point, since it must be tangent to the bettor’s perception of what a fair odds line would be. In this case, the kinked budget line could cross the demand curve and the bettor would place a bet on the Cowboys. 7. True. Refer to the following graph. If the sickly person with endowment E could insure at fair odds, he would select point A on the 45 degree-line, where he is indifferent between getting sick and staying well. If he can insure at odds that are better than fair, as indicated by the budget line labeled “actual odds,” he will move to point B. Note that the slope of the indifference curve at C must be the same as the slope of the indifference curve at A (both slopes reflect fair odds) so that B must lie to the right of C. Thus after insuring, this individual is better off if he gets sick than if he stays well. 45o Stay Well E C Actual Odds A B Fair Odds Get Sick 8. False. Exhibit 18-10 demonstrates that the speculator is harmful to society when he is wrong, and helpful when he is right. 18–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 9. Price Price A B C D E F D D 90 100 Quantity 80 90 100 110 Quantity (Tons) (Tons) a) The speculator stores wheat for delivery next year. b) He continues until this year's price is equal to his expectation of next year's price; this happens after he has stored ten tons of wheat. This year's supply is 90 tons. Next year's supply is 90 tons if he is right; 110 tons if he is wrong. c) Without speculator: social gain is A+B+ C With speculator: social gain is A+ C +D. Notice that D is bigger than B (same width, greater height), so the speculator improves social welfare. d) Without speculator: social gain is A+B+ C +D+E With speculator: social gain is A+ C +D+E+F Notice that F is smaller than B (same width, less height), so the speculator decreases social welfare. 10. False. Nobody would ever hold a portfolio that was below the efficient set, but the individual stocks that make up the portfolio can lie below it. Consider, for example, Exhibit 18-12. An investor who wants to hold portfolio D must hold equal quantities of GSB and GSS. Even though GSB is below the efficient set – it has both greater variance and lower expected return than D has – it is still an essential component of the efficient portfolio D. (In the Exhibit, the efficient set is the straight line connecting D with GSS. Can you see why?) 11. False; terrorists will take fewer hostages. 12. It is perfectly possible that alcohol mixes badly not with 18-year-olds as such, but with drivers who have relatively little experience with alcohol. Raising the drinking age will save 25 go 35 lives taken by 18-year-olds (taking the quoted studies as reliable) but could very well increase the number of lives taken by 19- year-olds, who would now be in the same position that the 18-year-olds are in. The net number of lives saved could be well under 25. This fits right in with the “Tweedledee/Tweedledum” and “Lumberjacks’ Income” examples in the text, where it is a mistake to assume blindly that a statistical relationship will continue to hold following a policy change. 13. a) C = A, D = B − Aπ, where π is the rate of inflation. b) As long as π doesn’t change, the expressions Ar + B and Ci + D are equal. c) Presumably, C is negative. Thus he will advise a reduction in the inflation rate π. 18–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. d) C stays the same. D changes to D0 = D − A(π 0 − π). Q remains unchanged. The change in government policy causes the coefficient D to change, rendering the old equation useless for making predictions. In this case the coefficient changes by just enough so that the policy has no effect at all on car sales. 18–6 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Chapter Nineteen: The Nature and Scope of Economic Analysis General Discussion and Random Thoughts 1) The text draws a number of analogies with physics. Here is another one that I have used to good effect at appropriate times. Holding a pen, or better yet an apple, at arm’s length, one can ask the physical question: will this pen drop to the floor within the next 30 seconds? No physicist can answer this question, but a physicist can give a fairly confident conditional answer: If you let go of the pen, and if you do not first put something between it and the floor that will catch it, and if nothing else intervenes, then the pen will drop to the floor. If you don’t let go, then it won’t. Similarly, the economist can not predict (say) the interest rate on treasury bills 6 months from now. But he can with some confidence make conditional predictions: if the harvest is as good as expected, and if the monetary authorities follow such-and-such policies, and if nothing else intervenes, then the interest rate should move in such-and- such a way. Predicting the weather, and to a large extent predicting government policy, is no more the business of the economist than predicting whether you will drop the pen is the business of the physicist. 2) More on the role of assumptions: by all means let us make it clear to our students that there is no such thing as a perfectly competitive firm, any more than there is any such thing as a perfectly frictionless billiard table. Each is a particularly useful fiction that captures certain important aspects of reality. 3) The textbook presents a naive version of the options pricing model and calls attention to its highly simplified nature (discrete time, only two possible future as- set values, and so forth). This simple model, however, leads to some remarkable conclusions with analogies that hold in the full- blown model: for example, the probabilities that the stock price will go up or down are not needed to calculate the option price. There is a general lesson here. A model is good when it suggests surprising conclusions that are then found to hold in far more general circum- stances. This is a good example with which to illustrate the notion of robustness. 