Exercises for Chapter 9

1. 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 wetland-fishers, 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 willingness-to-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.

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Exercises for Chapter 10

1. (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.

Year Dredging and Patrol Costs ($)

Saving to Shippers ($)

Value of Pleasure Boating ($)

0 2548000 0 0

1 60000 400000 60000

2 60000 440000 175000

3 70000 440000 175000

4 70000 440000 175000

5 80000 440000 175000

6 80000 440000 175000

7 90000 440000 175000

The channel would be navigable for seven years, after which silting would render it un-navigable. Local economists estimate that 75 percent of the savings to shippers would be directly invested by the firms, or their shareholders, and the remaining 25 percent would be used by shareholders for consumption. They also estimate that all government expenditures come at the expense of private investment. The social marginal rate of time preference is assumed to be 1.5 percent, the marginal rate of return on private investment is assumed to be 4.5 percent, and the shadow price of capital is assumed to be 1.3.

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. Discount at the marginal rate of return on private investment, as suggested by the U.S. Office of Management and Budget.

b. Discount at the social marginal rate of time preference, as suggested by the U.S. Environmental Protection Agency.

c. Discount using the shadow price of capital method. d. Discount using the shadow price of capital method. However, now assume that

the social marginal rate of time preference is 2.0 percent, rather than 1.5 percent.e. Discount using the shadow price of capital method. However, now assume that

the shadow price of capital is 1.1, rather than 1.3. Again assume that the social marginal rate of time preference is 1.5 percent.

f. Discount using the shadow price of capital method. However, now assume that only 50 percent of the saving to shippers would be directly invested by the firms or their shareholders, rather than 75 percent. Again assume that the social marginal rate of time preference is 1.5 percent and that the shadow price of capital is 1.3.

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The spreadsheet as provided is set up to answer immediately parts a, b, and c.

1.a. Using the marginal rate of return on private investment (4.5 percent) yields NPV = $503,523. Thus, if the marginal rate of return on private investment is used as the discount rate, then the project passes the net benefits test.

1.b. Using the social marginal rate of time preference (1.5 percent) yields NPV = $878,428. Thus, if the social marginal rate of time preference is used as the discount rate, then the project passes the net benefits test.

1.c. If we assume that all government expenditures on dredging and patrol displace private investment, then we must multiply these costs by the shadow price of capital (1.3). We should also multiply the 75 percent of the savings to shippers that they or their shareholders invest by the shadow price of capital. For example, if shippers save $440,000 in a year, the social value of these savings would be

(.25)($440,000) + (.75)($440,000)(1.3) = $539,000

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, which are direct consumption benefits. Once the costs and benefits for each year have been converted to consumption equivalents, they can be discounted using the social marginal rate of time preference (1.5 percent). This procedure results in NPV = $614,754, which passes the net benefits test.

The spreadsheet must be modified to answer parts d, e, and f.

1.d. Using 2.0 as the marginal rate of time preference and the shadow price of capital method results in NPV = $538,153, which does not pass the net benefits test. Note that the NPV is not highly sensitive to modest changes in the marginal rate of time preference.

1.e. Using 1.1 as the shadow price of capital and 1.5 as the marginal rate of time preference result in NPV = $790,536. Note that the NPV is not highly sensitive to modest changes in the value of the shadow price of capital.

1.f. Assuming that 50 percent of the savings to shippers would be directly invested, but again using 1.3 as the shadow price of capital and 1.5 as the marginal rate of time preference, result in NPV = $399,969.

2. 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. 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. It is, therefore, the appropriate discount rate for the agency to use in evaluating alternative investments.” Comment on the appropriateness of this discount rate.

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2. 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. Such an analysis may be administratively relevant for public agencies that are required to be self-financing; but from the social perspective, the appropriateness of using the effective borrowing rate facing the agency as the discount rate is less clear.

From a national perspective, it is appropriate to use the social discount rate. As discussed in the chapter, this rate is unlikely to correspond to the borrowing rate.

If we restrict standing to residents of the municipality, then there are two possibilities. On the one hand, one can argue that the borrowing rate in the national market may be the appropriate "social" discount rate, because it indicates what the municipality --"society" under the restricted standing-- must pay to trade future for current revenue. On the other hand, 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. Thus, projects that are funded by bonds affect the net consumption flows of the municipality's citizens over time. Hence, 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. As suggested in the chapter, because of taxes, the rate of time preference is probably substantially less than the rate the agency must pay to borrow on the national market.

