B. We did not develop the basic mathematics of natural monopolies in the text and therefore use the remainder of this exercise to do so. Suppose demand for x is characterized by the demand curve p1x2 5 A 2 ax. Suppose further that x is produced by a monopolist whose cost function is c1x2 5 B 1 bx.

a. Derive the monopolist’s profit-maximizing supply point, that is, the price and quantity 1p M, x M 2 under the implicit assumption of no price discrimination.

b. At the output level x M, what is the average cost paid by the monopolist?

c. How high can fixed costs be and still permit the monopolist to make non-negative profit by choosing the supply point you calculated in (a)?

d. How much is Microsoft willing to pay its lawyers to get copyright protection?