1Exercises for Chapter 9 11. Imagine a wilderness area of 200 square miles in the Rocky Mountains. How would you expect each of the following factors to affect people’s total willingness-to-pay for its preservation? a. The size of the total wilderness area still remaining in the Rocky Mountains. b. The presence of rare species in this particular area. c. The level of national wealth. 1.a. Other things equal, we would expect people to place a higher value on preserving this particular area, the smaller the total stock of Rocky Mountain wilderness remaining. The reason is that we generally expect declining marginal utility as more of any good is "consumed," whether through use or nonuse. 1.b. Other things equal, the "rarer" the wilderness area is in terms of either its physical characteristics or the species that make it their habitat, the higher people's willingness to pay to preserve it. One way to view rareness is in terms of the stock of comparable areas. People are likely to have the largest willingness-to-pay for areas that are unique in some significant way, because, if it is really unique, the area constitutes the total remaining stock. 1.c. Other things equal, the wealthier people are the more they are willing to pay for all normal goods, including those that offer nonuse value. This may be one reason why environmental movements appear stronger in more developed countries. 2. An analyst wishing to estimate the benefits of preserving a wetland has combined information obtained from two methods. First, she surveyed those who visited the wetlandfishers, duck hunters, and bird watchers-to determine their willingness-to-pay for these uses. Second, she surveyed a sample of residents throughout the state about their willingness-to-pay to preserve the wetland. This second survey focused exclusively on nonuse values of the wetland. She then added her estimate of use benefits to her estimate of nonuse benefits to get an estimate of the total economic value of preservation of the wetland. Is this a reasonable approach? (Note: In responding to this question assume that there was virtually no overlap in the persons contacted in the two surveys.) 2. There is a danger that summing the estimates will result in an overestimate of total willingness-to-pay. The reason is that some of the respondents from the state-wide survey may also be users and potential users. These respondents would probably give a smaller willingnessto-pay for nonuse if they were first asked to give their willingness-to-pay for use. It would be conceptually correct simply to ask respondents in the state-wide survey their willingness-to-pay amounts for use and nonuse together. This approach is problematic, however, if only a small fraction of state residents are users -- the sample may provide too few users to make reliable estimates of use values. On the other hand, estimating nonuse values based only on the responses of users would not be a good alternative because the users probably differ in important ways from the general population -- users are probably more familiar with the wetland and they also probably live closer. 0 percent. Again assume that the social marginal rate of time preference is 1. . Year 0 1 2 3 4 5 6 7 Dredging and Patrol Costs ($) 2548000 60000 60000 70000 70000 80000 80000 90000 Saving to Shippers ($) 0 400000 440000 440000 440000 440000 440000 440000 Value of Pleasure Boating ($) 0 60000 175000 175000 175000 175000 175000 175000 The channel would be navigable for seven years. and the shadow price of capital is assumed to be 1. b. rather than 1.S. now assume that the social marginal rate of time preference is 2.5 percent. However. as suggested by the U. They also estimate that all government expenditures come at the expense of private investment. However.2 Exercises for Chapter 10 11. rather than 75 percent. as suggested by the U. e.3.3. the marginal rate of return on private investment is assumed to be 4. Environmental Protection Agency. now assume that only 50 percent of the saving to shippers would be directly invested by the firms or their shareholders. rather than 1. and the remaining 25 percent would be used by shareholders for consumption. f. after which silting would render it un-navigable. Assuming that the costs and benefits accrue at the end of the year they straddle and using the market-based interest rate approach. calculate the present value of net benefits of the project using each of the following methods: a. c.3. Discount using the shadow price of capital method. Again assume that the social marginal rate of time preference is 1. Discount using the shadow price of capital method. Discount using the shadow price of capital method. Discount using the shadow price of capital method. (Spreadsheet required) The following table gives cost and benefit estimates in real dollars for dredging a navigable channel from an inland port to the open sea. Office of Management and Budget. The social marginal rate of time preference is assumed to be 1. Local economists estimate that 75 percent of the savings to shippers would be directly invested by the firms. However. Discount at the marginal rate of return on private investment.5 percent and that the shadow price of capital is 1. now assume that the shadow price of capital is 1. d.1. Discount at the social marginal rate of time preference.S.5 percent. or their shareholders.5 percent.5 percent. 