3. Assume the following: Society faces a marginal excess tax burden of raising public revenue equal to METB; the shadow price of capital equals θ; public borrowing displaces private investment dollar for dollar; and public revenues raised through taxes displace consumption (but not investment). Consider a public project involving a large initial capital expenditure, C, followed by a stream of benefits that are entirely consumed, B.

a. Discuss how you would apply the shadow price of capital method to the project if it is financed fully out of current taxes.

b. Discuss how you would apply the shadow price of capital method to the project if it is financed fully by public borrowing, which is later repaid by taxes.

3.a. If the project is financed fully by current taxes, then the first step is to multiply the capital expenditure by one plus the marginal excess burden --(1+METB)(C)-- to account for the deadweight loss resulting from the additional taxes. Second, find the fraction of the investment coming at the expense of investment, (1+METB)(C)(s), and the fraction coming from consumption, (1+METB)(C)(1-s). Third, 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, discount the stream of consumption benefits, B, at the social marginal rate of time preference.

3.b. If the project is financed fully by borrowing that displaces private investment, then the initial capital cost must be multiplied by the shadow price of capital: (Pc)(C). The fact that

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the borrowing will be repaid by taxes must also be taken into account. 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. (The payment itself need not be taken into account because it represents a transfer from taxpayers to creditors.) If we assume that the fraction of these social losses representing forgone investment is s, 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, 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. Finally, this adjusted stream of net benefits should be discounted at the social marginal rate of time preferences.

4. 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.

a. Compute the present value of these benefits using a time-constant discount rate of 3.5. b. Compute the present value of these benefits using the following time-declining discount rate schedule: 3.5 percent, years 1-50; 2.5 percent, years, 51-100; 1.5 percent, years 101-200; 0.5 percent, years 201-300; and 0 thereafter.

4.a. NPV = $1,000,000,000,000 x e-(0.035 x 500) = $25,110.

Note: This computation is most easily made using a spread sheet function for exponentials.

4.b. NPV = ($1,000,000,000,000) x (e-(0.035 x 50)) x (e-(0.025 x 50)) x (e-(0.015 x 100)) x (e-(0.005 x 100)) x (e-(0.00 x 200)) = $6,737,946,999.

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Exercises for Chapter 12

1. Consider the example presented in Figure 12.3. Imagine that the current price of waste disposal is $0.025/lb and the average waste disposal is 2.40 lb/p/d. As noted in the diagram, when the price was previously $0.01/lb, the average waste disposal was 2.52 lb/p/d. Assume that the marginal social cost of waste disposal is $0.06/lb, that marginal social costs are constant with respect to quantity, and that the town has a population of 100,000.

a. Fitting a linear demand curve to the two observed points, calculate the annual net benefits of raising the price of waste disposal to $0.05/lb.

b. Fitting a constant-elasticity demand curve to the observed points, calculate the annual net benefits of raising the price of waste disposal to $0.05/lb.

1. The social cost of not setting pricing equal to the social marginal cost is given by the area between the marginal social cost curve, which in this exercise is a horizontal line (p = $0.06/lb), and the marginal social benefits curve (the demand curve) where quantity ranges from the socially optimal quantity to the quantity at the current price. Pricing closer to the social marginal cost reduces this area. The (net) social benefit equals the reduction in the area.

1.a. Assuming a linear demand curve through the observed points, as the price rises from $0.25/lb to $0.50/lb, quantity falls by 0.20 lbs/p/d from 2.40 lbs/p/d to 2.20 lbs/p/d. The gain in benefits equals the total reduction in social cost [($0.06/lb)(2.40 lbs/p/d-2.20 lbs/p/d) = $0.012/p/d] minus the lost benefits given by the area under the demand curve [(.5)($0.025)(0.2 lbs/p/d)+($0.025)(0.2 lbs/p/d) = $0.0075/p/d], or $0.0045/p/d. If the town's population is 100,000 people, then the annual net benefits are $0.0045x100,000x365 = $164,250.

