The city of Gruberville is considering whether to build a new public swimming pool. This pool would have a capacity of 800 swimmers per day, and the proposed admission fee is $6 per swimmer per day. The estimated cost of the swimming pool, averaged over the life of the pool, is $4 per swimmer per day. Gruberville has hired you to assess this project. Fortunately, the neighboring identical town of Figlionia already has a pool, and the town has randomly varied the price of that pool to find how price affects usage. The results from their study follow:
a. If the swimming pool is built as planned, what would be the net benefit per day from the swimming pool? What is the consumer surplus for swimmers?
b. Given this information, is an 800-swimmer pool the optimally sized pool for Gruberville to build? Explain.