Question

1. There are important trade-offs involved in granting "Wild and Scenic River Status" to portions of a river. The critical issue is how much of this public good, a free-flowing river, should be protected from further development. As an analyst in the Office of Policy Analysis of the U.S. Department of the Interior, you are called upon to make a recommendation, based upon the following information. Each year, 1000 people benefit from the River's various services, exclusively for recreational purposes. A contingent valuation survey carried out by your office has estimated that each beneficiary has the same demand function for river preservation, Q = 40 - 0.4P where P is the price-per-mile which persons are willing to pay (per year) for Q miles of river preserved. You find that the marginal (opportunity) cost of preservation is $25,000 per mile per year. [Hint: You need to derive the market (aggregate) demand curve for a public good.]

e) What is the magnitude of the total (gross) annual benefits associated with this (efficient allocation) policy?

f) What is the magnitude of the total (gross) annual costs associated with this (efficient allocation) policy?

g) What is the magnitude of the net annual benefits associated with this (efficient allocation) policy?

Answer 1

The demand function of the river's preservation for each beneficiary is

Q=40-0.4P

The demand function remains the same for all the beneficiaries and there are 1000 people. Thus, the aggregate demand function of the public good is given as

1000Q=40,000-400P

Since P is the price-per-mile which persons are willing to pay (per year) for Q miles of river preserved, the total (gross) annual benefits associated with this efficient allocation policy is $1000PQ = $1000(40P-0.4P2).

The marginal (opportunity) cost of preservation is $25,000 per mile per year. Hence, the total (gross) annual costs associated with this (efficient allocation) policy is $(25,000*1000Q)=$25,000,000(40-0.4P).

The net annual benefits associated with this (efficient allocation) policy is $[1000(40P-0.4P2)-25,000,000(40-0.4P)]