1.b. Assuming a constant-elasticity demand curve, as the price rises to $0.05/lb, quantity only falls to 2.31 lbs/p/d. The total reduction in social cost is ($0.06/lb)(2.40 lbs/p/d-2.31 lb/p/d) = $0.0054/p/d. The total reduction in social benefits equals the area under the constant elasticity demand curve, which is given by

Where ß0 = 1.97, ß1 = -0.053 and p = [1+ ß1] = -17.868. Using a calculator enables us to find the reduction in benefits from the price increase equals $0.00317/p/d. Thus, the net benefits are $0.0054/p/d - $0.00317/p/d = $0.00223/p/d. On an annual basis, the net benefits of raising the price to $0.05/lb are $81,310.

2. (Regression software required; spreadsheet provided.) An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 70,230 people and a median household income of $31,500. The analyst identified 24 towns in the region that already had public swimming pools. 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). In addition, she was able to find each town’s population (POP) and median

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household income (INCOME) in the most recent census. Her data are as follows:

VISITS FEE INCOME POP

1 168,590 0 20,600 36,879

2 179,599 0 33,400 64,520

3 198,595 0 39,700 104,123

4 206,662 0 32,600 103,073

5 170,259 0 24,900 58,386

6 209,995 0.25 38,000 116,592

7 172,018 0.25 26,700 49,945

8 190,802 0.25 20,800 79,789

9 197,019 0.25 26,300 98,234

10 186,515 0.50 35,600 71,762

11 152,679 0.50 38,900 40,178

12 137,423 0.50 21,700 22,928

13 158,056 0.50 37,900 39,031

14 157,424 0.50 35,100 44,685

15 179,490 0.50 35,700 67,882

16 164,657 0.75 22,900 69,625

17 184,428 0.75 38,600 98,408

18 183,822 0.75 20,500 93,429

19 174,510 1.00 39,300 98,077

20 187,820 1.00 25,800 104,068

21 196,318 1.25 23,800 117,940

22 166,694 1.50 34,000 59,757

23 161,716 1.50 29,600 88,305

24 167,505 2.00 33,800 84,102

a. 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.

b. Predict gross benefits if admission is set at $1.00 and Dryville has marginal excess tax burden of 0.25. In answering this question, 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.

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2. The following tables provide the basic statistical analysis. The provided spreadsheet also provides estimates.

Table 1: Summary of Variables

Variable | Obs Mean Std. Dev. Min Max------------ +----------------------------------------------------------------------------------------------------- VISITS 24 177191.5 17876.56 137423 209995 FEE 24 .6041667 .5413182 0 2 INCOME 24 30675 6843.674 20500 39700 POP 24 75488.25 27360.7 22928 117940

Table 2: Correlation Matrix

| VISITS FEE INCOME POP------------+--------------------------------------------------------------------------- VISITS 1.0000 FEE -0.2516 1.0000INCOME 0.0861 0.0582 1.0000 POP 0.8309 0.2077 0.1217 1.0000

Table 3: Regression on VISITS on FEE Only

Source | SS df MS Number of obs = 24--------- +--------------------------------------- F( 1, 22) = 1.49 Model 465177728 1 465177728 Prob > F = 0.2357Residual 6.8850e+09 22 312952817 R-square = 0.0633----------+--------------------------------------- Adj R-square = 0.0207 Total 7.3501e+09 23 319571291 Root MSE = 17690

--------------------------------------------------- VISITS | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------- +-------------------------------------------------------------------------------------------------------- FEE -8307.932 6814.326 -1.219 0.236 -22439.98 5824.115 _cons 182210.9 5476.248 33.273 0.000 170853.8 193567.9-------------------------------------------------------

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Table 4: Regression of VISITS on FEE, INCOME, and POP

Source | SS df MS Number of obs = 24--------- +----------------------------------------- F( 3, 20) = 48.14 Model 6.4561e+09 3 2.1520e+09 Prob > F = 0.0000Residual 894055106 20 44702755.3 R-square = 0.8784--------- +----------------------------------------- Adj R-square = 0.8601 Total | 7.3501e+09 23 319571291 Root MSE = 6686.0

