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Berkeley ECON 100A - Section Notes 23

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Section Notes 23, Econ 100A Spring ’06 1Section Notes 23Covering material from Lecture on April 18thClass Outline1. Collusion with Constant Marginal Costs2. Practice Noncooperative Games1 Collusion with Constant Marginal CostsProblem: (P&R, Chapter 12, Exercise 2a)Consider two firms facing the demand curve P = 50 − 5Q, where Q = Q1+ Q2. The firms’ cost functionsare C1(Q1) = 20 + 10Q1and C2(Q2) = 10 + 12Q2.Suppose both firms have entered the industry. What is the joint profit-maximizing level of output?How much will each firm produce? How would your answer change if the firms have not yet entered theindustry?Section Notes 23, Econ 100A Spring ’06 22 Practice Noncooperative GamesProblem: (P&R, Chapter 12, Exercise 9)Demand for light bulbs can be characterized by Q = 100 − P , where Q is in millions of boxes of lights soldand P is the price per box. There are two producers of lights, Everglow and Dimlit. They have identicalcost functions:Ci= 10Qi+12Q2i(i = E, D)Q = QE+ QDa. Unable to recognize the potential for collusion, the two firms act as short-run perfect competitors. Whatare the equilibrium values of QE, QD, and P ? What are each firm’s profits?b. Top management in both firms is replaced. Each new manager independently recognizes the oligopolisticnature of the light bulb industry and plays Cournot. What are the equilibrium values of QE, QD,and P ? What are each firm’s profits?c. Suppose the Everglow manager guesses correctly that Dimlit is playing Cournot and publicly announces(commits) to a level of production, therefore making Everglow a Stackelberg leader. What areequilibrium values of QE, QD, and P ? What are each firm’s profits?d. If the managers of the two companies collude, what are the equilibrium values of QE, QD, and P ?What are each firm’s


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Berkeley ECON 100A - Section Notes 23

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