Jellystone National Park is located 10 minutes away from city A and 20 minutes a

Question

Jellystone National Park is located 10 minutes away from city A and 20 minutes away from city B. Cities A and B have 200,000 inhabitants each, and residents in both cities have the same income and preferences for national parks. Assume that the cost for an individual to go to a national park is represented by the cost of the time it takes her to get into the park. Also assume that the cost of time for individuals in cities A and B is $.50 per minute.

You observe that each inhabitant of city A goes to Jellystone ten times a year while each inhabitant of city B goes only five times a year. Assume the following: the only people who go to the park are the residents of cities A and B; the cost of running Jellystone is $1,500,000 a year; and the social discount rate is 10%. Also assume that the park lasts forever.

A) Compute the cost per visit to Jellystone for an inhabitant of each city. b. Assuming that those two observations (cost per visit and number of visits per inhabitant of city A, and cost per visit and number of visits per inhabitant of city

B) correspond to two points of the same linear individual demand curve for visits to Jellystone, derive that demand curve. What is the consumer surplus for inhabitants of each city? What is the total consumer surplus?

C) There is a timber developer who wants to buy Jellystone to run his business. He is offering $100 million for the park. Should the park be sold?

Explanation / Answer

(A)

(a) Cost per visit

Cost of visit, City A = 10 minutes x $0.50

= $5

Cost of visit, City B = 20 minutes x $0.50

= $10

(B)

A linear demand curve is of the form:

P = a - bQ [Q: Quantity/Number of visits, P: Price]

(i) City A

Number of visits (Per year) = 10

Price per visit is equal to Cost per visit = 5

In the form P = a - bQ, When Q = 0, P = a (Vertical intercept of demand curve]

So, a = 5 [Maximum price that buyers are willing to pay]

Again, when P = 0, b x Q = a, Or (b x 10) = 5, Hence b = 5 / 10 = 0.50

So, demand curve can be written as:

P = 5 - 0.5Q

This is the demand curve for City A.

Consumer surplus = 0, since maximum price buyers are willing to pay equals the actual price they pay (=$5)

(ii) City B

In the form P = a - bQ, When Q = 0, P = a (Vertical intercept of demand curve]

So, a = 10 [Maximum price that buyers are willing to pay]

Again, when P = 0, b x Q = a, Or (b x 10) = 10, Hence b = 10 / 10 = 1

So, demand curve can be written as:

P = 10 - Q

This is the demand curve for City A.

Consumer surplus = 0, since maximum price buyers are willing to pay equals the actual price paid (=$1).

(C)

(i) Total annual benefit = Total revenue from visits from both cities

= $5 per visit x 200,000 visitors x 10 visits a year [City A] + $10 x 200,000 visitors x 5 visits a year [City B]

= $(10,000,000 + 10,000,000) = $20,000,000

Total annual cost = $1,500,000

Net annual income = $(20,000,000 - 1,500,000) = $18,500,000

This net annual income occurs in perpetuity.

So, Present value of this perpetual income = Net Annual income / Discount rate

= $18,500,000 / 0.10 = $185,000,000 = $185 million

Purchase Offer received for $100 million, which is lower than the Lifetime Value of Income from the park.

So the purchase offer should be refused.

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