------------------------------------------------------------------------------ VISITS | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+------------------------------------------------------------------------------------------------------ FEE -14638.37 2634.376 -5.557 0.000 -20133.58 -9143.158 INCOME -.0011269 .2053551 -0.005 0.996 -.4294902 .4272364 POP .6030525 .0524211 11.504 0.000 .4937039 .7124011 _ con 140546.7 7135.002 19.698 0.000 125663.4 155430.1---------------------------------------------------------------------------------------------------------------------

2.a. Using the regression results presented in Table 4 and rounding, we can write the demand equation estimated from the sample as:

VISITSS = 140547 - 14638*FEE -0.001127*INCOME + 0.6031*POP

To predict a demand curve for Dryville, we set INCOME=$31,500 and POP=70,200, the values for Dryville. The resulting demand curve for Dryville is:

VISITSdv = 182849 - 14638*FEE

The "choke price," the price at which demand falls, to zero is FEE=$12.49. When price is zero, VISITSdv = 182,849. The area under this demand curve from VISITSdv=0 to VISITSdv=182,849 is computed as:

(.5)($12.49)(182,849)=$1,141,892 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.

2.b. To predict the benefits with a $1.00 fee, we must subtract the consumer surplus reduction caused by fewer visits from the above estimate. At a fee of $1.00, VISITSdv=168,207. The consumer surplus loss resulting from the reduction in visits by 14,638 is computed as:

(.5)($1.00)(14,638) = $7,319

Therefore, the gross benefit from swimming when there is a $1.00 fee is ($1,141,892-$7,319)=$1,134,573. Of this, $168,211 would be received as revenues by the government of

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Dryville, while $966,362 would be received by swimmers as consumer surplus.

Although the $168,211 in revenue that Dryville would realize is a transfer from swimmers to the town, it would result in an additional benefit in the form of reduced excess burden of taxation. This amount is (.25)($168,211)=$42,053. So the total gross benefits would be:

($1,134,573+$42,053)=$1,176,626.

Of course, the marginal excess burden resulting from the government expenditure needed to construct the pool must also be taken into account.

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Exercises for Chapter 13

1. Day care services in a small Midwestern city cost $30 per day per child. The high cost of these services is one reason why very few mothers who are on welfare work; given their low potential wages, virtually no welfare mothers are willing to pay these high costs. To combat this problem, the city establishes a new program: In exchange for their welfare benefits, a group of welfare recipients is required to provide day care for the children of other welfare recipients who obtain private-sector employment. The welfare mothers who use these day care services are required to pay a fee of $3 per day per child. These services prove very popular; 1,000 welfare children receive them each day and an additional 500 welfare children are on a waiting list to receive them. Do the mothers of the 1,000 children who receive services under the program value these services at $30,000 ($30 x 1,000) a day, $3,000 a day ($3 x 1,000), or at a value that is greater than $3,000 but less than $30,000? Explain.

1. On the one hand, 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. Hence, the welfare mothers who receive day care under the program must value it at considerably more than $3,000. On the other hand, the fact that virtually no welfare mothers are willing to pay $30 per day per child for day care suggests that $30,000 surely greatly exceeds the value that the welfare mother who receive day care under the program place on it. Unfortunately, in the absence of more information about willingness-to-pay, benefits from the program cannot be valued more precisely. We know only that they are likely to be substantially over $3,000 and substantially less than $30,000.

2. A worker, who is typical in all respects, works for a wage of $30,000 per year in a perfectly safe occupation. Another typical worker does a job requiring exactly the same skills as the first worker, but in a risky occupation with a known death probability of 1 in 1,000 per year, and receives a wage of $36,000 per year. What value of a human life for workers with these characteristics should a cost-benefit analyst use?

2. The workers require $4,000 to accept a death risk of .001. The value of life implied by this is $4,000/.001 = $4,000,000.

3. (Spreadsheet software recommended.) Happy Valley is the only available camping area in Rural County. It is owned by the county, which allows free access to campers. Almost all visitors to Happy Valley come from the six towns in the county.

Rural County is considering leasing Happy Valley for logging, which would require that it be closed to campers. Before approving the lease, 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.