5 as the marginal rate of time preference. . and c.c. The spreadsheet must be modified to answer parts d. which are direct consumption benefits.5 as the marginal rate of time preference result in NPV = $790. 2.b.969.e.d.5 percent).5 percent) yields NPV = $878. 1. 1. then the project passes the net benefits test. if shippers save $440. If we assume that all government expenditures on dredging and patrol displace private investment. 1.3). Once the costs and benefits for each year have been converted to consumption equivalents. 1. and f. Using 1. It is. then we must multiply these costs by the shadow price of capital (1. Thus.000 Applying these adjustments to government expenditures and savings to shippers converts them to consumption equivalents that can be added directly to the pleasure boating benefits. This procedure results in NPV = $614. if the social marginal rate of time preference is used as the discount rate. 1.000)(1. the appropriate discount rate for the agency to use in evaluating alternative investments. We should also multiply the 75 percent of the savings to shippers that they or their shareholders invest by the shadow price of capital.536.5 percent) yields NPV = $503. they can be discounted using the social marginal rate of time preference (1. if the marginal rate of return on private investment is used as the discount rate. Using the social marginal rate of time preference (1.3) = $539.428. then the project passes the net benefits test.000) + (. Thus. 1.523. result in NPV = $399. Note that the NPV is not highly sensitive to modest changes in the value of the shadow price of capital. therefore.1 as the shadow price of capital and 1. which does not pass the net benefits test. which passes the net benefits test.3 as the shadow price of capital and 1. The effective interest rate that we pay on the bonds is the cost that the agency faces in shifting revenue from the future to the present.3 The spreadsheet as provided is set up to answer immediately parts a. Using 2. e. For example.000 in a year.25)($440. Assuming that 50 percent of the savings to shippers would be directly invested. but again using 1. An analyst for a municipal public housing agency explained the choice of a discount rate as follows: “Our agency funds its capital investments through nationally issued bonds.153.754.” Comment on the appropriateness of this discount rate.f. Using the marginal rate of return on private investment (4. the social value of these savings would be (. Note that the NPV is not highly sensitive to modest changes in the marginal rate of time preference. b.75)($440.a.0 as the marginal rate of time preference and the shadow price of capital method results in NPV = $538. one can argue that the borrowing rate in the national market may be the appropriate "social" discount rate. at the social marginal rate of time preference. 3. As suggested in the chapter.b.a. Such an analysis may be administratively relevant for public agencies that are required to be self-financing. From a national perspective. Thus. (1+METB)(C)(s). If the project is financed fully by borrowing that displaces private investment. because it indicates what the municipality --"society" under the restricted standing-. because of taxes. Assume the following: Society faces a marginal excess tax burden of raising public revenue equal to METB. a. The fact that . public borrowing displaces private investment dollar for dollar. On the other hand. The use of the effective rate of interest on the agency's bonds is appropriate as the agency's discount rate from the perspective of a purely financial analysis. the shadow price of capital equals θ. Third. projects that are funded by bonds affect the net consumption flows of the municipality's citizens over time. but from the social perspective. C. B. find the fraction of the investment coming at the expense of investment. 