Past Economics Exam

EC202-6-FY1 UNIVERSITY OF ESSEX Diploma Examinations 2011 MICROECONOMICS (INTERMEDIATE) Time allowed: 3 hours Candidates must answer FOUR questions, at least ONE from each section. The paper consists of TEN questions, divided into two sections each of FIVE questions. All questions carry equal weight. Candidates are allowed to bring into the examination room: calculators (hand held, containing no textual information). Please do not leave your seat unless you are given permission by an Invigilator. Do not communicate in any way with any other candidate in the examination room. Do not open the question paper until told to do so. All answers must be written in the answer book(s) provided. All rough work must be written in the answer books provided. A line should be drawn through any rough work to indicate to the examiner that it is not part of the work to be marked. At the end of the examination, remain seated until your answer book(s) have been collected and you have been told you may leave. EC202-6-FY 2 Section A You must answer at least ONE question from this section. 1. Answer all parts (a) – (f) of this question. A perfectly competitive firm has a production technology that can be described by the following production function: µ = I 1 4 K 1 4 where K is capital and I is labour. The firm can change K and I freely. The corresponding marginal productivities are HP L = 1 4 I - 3 4 K 1 4 anu HP K = 1 4 K - 3 4 I 1 4 The unit price of labour is w, and the unit price of capital is r. The unit price of the final product is P = 4. (a) [5 marks] Assume w = 1 anu r = 1. Find the cost function C(µ). (b) [5 marks] Assume w = 1 anu r = 1. Find the output µ - that maximizes the firm’s profit. (c) [5 marks] Assume w = 4 anu r = 1. Find the cost function C(µ) and the output µ that maximizes the firm’s profit. (d) [5 marks] Assume r = 1. Derive the (unconditional) demand for labour as a function of the wage w. (e) [3 marks] Assume r = 1. Suppose that the wage has increased from w = 1 to w = 4. What is the substitution effect for labour demand? (f) [2 marks] Is the conditional input demand curve for labour steeper than the unconditional demand? Explain. EC202-6-FY 3 2. Answer all parts (a), (b), (c) and (d) of this question. A consumer has income consisting of 6 units of good x but zero units of good y. The preferences of the consumer are represented by u(x, y) = √x¸y where x and y denote the quantities of the goods that the consumer consumes. The corresponding marginal utilities are Hu x = 1 2 x - 1 2 y 1 2 anu Hu x = 1 2 y - 1 2 x 1 2 The unit price of good x is p x , and the unit price of good y is p ¡ . (a) [5 marks] Assume p x = 1 anu p ¡ = 1. Find the optimal consumption bundle. What is the consumer’s utility level? (b) [5 marks] Assume p ¡ = 1. Suppose that p x has increased from p x = 1 to p x = 2. Find the substitution effect on the consumption of good x and the income effect as well. (c) [5 marks] Is x a normal good or an inferior good? Explain. (d) [10 marks] As in part (b), suppose that p x has increased from p x = 1 to p x = 2. The government still wants to maintain the utility level of part (a) by a lump-sum tax or a lump-sum subsidy. Does the government need to use a lump-sum tax or a lump-sum subsidy? Moreover, suppose that the tax or the subsidy must be paid in commodity x. What amount of x should the government give or receive from the consumer? 3. Answer both parts (a) and (b) of this question. (a) [12 marks] State the axioms of consumer preference. Provide an explanation for each axiom. (b) [13 marks] Distinguish between the decreasing marginal rate of substitution and the decreasing marginal utility. Does one imply the other, or are they equivalent? Explain. EC202-6-FY 4 4. Answer all parts (a), (b), (c) and (d) of this question. Consider the following exchange economy with two goods, x and y, and two consumers, A and B. The tastes of the two consumers are represented by the following utility functions: u A = x A y A anu u B = x B y B 2 where x ì and y ì are the quantities of consumed goods x and y, by consumer i e {A, B]. For individual A, the marginal utility of x is Hu x A = y A , and the marginal utility of y is Hu ¡ A = x A . For individual B, the marginal utility of x is Hu x B = y B 2 , and the marginal utility of y is Hu ¡ B = 2x B y B . There are 5 units of good x and 10 units of good y available in this exchange economy, so that x A + x B = S and y A + y B = 1u. (a) [ 5 marks] Draw the Edgeworth