Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 30

The town of Pleasantville is thinking of building a swimming pool. Building and operating the pool will cost the town $5,000 per day. There are three groups of potential pool users in Pleasantville: (1) 1,000 families who are each willing to pay $3 per day for the pool, (2) 1,000 families who are each willing to pay $2 per day for the pool, and (3) 1,000 families who are each willing to pay $1 per day for the pool. Suppose also that the intended pool is large enough so that whatever number of families come on any day will not affect what people are willing to pay for the pool.
a. Which property of public goods does this pool have? Which does it not have?
b. Would building the pool be an efficient use of resources?
c. Consider four possible prices for family admission to the pool: (1) $3, (2) $2, (3) $1, and
(4) $0. Which of these prices would result in covering the cost of the pool? Which of the prices would achieve an efficient allocation of resources?
d. Is there any pricing scheme for admission to this pool that would both cover the pool's cost and achieve an efficient allocation of resources?
e. Suppose that this pool has a capacity of only 2,000 families per day. If more than 2,000 families are admitted, the willingness to pay of any family (with children or not) falls to $0.50 per day. Now what is the efficient pricing scheme for the pool?