3. this rate is unlikely to correspond to the borrowing rate. projects that the municipality funds through bonds typically result in a flow of benefits to its citizens that are realized at different points in time than the flow of tax expenditures that the citizens must make to repay the loan. discount the stream of consumption benefits. Hence. then the first step is to multiply the capital expenditure by one plus the marginal excess burden --(1+METB)(C)-. Discuss how you would apply the shadow price of capital method to the project if it is financed fully by public borrowing. the appropriateness of using the effective borrowing rate facing the agency as the discount rate is less clear. it is appropriate to use the social discount rate. As discussed in the chapter. and the fraction coming from consumption. and public revenues raised through taxes displace consumption (but not investment). If the project is financed fully by current taxes. B. the rate of time preference is probably substantially less than the rate the agency must pay to borrow on the national market. followed by a stream of benefits that are entirely consumed. Second.must pay to trade future for current revenue. then there are two possibilities.to account for the deadweight loss resulting from the additional taxes. calculate an adjusted investment cost by applying the shadow price of capital to forgone investment: (Pc)(1+METB)(C)(s) + (1+METB)(C)(1-s) Fourth. (1+METB)(C)(1-s). Consider a public project involving a large initial capital expenditure. 3. the rate of time preference of the citizens of the municipality may be the appropriate discount rate. because it represents their trade-off between consumption that occurs in different time periods. then the initial capital cost must be multiplied by the shadow price of capital: (Pc)(C). If we restrict standing to residents of the municipality. Discuss how you would apply the shadow price of capital method to the project if it is financed fully out of current taxes.4 2. On the one hand. b. which is later repaid by taxes. 000. years 1-50. years 201-300. and 0 thereafter.5 the borrowing will be repaid by taxes must also be taken into account. years 101-200. 4. Compute the present value of these benefits using the following time-declining discount rate schedule: 3. Note: This computation is most easily made using a spread sheet function for exponentials. this adjusted stream of net benefits should be discounted at the social marginal rate of time preferences. 4. Finally.00 x 200)) = $6.737.000.) If we assume that the fraction of these social losses representing forgone investment is s. 1.999. NPV = ($1.015 x 100)) x (e-(0.946. the expression appearing above should be multiplied by the dollars of taxes used for repayment purposes each year and then subtracted from the dollars of consumption benefits generated by the project during the year.5 percent. b.000.b. Compute the present value of these benefits using a time-constant discount rate of 3.5 percent.035 x 50)) x (e-(0.000. 51-100. (The payment itself need not be taken into account because it represents a transfer from taxpayers to creditors.000.025 x 50)) x (e-(0. . 2.5 percent.035 x 500) = $25.5 percent. a. years.000 x e-(0. Assume a project will result in benefits of $1 trillion in 500 years by avoiding an environmental disaster that otherwise would occur at that time.5. 4.a.000) x (e-(0. NPV = $1. then a cost equal to the following would be recorded for each dollar of repayment: (METB)(1-s) + (METB)(s)(Pc) To obtain an adjusted stream of net benefits.110.000.005 x 100)) x (e-(0. 0. Each repayment of the loan must be multiplied by (METB) to take account of the social losses associated with raising the revenue to repay the loan. 6 . Consider the example presented in Figure 12. Assuming a linear demand curve through the observed points.31 lbs/p/d. Imagine that the current price of waste disposal is $0.01/lb. 1. 1.50/lb.05/lb.20 lbs/p/d from 2.00317/p/d. Fitting a linear demand curve to the two observed points. Fitting a constant-elasticity demand curve to the observed points.500.05/lb.5)($0.025)(0. b.40 lbs/p/d-2. the average waste disposal was 2.40 lbs/p/d to 2. The analyst identified 24 towns in the region that already had public swimming pools. calculate the annual net benefits of raising the price of waste disposal to $0.7 Exercises for Chapter 12 11. and the marginal social benefits curve (the demand curve) where quantity ranges from the socially optimal quantity to the quantity at the current price.00317/p/d = $0.0075/p/d].0045x100.250. Assume that the marginal social cost of waste disposal is $0. which in this exercise is a horizontal line (p = $0. the net benefits are $0. Assuming a constant-elasticity demand curve.000 people. Pricing closer to the social marginal cost reduces this area.05/lb are $81.52 lb/p/d. quantity only falls to 2.40 lbs/p/d-2.868.) An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville. (Regression software required.$0.31 lb/p/d) = $0. The total reduction in social benefits equals the area under the constant elasticity demand curve.05/lb.40 lb/p/d.b. a. She conducted a telephone interview with the recreation department in each town to find out what fee it charged per visit (FEE) and how many visits it had during the most recent summer season (VISITS). Using a calculator enables us to find the reduction in benefits from the price increase equals $0.000x365 = $164. On an annual basis. as the price rises to $0.2 lbs/p/d)+($0. when the price was previously $0. 