Question

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. With cooperation from the state motor vehicle department, he was able to find the town of residence of the owner 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.

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 $0.36 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.

1. Calculate the time spent travelling from each town for the round-trip (Hint: Time = Distance/Speed). Note that the data posted on distance is for only one way.
2. Calculate the opportunity cost of time spent travelling for adults per vehicle from each town for the roundtrip.
3. Calculate the operating vehicle cost from each town for the round-trip.
4. Calculate the total cost of travelling per vehicle from each town (Hint: add the values you got from (b) and (c))
5. Calculate the total cost of travelling per vehicle per person (Hint: divide the values you derived from (d) by

3.2 for each town).

6. For the six observations, regress visit rate on Total Cost of travelling per person (TC) derived from (e) and a constant.

Town	Miles from Happy Valley (one-way)	Population (thousands)	Estimated Number of Visitors for Season	Visit Rate (Visits per 1,000 People)
A	22	50.1	3,893	77.7
B	34	34.9	2,267	65.0
C	48	15.6	587	37.6
D	56	89.9	4,800	53.4
E	88	98.3	1,947	19.8
F	94	60.4	666	11.0
Total			14,160

Answer 1

Given the following information:

Each vehicle carried = 3.2 person ( 1.6 adults)

Average operating cost of vehicle = $ 0,36 per mile

Average speed = 50 miles per hour

Oppurtunity cost to adults of travel time = 40% of their wage rate

Wage rate per hour is $ 9.25

a). Caluculation of time spent for travelling from each town for the round trip:

Time spent = number of miles X 2 way X Number of visitors / miles per hour

Town A = 22 X 2 X 3893 = 171292 miles / 50 miles per hour = 3425. 84 total hours.

  Town B = 34 X 2 X 2267 = 154156 miles / 50 miles per hour = 3083.12 total hours

Town C = 48 X 2 X 587 = 56352 miles / 50 miles per hour = 1127.04 total hours.

Town D = 56 X 2 X 4800 = 537600 miles / 50 miles per hour = 10752 total hours

Town E = 88 X 2 X 1947 = 342672 miles / 50 miles per hour = 6853.44 total hours

Town F = 94 X 2 X 666 = 125208 miles / 50 miles per hour = 2504. 16 total hours.

b). Caluculation of oppurtunity cost of time spent on travelling for adults per vehicle from each town.

Oppurtunity cost = Total adult hours X wage rate per hour X 40%

Adult hours = total hours / 1.6 person

Number of vehicles = total number of visitors / 1.6 person

Oppurtunity cost :

Town A = 3425.84 / 1.6 = 2141.15 adult hours X $ 9.25 X 40% = $ 7922.25

Number of vehicles = 3893 / 1.6 = 2433.12

Oppurtunity cost per vehicle = $ 7922.25 / 2433.12 = $ 3.25

Town B = 3083.12 / 1.6 = 1926.95 adult hours X $ 9.25 X 40 % = $ 7129.72

Number of vehicles = 2267 / 1.6 = 1416. 88

   Oppurtunity cost per vehicle = $ 7129.72/ 1416.88 = $ 5.03

Town C = 1127.04 / 1.6 = 704.4 Adult hours X $ 9.25 X 40% = $ 2606.28

Number of vehicles = 587 / 1.6 = 366.87

oppurtunity cost per vehicle = $ 2606.28 / 366.87 = $ 7.1

Town D = 10752 / 1.6 =6720 adult hours X $ 9.25 X 40% = $24864

Number of vehicles = 4800 / 1.6 = 3000

oppurtunity cost per vehicle = $ 24864 / 3000 = $ 8.29

Town E = 6853.44 / 1.6 = 4283.4 adult hours X $ 9.25 X 40% = 15848.58

Number of vehicles = 1947 / 1.6 = 1216.88

oppurtunity cost per vehicle = $ 15848.58 / 1216.88 = $ 13.02

Town F = 2504.16 / 1.6 = 1565.1 adult hours X $ 9.25 X 40% = $ 5790. 87

Number of vehicles = 666/ 1.6 = 416.25

  oppurtunity cost per vehicle = $ 5790.87 / 416.25 = $13.91

c). caluculation of operating cost

OPERATING COST = total number of miles X rate per mile

Town A = 171292 X $ 0.36 =$ 61665.12

Town B = 154156 X $ 0.36 = $ 55496.16

Town C = 56352 X $ 0,36 = $ 20286.72

Town D = 537600 X $ 0.36 = $ 193536

Town E = 342672 X $ 0.36 = $ 123361.92

Town F = 125208 X $ 0.36 = $45074.88

d). caluculate the total cost of travelling for each town

total cost =( b) + (c)

e). caluculation total cost of travelling per vehicle per person

divide the values derived from (d) / 3.2