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midterm2_460_S06_Boyer_answers - Your name MICHIGAN STATE...

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Your name: ____________________________________ MICHIGAN STATE UNIVERSITY Department of Economics Econ 460 Prof. Boyer Spring 2006 Second Midterm Exam Answer any 8 of the following 10 questions. Questions are 10 minutes and worth 8 points. 1) A market contains two firms, A and B. The price of products is determined by the formula: P = 100-2Q where Q is the combined output of both firms. Firm A has a marginal cost of 20 with no fixed cost. Firm B has a marginal cost of 10 with no fixed cost. There are no capacity constraints. Find the price that would be established in the market if both firms used Cournot strategies. Set up the profit maximizing conditions for each firm as MR 1 = 100-2Q 2 – 4 Q 1 = 20 and MR 2 = 100-2Q 1 – 4 Q 2 =10. (3 points) Solve simultaneously to find Q 1 = 70/6 = 11.67 and Q 2 = 100/6 = 16.67 (3 points). Plugging in the demand curve shows P = 100-2(11.67+16.67)=41.33(2 points) 2) The diagram below shows two reaction curves, one for firm A and one for firm B. Where the two lines cross is the market equilibrium. Based on the diagram, describe as much as you can about the goods in the market, the nature of competition in the industry, and the characteristics of the firms. The goods are not homogeneous and identical since increasing the price of one good does not shift the entire market to the other. (3 points) Competitive strategy is a matter of picking the best price consistent with the reaction of your competitor—that is a Bertrand game. (3 points) The firms are not identical since the reaction curves are not symmetric around the 45 degree line. (2 points ) P 2 Firm 1’s best response curve Firm 2’s best response curve P 1 1
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3) Consider the following game. Firm 1, the leader, selects an output, q 1 , after which firm 2, the follower, observes the choice of q 1 and then selects its own output, q 2 . The resulting price is one satisfying the industry demand curve P = 200-q 1 -q 2 . Both firms have zero fixed costs and a constant marginal cost of 60. Calculate the dollar amount of the first mover advantage that firm 1 gets by being the leader rather than the follower. (7 points for demonstrating that you know how to work the problem, 1 points for getting the right number.) Find the reaction curve for firm 2 by solving 200- q 1 - 2q 2 =0 to find q 2 =100-q 1 /2. (3 points). Use this q 2 in the demand curve for firm 1 to give: P = 100 -.5q 1 . The profit maximizing output for firm 1 is then found by solving MR 1 = 100 –q 1 =60 So q 1 = 40 and q 2 =20. (3 points.) The price is then 200 – 60 = 140. The price –cost margin is 140 – 60 = 80. So the profit of the leader is 40*80 = 320 while the profit of the follower is 20*80 = 160. So the leader gets 80 more profit for being the leader. (2 points) 4) On the diagram below, show the approximate position of the following: a) The Nash equilibrium. b)
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