2.025)(0.025/lb and the average waste disposal is 2. The gain in benefits equals the total reduction in social cost [($0. The social cost of not setting pricing equal to the social marginal cost is given by the area between the marginal social cost curve. If the town's population is 100.0054/p/d .00223/p/d. spreadsheet provided. she was able to find each town’s population (POP) and median . 1.97.012/p/d] minus the lost benefits given by the area under the demand curve [(. The (net) social benefit equals the reduction in the area.06/lb)(2.20 lbs/p/d) = $0. the net benefits of raising the price to $0. that marginal social costs are constant with respect to quantity. which is given by ( 1 1 / β1 ) βo q1p − q 0p p Where ß0 = 1. As noted in the diagram.053 and p = [1+ ß1] = -17. The total reduction in social cost is ($0. Thus.310. then the annual net benefits are $0.20 lbs/p/d. quantity falls by 0. calculate the annual net benefits of raising the price of waste disposal to $0.230 people and a median household income of $31.000. ß1 = -0.06/lb)(2.06/lb). as the price rises from $0.25/lb to $0.0045/p/d.06/lb.a.3. and that the town has a population of 100.2 lbs/p/d) = $0. which has a population of 70.0054/p/d. In addition. or $0. 685 67.300 25.400 39.515 152.300 35.657 184.318 166.386 116.679 137.900 35.25.762 40.50 0.000 29.800 34.945 79.940 59.056 157. Her data are as follows: VISITS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 168.031 44.625 98.423 158.802 197.694 161.882 69.428 183.50 2.995 172.700 22.25 0.305 84. In answering this question.8 household income (INCOME) in the most recent census.599 198. b. Predict gross benefits if admission is set at $1.102 a.073 58.822 174.505 FEE 0 0 0 0 0 0.50 0.700 20. assume that the fees are used to reduce taxes that would otherwise have to be collected from the citizens of Dryville to pay for expenses incurred in operating the pool.700 32.259 209.50 0.716 167.408 93.600 33.490 164.00 1.600 20.234 71.178 22. Show how the analyst could use these data to predict the gross benefits of opening a public swimming pool in Dryville and allowing free admission.900 38.75 0.820 196.50 0.50 0. .757 88.592 49.600 38.510 187.068 117.50 0.590 179.25 1.662 170.424 179.520 104.600 24.00 1.25 0.928 39.077 104.429 98.00 and Dryville has marginal excess tax burden of 0.123 103.000 26.600 33.018 190.700 37.25 0.100 35.25 0.800 26.50 1.75 1.75 0.879 64.900 21.019 186.800 POP 36.789 98.00 INCOME 20.595 206.800 23.500 39.900 38. 932 6814.9 ------------------------------------------------------- .674 20500 39700 POP 24 75488.49 0.0000 POP 0. Std. Table 1: Summary of Variables Variable | Obs Mean Std.2516 1. The following tables provide the basic statistical analysis.8850e+09 22 312952817 ----------+--------------------------------------Total 7.2077 0.5 17876.273 0. Dev.0633 0.248 33. The provided spreadsheet also provides estimates.2357 0.+--------------------------------------Model 465177728 1 465177728 Residual 6. Err.+-------------------------------------------------------------------------------------------------------FEE -8307.0000 INCOME 0.25 27360.9 5476.0861 0. 22) Prob > F R-square Adj R-square Root MSE = = = = = = 24 1.0207 17690 --------------------------------------------------VISITS | Coef.5413182 0 2 INCOME 24 30675 6843.1217 1.6041667 .236 -22439.56 137423 209995 FEE 24 .115 _cons 182210.7 22928 117940 Table 2: Correlation Matrix | VISITS FEE INCOME POP ------------+--------------------------------------------------------------------------VISITS 1.8309 0. t P>|t| [95% Conf.8 193567.219 0.0000 Table 3: Regression on VISITS on FEE Only Source | SS df MS --------.326 -1. Min Max -----------.0582 1. Interval] ---------.0000 FEE -0.3501e+09 23 319571291 Number of obs F( 1.9 2.000 170853.98 5824.+----------------------------------------------------------------------------------------------------VISITS 24 177191. 8601 6686.37 2634.0000 0.00)(14.849.7 7135.14 0.638) = $7. Std.3 --------.+----------------------------------------Model 6. When price is zero.4272364 POP .5)($12.557 0.14638*FEE -0. t P>|t| [95% Conf.0524211 11.49)(182. Using the regression results presented in Table 4 and rounding. we must subtract the consumer surplus reduction caused by fewer visits from the above estimate.6030525 . Interval] -------------+-----------------------------------------------------------------------------------------------------FEE -14638.1520e+09 Residual 894055106 20 44702755. 2.698 0.638 is computed as: (.2053551 -0.