## Problem 9 Suppose the state is trying to decide how many miles of a very scenic river it should preserve. There are 10,000 people in the city, each of whom has an identical inverse demand function given by p = 36 – 0.08q, where q is the number of miles preserved and p is the per-mile price he or she is willing to pay for q miles of preserved river.

Problem 9

Suppose the state is trying to decide how many miles of a very scenic river it should preserve. There are 10,000 people in the city, each of whom has an identical inverse demand function given by p = 36 – 0.08q, where q is the number of miles preserved and p is the per-mile price he or she is willing to pay for q miles of preserved river.

a. If the marginal cost (dollars per mile) of preservation is p = 2500 + 8q2, how many miles would be preserved in an efficient allocation? Round to three decimal places.

b. What would be the marginal value of saving the last mile up to the efficient allocation?

c. What would be the total costs of preservation?

Total cost is the area under the marginal cost curve up to the quantity produced (or in this case preserved). On the graph below, this is Area C. So to find this, integrate the marginal cost function between 0 and the efficient allocation, 31.777 miles.

The total cost function is thus 2500q + (8/3)q3. This gives us a total cost of

d. How large would the net benefits be

Problem 10

The marginal private cost of the production of stooges is described by the following equation, where Q is the quantity of stooges produces.

MPC = 8 + 0.8Q

Unfortunately, the production of stooges has a detrimental impact on the environment, estimated by the following damage function:

MD = 1.2Q

The private market demand for the production of stooges is described by the following equation:

MPB = 80 – 4Q

The government decides to set a Pigouvian tax to account for the environmental damages caused by stooges. What is the optimal Pigouvian tax? What is the expected government revenue generated from this tax?