box that represents this economy (make sure to include at least two difference curves for each of the two individuals). (b) [5 marks] Verify that the allocation (x A = 2, y A = 5 2 , x B = S, y B = 15 2 ) is Pareto efficient. (c) [10 marks] Find all Pareto-efficient allocations. (d) [5 marks] Suppose that the initial allocation (c A x , c A ¡ , c B x , c B ¡ ) leads to a Walrasian equilibrium allocation (x A = 2, y A = 5 2 , x B = S, y B = 15 2 ). Find the equilibrium price ratio and all initial allocation (c A x , c A ¡ , c B x , c B ¡ ) that is different from (x A = 2, y A = 5 2 , x B = S, y B = 15 2 ) and that leads to the Walrasian equilibrium allocation. EC202-6-FY 5 5. Answer all parts (a), (b), (c), (d) and (e) of this question. Suppose there is a railway that runs coal-burning steam locomotives through a farming area and causes fires in the crop fields at harvest time. The crop damage from each train run is £200. Suppose the revenue and the cost of running trains on a line next to a farming area are as follows: Number of trains per day Revenue Private cost Crop damage 1 £350 £100 £200 2 £700 £200 £400 3 £1050 £400 £600 4 £1400 £700 £800 5 £1700 £1100 £1000 6 £2100 £1600 £1200 In other words, the revenue from running each train is constant at £350, the marginal crop damage is constant at £200, and the marginal private cost is increasing in the number of runs. (a) [5 marks] How many runs would the railway run to maximize its profit if no compensation were required for crop damage? (b) [5 marks] What is the socially efficient number of runs when you include the cost due to the crop damage? (c) [5 marks] The Coase Theorem states that (in the absence of transaction costs) the level of production of goods in an industry in which there are externalities is independent of whether or not the party who generates negative externalities is legally liable for the costs of the externalities on other parties. Assume that the railway company has the legally enforceable property right of running trains. Show that the railway company and the farmer can agree upon the efficient number of train runs with an appropriate payment from the farmer to the railway company. (d) [5 marks] Alternatively, the government can impose a tax on the railway company to achieve the socially efficient number of train runs. Let t be the tax for running each train. At which level of tax does the railway company choose the socially efficient number of runs? (e) [5 marks] Briefly discuss the weaknesses and the strengths of the Coase theorem compared to the taxation method in part (d). END OF SECTION A EC202-6-FY 6 Section B. You must answer at least ONE question from this section. 6. Answer both parts (a) and (b) of this question. (a) Assume a monopolist operates in a market with inverse demand given by P = 8u - 4µ. Marginal cost is constant at 8 and there are no fixed costs. (i) [3 marks] Calculate the profit-maximising price and quantity of the monopolist. (ii) [3 marks] Illustrate graphically and calculate the consumer surplus, the producer surplus and the total welfare. (iii) [2 marks] What price will maximise the sum of producer and consumer surplus in this market? (iv) [2 marks] Calculate the loss in consumer surplus and the loss in total welfare resulting from monopoly. Illustrate graphically. (v) [5 marks] The government plans to impose on the monopolist a tax, t, per unit of output produced and sold. Explain how this would affect the consumer surplus, the producer surplus and the total welfare. A policy think tank proposes raising the same amount of revenue by imposing a lump-sum tax instead of a per unit tax. Do you agree or disagree with them and why? What policy do you think the government should implement if it wants to maximize total welfare? (b) [10 marks] Consider a homogeneous good market with demand curve µ = 19u -P, where µ is the quantity of the good demanded when the price is P. There are two firms which compete by simultaneously setting quantities. Each firm has a constant marginal cost equal to 22. Explain why it is not an equilibrium for the two firms to split the monopoly level of output equally. Then compute the Cournot equilibrium quantities and profits for the two firms. EC202-6-FY 7 7. Answer both parts (a) and (b) of this question. (a) [8 marks] Define, explain and describe an example of second-degree price discrimination. (b) A monopolist can supply its product in two distinct markets. Inverse demands in the two markets are