ASSIGNMENT 2_ECON 384_FALL 2016

ASSIGNMENT 2_ECON 384_FALL 2016 - INTERMEDIATE...

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1 I NTERMEDIATE M ICROECONOMIC T HEORY II P ROFESSOR C LAUDIA M. L ANDEO A SSIGNMENT 2 Due on Thursday, November 3, 2016 (Beginning of Class. Late Assignments Will NOT Be Accepted.) 1. Two software companies, Firm 1 and Firm 2 sell competing products. Let pi and xi be the price and quantity sold by Firm i, i = 1, 2. The demand functions for Firm 1 and Firm 2are given by x1 = 1000(90 1/2 p1 + 1/4 p2) and x2 = 1000(90 -1/2 p2 + 1/4 p1), respectively. For each firm, the cost of selling to an extra user is zero. Therefore, each company will maximize its profits by choosing the price that maximizes its total revenues. Suppose that the firms operate under Bertrand competition. a. What are the market prices? b. Are the firms enjoying market power? Explain. Suppose now that Firm1 sets its price first. After observing Firm 1’s price, Firm 2 decides its own price. c. What are the market prices? 2. Consider an industry that consists of two firms: Intercom (I) and Acme (A). The demand in this industry is p = 1 – q I – q A , and the two firms have cost functions of C I = ½ q I and C A = ½ q A . Assume the following strategic environment: Acme moves first and makes an announcement about its output level. It may announce that unless
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2 the Intercom stays out of the market, it will drive the price to zero by producing an
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