+----------------------------------------Total | 7. we can write the demand equation estimated from the sample as: VISITSS = 140547 .000 125663. we set INCOME=$31.4 155430." the price at which demand falls.58 -9143. to zero is FEE=$12.376 -5.4294902 . INCOME. Err. The area under this demand curve from VISITSdv=0 to VISITSdv=182. To predict the benefits with a $1. At a fee of $1.207.158 INCOME -.000 -20133. The resulting demand curve for Dryville is: VISITSdv = 182849 .4937039 .00.849)=$1.8784 0.000 .4561e+09 3 2. VISITSdv = 182.1 -------------------------------------------------------------------------------------------------------------------2. 20) = Prob > F = R-square = Adj R-square = Root MSE = 24 48.849 is computed as: (.00 fee.002 19. The consumer surplus loss resulting from the reduction in visits by 14.319 .0 -----------------------------------------------------------------------------VISITS | Coef.6031*POP To predict a demand curve for Dryville.3501e+09 23 319571291 Number of obs = F( 3.504 0.892 which is an estimate of the annual gross social benefits of the Dryville pool based on the observed demand behavior in the sample of towns with pools.14638*FEE The "choke price.5)($1. the values for Dryville.200.500 and POP=70.a.b.0011269 .001127*INCOME + 0. and POP Source | SS df MS --------. VISITSdv=168. 7124011 _ con 140546.141.005 0.49.10 Table 4: Regression of VISITS on FEE.996 -. 134.211)=$42. . This amount is (.00 fee is ($1.25)($168.362 would be received by swimmers as consumer surplus.134. Of course.626.211 in revenue that Dryville would realize is a transfer from swimmers to the town. the gross benefit from swimming when there is a $1. So the total gross benefits would be: ($1.573.211 would be received as revenues by the government of Dryville.176. $168.892$7.053)=$1. the marginal excess burden resulting from the government expenditure needed to construct the pool must also be taken into account.11 Therefore. Of this.141.319)=$1. while $966. Although the $168.573+$42. it would result in an additional benefit in the form of reduced excess burden of taxation.053. he recorded the license plates of vehicles parked overnight in the Happy Valley lot.000) a day.000 surely greatly exceeds the value that the welfare mother who receive day care under the program place on it. the fact that virtually no welfare mothers are willing to pay $30 per day per child for day care suggests that $30. On the other hand. a group of welfare recipients is required to provide day care for the children of other welfare recipients who obtain private-sector employment. (Spreadsheet software recommended. virtually no welfare mothers are willing to pay these high costs.000 per year. Do the mothers of the 1. the city establishes a new program: In exchange for their welfare benefits.000 per year in a perfectly safe occupation. On the one hand. 3. he was able to find the town of residence of the owner . the welfare mothers who receive day care under the program must value it at considerably more than $3. The welfare mothers who use these day care services are required to pay a fee of $3 per day per child. works for a wage of $30.12 Exercises for Chapter 13 11.000 children who receive services under the program value these services at $30.000 a day ($3 x 1.000 welfare children receive them each day and an additional 500 welfare children are on a waiting list to receive them. On five randomly selected days. but in a risky occupation with a known death probability of 1 in 1.001. the fact that there is a long waiting list for day care services when welfare mothers are required to pay only $3 per day per child suggests that many welfare mothers are willing to pay well over $3 to receive this service. 1.001 = $4. The value of life implied by this is $4. he assumed that this would constitute a 5 percent sample. Rural County is considering leasing Happy Valley for logging. which allows free access to campers.000 to accept a death risk of . The workers require $4. Almost all visitors to Happy Valley come from the six towns in the county.000 ($30 x 1.000 per year. or at a value that is greater than $3. What value of a human life for workers with these characteristics should a cost-benefit analyst use? 2. Another typical worker does a job requiring exactly the same skills as the first worker.) Happy Valley is the only available camping area in Rural County. An analyst for the county has collected data for a travel cost study to estimate the benefits of Happy Valley camping. (As the camping season is 100 days. given their low potential wages. in the absence of more information about willingness-to-pay. Before approving the lease.000? Explain. Unfortunately.000.000 but less than $30. and receives a wage of $36. The high cost of these services is one reason why very few mothers who are on welfare work. To combat this problem. It is owned by the county. Hence. Day care services in a small Midwestern city cost $30 per day per child. $3.000 and substantially less than $30.000.000). benefits from the program cannot be valued more precisely.000/.000. which would require that it be closed to campers. A worker. These services prove very popular. who is typical in all respects. the county executive would like to know the magnitude of annual benefits that campers would forgo if Happy Valley were to be closed to the public.) With cooperation from the state motor vehicle department.000. We know only that they are likely to be substantially over $3. 