3) Regarding the rationality assumption, there is much more to say. I con- sidered including a section on alternatives, such as the “bounded rationality” and “satisficing” models, but became convinced that this was too far afield for an in- termediate course. Nevertheless, I think it is an interesting topic for some informal class discus- sion. Before opening this Pandora’s box, however, I strongly recommend assigning the reading on celebrity endorsements, where I have tried to make a strong case for extreme caution in abandoning successful assumptions. That said, there is no harm in some speculation about what might someday replace rationality. (Likewise, if I can be allowed one more analogy with physics, there is no harm in some speculation about what might someday replace quantum electrodynamics; but there would be considerable harm in being too hasty to scrap the only successful theory we have. Let us make sure that students understand the distinction.) To me, the most interesting inspiration for such speculation is the work of Tversky and Kahneman (see for example “Judgment under uncertainty: Heuristics and biases” in Science 185 (1974), p.1123–1131, and reprinted in Diamond and Rothschild’s Uncertainty in Economics. These two psychologists have made a fas- 19–1 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. cinating attempt to categorize the systematic errors in judgment that people seem to make. These include insensitivity to priors, insensitivity to sample size, etc. In one study they found that instructors systematically overestimate the effectiveness of punishments and underestimate the effectiveness of rewards. The reason is that students who are punished for poor performance are more likely to improve just by virtue of the fact that their initial performance was poor; students who are rewarded for good perfomances are more likely to disimprove for the analogous reason. The interesting phenomenon is that highly experienced teachers systemat- ically fail to correct for this statistical phenomenon in their gut assessments of the efficacy of various teaching strategies. Perhaps one day the discoveries of researchers like Tversky and Kahneman will be fully incorporated into a more general theory of rationality, which takes account of the costs of correcting certain systematic errors and hypothesizes that people only behave “rationally” when the expected benefits outweigh the expected costs—that is, they behave rationally when it is rational to do so. 4) Another Tversky-Kahneman-like example is in Raiffa’s book Statistical De- cision Theory. Consider two urns, one containing 70 red balls and 30 white; one containing 30 white balls and 70 red. An urn is chosen at random, and 12 balls are drawn with replacement. 8 are red and 4 are white. How likely is it that the selected urn is the one with 70 red balls? Raiffa reports that his informal surveys indicate that people grossly underestimate the probability. In particular, attorneys, when asked whether the urn is “beyond a reasonable doubt” the predominantly red one, almost invariably reply in the negative. My own informal research bears this out. In fact, a quick calculation reveals that by any reasonable definition of a reasonable doubt, the correct answer is yes. And yet, people whose profession it is to make such determinations are systematically wrong. 19–2 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Additional Problems 1. Suppose there are three goods in the world: X, Y and Z. An X can be traded for 3 Y’s, a Y can be traded for 2 Z’z, and an X can be traded for 5 Z’s. Why do you not expect this situation to last? 2. In order to combat the used book market, the publisher of this textbook considered sewing a $100 bill into the binding of every 100th book. You would have had to rip the book apart to see if you’d won. Would this have worked? (Take into account the circumstances under which it would even be desirable for a publisher to combat the used book market. What effect would this strategy have on the price of used books? On the price of new books? 3. The Jolly Time Amusement Center offers its patrons the opportunity to play Skee-Ball and other games for 25 cents a play. Perfomance is rewarded with tickets, and large numbers of tickets can be exchanged for prizes, whose market value is typically far less than the cost of playing long enough to win them. Sometimes customers sell tickets to each other for cash. Suppose that Jolly Time could prevent these resales. Do you think it would want to? In the remaining problems, attempt to explain the following phenomena by con- structing theories based on rational behavior. In each case, try to say something about how you might test your theory. 4. People give each other gifts that they are not sure the recipient will like, when they could simply give cash instead. Recipients seem to prefer this. (Note: saying that gift-giving demonstrates that the giver cared enough to spend time shopping is no answer. The giver could demonstrate the same amount of caring by increasing his cash gift sufficiently.) 5. Bank certificates of deposit are usually very ordinary looking pieces of paper, whereas shares of corporate stock are printed on very expensive paper with lots of artwork and calligraphy. 6. People like to all celebrate Christmas on the same day, but they also like to all celebrate their birthdays on different days. 7. A man paid $50 for a ticket to a Broadway show, indicating that he valued the ticket at least at $50. When he arrived at the theater, someone offered him $50 for his ticket, and he refused, indicating that he still felt the same way. Then, when he looked in his pocket, he discovered that he had lost the ticket and would have to pay $50 for a new one. This he refused to do, and went home, indicating that he valued a ticket at less than $50. 8. Camera store owners often offer discounts on merchandise to their own em- ployees. 9. 60 years ago, the minimum allow bet at the racetrack was $2. Today the mini- mum allowable bet at the racetrack is $2. Yet everything else has skyrocketed in price. 10. In every culture, parents of daughters are more likely to divorce than parents of sons. 19–3 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. 19–4 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part. Price Theory and Applications by Steven E. Landsburg Solutions to Problem Set for Chapter 19 Most of the problems in this chapter are intended to encourage speculation on your part, and therefore the answers are not given here. In many cases, the author of your textbook does not know the answers. 19–5 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied or duplicated, or posted to a publicly available website, in whole or in part.
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