A standard question Consider a natural monopoly, with cost function c(q) = F and facing demand function p(q) = A Bq.

a) Suppose the monopolist were regulated so that it must produce the quantity that maximizes social surplus. What is this quantity? What is the social surplus? What is the monopolists profit?

b) Suppose instead that the monopolist is not regulated. What quantity does it choose to maximize its profit? What is the social surplus?

c) Now suppose the firm is regulated to receive a rate of return R on its fixed costs. This means it must produce a quantity such that its profit is RF, or equivalently such that its producer 5 surplus is (1 + R)F. Suppose that R = 0, so the monopolist is supposed to just cover its fixed costs. What quantity q must it choose?