1. 2. b.4 19. Third. the average speed on county highways is 50 miles per hour. plot the points and fit a line by sight.3 60. Specifically. assist with the following tasks: a. the opportunity cost to adults of travel time is 40 percent of their wage rate. . For the six observations. He also observed a sample of vehicles from which he estimated that each vehicle carried 3. regress visit rate (VR) on TC and a constant.160.8 11 In order to translate the distance traveled into an estimate of the cost campers faced in using Happy Valley.9 98. Find the slope of the fitted line. the number of camping visits demanded is 14.25 per hour. the analyst made the following assumptions.13 of each vehicle. the average operating cost of vehicles is $0.6 53. The analyst has asked you to help him use this information to estimate the annual benefits accruing to Happy Valley campers. Third.4 146 85 22 180 73 25 77. calculate the travel cost of a vehicle visit (TC) from each of the towns. Using the preceding information. Second. on average. adult campers have the average county wage rate of $9. multiply the predicted VR of each town by its population to get a predicted number of visitors. use the coefficient of TC from the regression to predict a new VR for each town.6 adults). Second. sum the visitors from each town to get the total number of predicted visits.7 65 37.000 People) A B C D E F Total 22 34 48 56 88 94 50. Estimate the area under the demand curve as the annual benefits to campers. Fourth.2 persons (1. This is done in three steps at each price: First.12 per mile. Find additional points on the demand curve by predicting the reduction in the number of campers from each town as price is increased by $5 increments until demand falls to zero. If you do not have regression software available.6 89. The following table summarizes the data he collected: Town Miles from Happy Valley Population (thousands) Number of Vehicles in Sample Estimated Number of Visitors for Season 3893 2267 587 4800 1947 666 14160 Visit Rate(Visits per 1. First. c. You know that with the current free admission.1 34. it is zero for children. d.9 15. The estimated regression equation (standard errors in parentheses.2 persons/vehicle. the average travel cost per person is: $21. estimated as $0.74 26.36/m)(44 m) + (0.88)(10) = 36.88 visits per 1000 residents.4-(2. The following table summarizes the calculation procedure: Town A B C D New Visit Rate (with $10 admission fee) 77.47) The estimated equation indicates that each dollar of additional travel cost reduces the visit rate by 2.6 adults)(44 m)/(50 m/h) = $21.c. the impact of a $10 admission fee. The second is the opportunity cost of time.05/3.7-(2.25/h)(1. The first is vehicle operating expense. 3.88)(10) = 48.88 TC (11.2 = $6.a.31 28.88)(10) = 24.17 14.11 3. is: ($0.53 $45.93 $53.14 3.0-(2.35 16.05/vehicle-visit Because there are 3.94 Travel Cost/person 6.2 37.12 per mile times the round trip distance. which is estimated as the travel time of adults multiplied by 40 percent of the wage rate. which is 22 miles from Happy Valley (44 miles round trip). The costs per person (and the cost/trip) for the towns are thus: Town A B C D E F Travel Cost/trip $21.6-(2.58 $84.20 $89.96) is: VR = 93. For example.2.40)($9.9 65. The travel cost from each town consists of two components (admission is free). for example.50/person. R2=0.15) (-6.14 .88)(10) = 8.6 Predicted Visits (VR times population) 2450 1263 137 2212 .b. the travel cost for a visit from Town A.05 $32.58 10. Consider.8 53. 8-(2. Repeating this procedure leads to the following points on the derived demand curve: Price 0 $5 $10 $15 $20 $25 Number of Visits 14. we set these predicted visit rates to zero.88)(10) = -9.175 Therefore.15 E F 19.406 1. our estimate of the annual benefits from camping in Happy Valley is $137.175.336 6. To estimate the area under this demand curve. .0 11. $5.435x5 = $137.0-(2.062 3.8 0 0 Note that a $10 admission fee leads to a prediction of negative visit rates for Towns E and F. Summing the predicted number of visits for the towns gives a total 6.98.88)(10) = -17. (The calculated choke price is $26. but the accuracy of the estimation procedure does not justify such a precise prediction) 3.160 9. multiply the average heights of adjacent points times their width.062 visits.d. and sum: area = {[(14160+9336)/2]+[(9336+6062)/2]+[(6062+3406)/2] +[(3406+1265/2]+[(1265+286)/2]+[(286+0)/2] }($5) = $27.265 286 Demand approximately falls to zero between $25 and $30. As visit rates cannot be negative. 16 .