Ans homework 5 EE 311
1. Suppose that Intel has a monopoly in the market for microprocessors in Brazil. During the year 2005, it faces a market demand curve given by P = 9 - Q, where Q is millions of microprocessors sold per year. Suppose you know nothing about Intel’s costs of production. Assuming that Intel acts as a profit-maximizing monopolist, would it ever sell 7 million microprocessors in Brazil in 2005?

If demand is P  9  Q , then MR  9  2Q . If the firm sets Q  7 , then MR  5 . At this point, if the firm lowered its output it would increase total revenue, and with the lower level of output total cost would fall. Thus, decreasing output would increase profit. Therefore, a profit-maximizing monopolist facing this demand curve would never choose Q  7 .

2. A monopolist faces a demand curve P = 210 - 4Q and initially faces a constant marginal cost MC = 10. a) Calculate the profit-maximizing monopoly quantity and compute the monopolist’s total revenue at the optimal price. b) Suppose that the monopolist’s marginal cost increases to MC = 20. Verify that the monopolist’s total revenue goes down. c) Suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost MC = 10. Find the long-run perfectly competitive industry price and quantity. d) Suppose that all firms’ marginal costs increased to MC = 20. Verify that the increase in marginal cost causes total industry revenue to go up.

a)

With demand P  210  4Q , MR  210  8Q . Setting MR  MC implies 210  8Q  10

Q  25
With Q  25 , price will be P  210  4Q  110 . At this price and quantity total revenue will be

TR  110(25)  2,750 .

b)

If MC  20 , then setting MR  MC implies 210  8Q  20

Q  23.75

At Q  23.75 , price will be P  115 . At this price and quantity total revenue will be

TR  115(23.75)  2,731.25 . Therefore, the increase