A water supplier faces demand characterized by inverse demand function p = 100 − 2q. The supplier has somewhat unusual cost structure that results in a marginal cost function of the form MC(q) = 44 − (3/5)(q).
(a) Show how you find the economically efficient price and quantity.
(b) What are the net returns (i.e., profits) that the water supplier “enjoys” if they price at the economically efficient price?
(c) Suppose that the supplier can now employ simple two-tier pricing: one price for the first ¯q volume of water, and the economically efficient price after that. If the only goal is that the water supplier break even, what should be the “early” price, and at what quantity should the price drop to the economically efficient price? You may make any assumption you like about fixed costs, but be sure to state those assumptions explicitly in your answer.