given, respectively, by P 1 = 2uu -µ 1 and P 2 = 1uu - µ 2 , where Q 1 and Q 2 are quantities sold in markets 1 and 2, and P1 and P2 are prices charged in markets 1 and 2, respectively. The marginal cost of production is zero and there are no fixed costs. (i) [8 marks] Suppose that the firm can price discriminate between the two markets. Calculate the price the firm will set in each market. For each market, calculate also the output, profit and consumer surplus. (ii) [6 marks] Now suppose that the monopolist is constrained to charge a uniform price across the two markets. Calculate the profit maximising price, total quantity supplied, the monopolist’s total profits and consumer surplus. (iii) [3 marks] A regulator for this market wishes to maximize the sum of profit and consumer surplus. Should the regulator ban or allow price discrimination? Explain your answer in light of your results in parts (i) and (ii). EC202-6-FY 8 8. Answer both parts (a) and (b) of this question. (a) Consider the following game, called “Picking stones”. There are three players, A, B and C, who have four stones set in front of them. The rules of the game are as follows. A moves first and takes one or two stones. B moves next and takes one or two stones. Then, if there are any stones left, C moves and takes one or two stones. Finally, A picks up the last stone, if there is one left. Whoever picks up the last (fourth) stone wins. (i) [5 marks] Draw the extensive form of the game. (ii) [4 marks] Is it ever possible for A to win this game? Explain your answer. (iii) [3 marks] What are the subgame perfect equilibria of this game? (b) Two firms, one in Great Britain and the other in France, act as Cournot competitors in supplying mussels to Germany. The demand for mussels in Germany is p = 1uu -2µ, where p is the price and µ the total quantity of mussels. The marginal cost for both firms (including production and shipping) is 25. (i) [8 marks] Calculate the equilibrium quantity sold by each firm in Germany. What is the profit of each firm? (ii) [5 marks] Now suppose that the French government decides to subsidise French mussel producers at a level of s per unit. How will this affect the Cournot equilibrium? 9. Answer all parts (a), (b) and (c) of this question. (a) [5 marks] If A and B are mutually exclusive projects, and A offers a rate of return of 10% while B offers a rate of return of 20%, a rational investor should never choose A. True or false (and why)? (b) [8 marks] A firm may invest in a project that yields a payoff of 110 with probability 0.5 and a payoff of £90 with probability 0.5. The cost of the project is £100. The firm is risk neutral and there is no discounting. Suppose that a market research report could be obtained that would reveal whether the true payoff of the project would be £110 or £90. The report costs £2.5 and will take 2 months to write. Should the firm commission the report, proceed immediately with the project without the report, or decline the project? (c) John has preferences represented by the utility function 0 = W 1 2 , where W represents income. (i) [4 marks] Is J ohn risk-loving, risk-neutral or risk-averse? Explain. (ii) [4 marks] Suppose J ohn’s income in his current job is £10,000. He is offered a new job, which offers a 50% probability of earning £16,000 and a 50% probability of earning £5,000. Should he take the new job? (iii) [4 marks] Suppose J ohn took the new job. Would he be prepared to buy insurance to protect himself against the low income outcome? If so, how much would he be willing to pay for that insurance? EC202-6-FY 9 10. Answer both parts (a) and (b) of this question. (a) [13 marks] Explain the statement "bad quality drives out good quality" Illustrate your answer with an example. (b) [12 marks] Nick owns a restaurant and needs to hire a new waiter. Bob is considering working for Nick. Currently, Bob is working in a job where he can make £18,000 a year without exerting any effort. Nick offers to pay Bob a base salary of £14,000 a year plus tips (which are £10 per table served) if Bob serves at least 1,000 tables over the year. If Bob serves less than 1,000 tables, Nick can see this and he will pay him nothing. Of course, Bob can still keep his tips. Bob’s cost of effort is C (t) = t 2 ¡2uu, where t is the number of tables served. Hence his marginal cost of effort is HC (t) = t¡1uu. Show that Bob will accept this contract and will serve exactly 1000 tables. 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