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Unformatted text preview: more power in the market. Using the same demand curve as before... P = 600 - QA - QB 290 and we will assume no marginal costs once again, so we can focus on only the difference in quantity announcement timing. When firm A calculates their decision they take firm B's reaction to their decision into account, thus they calculate firm B's reaction function... B = P QB B = (600 - QA - QB) QB B = 600QB QB2 - QAQB FOCQB 600 QA - 2QB = 0 2QB = 600 QA QB = 300 0.5QA (1) Now, firm A will anticipate firm B's response when they maximize profits. A = P QA A = (600 - QA - QB) QA and firm A knows what firm B will do based on (1)... subbing (1) in for QB, gives us A = [600 - QA (300 0.5QA)] QA = 600 QA - QA2 - 300 QA + 0.5 QA2 = 300 QA 0.5 QA2 and we can now find the profit maximizing output for the leading firm, firm A, as: A = 0 QA or, 300 - QA = 0 QA* = 300 It follows (by using firm B's reaction function) from (1) that if firm A produces QA* = 300, then firm B produces... 291 QB = 300 0.5QA = 300 0.5(300) QB* = 150 We can find the market price, P*, using QA* = 300 and QB* = 150 in the demand equation, P* = 600 - QA* - QB* = 600 300 150 = 150 and thus, the firms profits are, A* = P* QA* = 150 300 = 45,000 B* = P* QB* = 150 150 = 22,500 Remember, in the first example, the Cournot (simultaneous decision game)gave us a result of P* = 200, QA* = 200, and QB* = 200 with profits for the firms as follows: A* = P* QA* = 200 200 = 40,000 B* = P* QB* = 200 200 = 40,000 Clearly, the first mover advantage benefits firm A. In the sequential model, when firm A is a Stackelberg leader, firm A is able to commit to a higher quantity than in the Cournot scenario. This forces firm B to cut back their "best response" production. This enables firm A to take a 2/3 share of the market as opposed to the share they had in the simultaneous move game. We should note that while the Stackelberg leadership model results in a higher firm A profit, the joint profits in the market fall from $80,000 to $67,500. 292 HOMEWORK 1. Consider the market for automobiles. Let's assume there are two auto manufacturers, Toyota and Honda. Suppose Honda has an ATC of 9,000 per unit and Toyota has an ATC of $11,000 per unit. Assume the following market demand in this automobile market: P = 54,000 QHONDA QTOYOTA Solve the Cournot quantity competition to get Q*HONDA, Q*TOYOTA, and P*. Also, find the equilibrium profits for each firm as *HONDA and *TOYOTA. 2. . Consider the sam...
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- Spring '10