The city of Glassboro 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 $5 per swimmer per day. The estimated cost of the swimming pool, averaged over the life of the pool, is $3 per swimmer per day. Glassboro has hired you to assess this project. Fortunately, the neighboring identical town of Pitman 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:

Swimming pool price per day Number of swimmers per day
$8 500
$10 200
$4 1,100
$6 800
$2 1,400

(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 a 1,400-swimming pool the optimally sized swimming pool for Calgary to build? Explain.