An analyst for the county has collected data for a travel cost study to estimate the benefits of Happy Valley camping. On five randomly selected days, he recorded the license plates of vehicles parked overnight in the Happy Valley lot. (As the camping season is 100 days, he assumed that this would constitute a 5 percent sample.) With cooperation from the state motor vehicle department, he was able to find the town of residence of the owner

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of each vehicle. He also observed a sample of vehicles from which he estimated that each vehicle carried 3.2 persons (1.6 adults), on average. 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

Visit Rate(Visits per

1,000 People)

A 22 50.1 146 3893 77.7

B 34 34.9 85 2267 65

C 48 15.6 22 587 37.6

D 56 89.9 180 4800 53.4

E 88 98.3 73 1947 19.8

F 94 60.4 25 666 11

Total 14160

In order to translate the distance traveled into an estimate of the cost campers faced in using Happy Valley, the analyst made the following assumptions. First, the average operating cost of vehicles is $0.12 per mile. Second, the average speed on county highways is 50 miles per hour. Third, the opportunity cost to adults of travel time is 40 percent of their wage rate; it is zero for children. Fourth, adult campers have the average county wage rate of $9.25 per hour.

The analyst has asked you to help him use this information to estimate the annual benefits accruing to Happy Valley campers. Specifically, assist with the following tasks:

a. Using the preceding information, calculate the travel cost of a vehicle visit (TC) from each of the towns.

b. For the six observations, regress visit rate (VR) on TC and a constant. If you do not have regression software available, plot the points and fit a line by sight. Find the slope of the fitted line.

c. You know that with the current free admission, the number of camping visits demanded is 14,160. 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. This is done in three steps at each price: First, use the coefficient of TC from the regression to predict a new VR for each town. Second, multiply the predicted VR of each town by its population to get a predicted number of visitors. Third, sum the visitors from each town to get the total number of predicted visits.

d. Estimate the area under the demand curve as the annual benefits to campers.

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3.a. The travel cost from each town consists of two components (admission is free). The first is vehicle operating expense, estimated as $0.12 per mile times the round trip distance. The second is the opportunity cost of time, which is estimated as the travel time of adults multiplied by 40 percent of the wage rate. For example, the travel cost for a visit from Town A, which is 22 miles from Happy Valley (44 miles round trip), is:

($0.36/m)(44 m) + (0.40)($9.25/h)(1.6 adults)(44 m)/(50 m/h) = $21.05/vehicle-visit

Because there are 3.2 persons/vehicle, the average travel cost per person is:

$21.05/3.2 = $6.50/person.

The costs per person (and the cost/trip) for the towns are thus:

Town Travel Cost/trip Travel Cost/person A $21.05 6.58 B $32.53 10.17 C $45.93 14.35 D $53.58 16.74 E $84.20 26.31 F $89.94 28.11

3.b. The estimated regression equation (standard errors in parentheses, R2=0.96) is:

VR = 93.14 - 2.88 TC (11.15) (-6.47)

The estimated equation indicates that each dollar of additional travel cost reduces the visit rate by 2.88 visits per 1000 residents.

3.c. Consider, for example, the impact of a $10 admission fee. The following table summarizes the calculation procedure:

Town New Visit Rate (with $10 admission fee)

Predicted Visits(VR times population)

A 77.7-(2.88)(10) = 48.9 2450

B 65.0-(2.88)(10) = 36.2 1263

C 37.6-(2.88)(10) = 8.8 137

D 53.4-(2.88)(10) = 24.6 2212

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E 19.8-(2.88)(10) = -9.0 0

F 11.0-(2.88)(10) = -17.8 0

Note that a $10 admission fee leads to a prediction of negative visit rates for Towns E and F. As visit rates cannot be negative, we set these predicted visit rates to zero. Summing the predicted number of visits for the towns gives a total 6,062 visits.

Repeating this procedure leads to the following points on the derived demand curve:

Price Number of Visits

0 14,160

$5 9,336

$10 6,062

$15 3,406

$20 1,265

$25 286

Demand approximately falls to zero between $25 and $30. (The calculated choke price is $26.98, but the accuracy of the estimation procedure does not justify such a precise prediction)

3.d. To estimate the area under this demand curve, multiply the average heights of adjacent points times their width, $5, and sum:

area = {[(14160+9336)/2]+[(9336+6062)/2]+[(6062+3406)/2] +[(3406+1265/2]+[(1265+286)/2]+[(286+0)/2] }($5)

= $27,435x5 = $137,175

Therefore, our estimate of the annual benefits from camping in Happy Valley is $137,175.

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