Book solutions starts at ch 13

Book solutions starts at ch 13 - P13.6 SOLUTION A Because...

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P13.6 SOLUTION A. Because MC A = 0, Firm A’s profit -maximizing output level is found by setting MR A = MC A : MR A = MC A $1,250 - $2Q A - Q B = 50 $2Q A = $1,200 - Q B Q A = 600 - 0.5Q B Notice that the profit-maximizing level of output for Firm A depends upon the level of output produced by itself and Firm B. Similarly, the profit-maximizing level of output for Firm B depends upon the level of output produced by itself and Firm A. These relationships are each competitor’s output -reaction curve Firm A output-reaction curve: Q A = 600 - 0.5Q B Firm B output-reaction curve: Q B = 600 - 0.5Q A B. The Cournot market equilibrium level of output is found by simultaneously solving the output-reaction curves for both competitors. To find the amount of output produced by Firm A, simply insert the amount of output produced by competitor Firm B into Firm A’s output -reaction curve and solve for Q A . To find the amount of output produced by Firm B, simply insert the amount of output produced by competitor Firm A int o Firm B’s output -reaction curve and solve for Q B . For example, from the Firm A output-reaction curve Q A = 600 - 0.5Q B Q A = 600 - 0.5(600 - 0.5Q A ) Q A = 600 - 300 + 0.25Q A 0.75Q A = 300 Q A = 400 (000) units Similarly, from the Firm B output-reaction curve, the profit-maximizing level of output for Firm B is Q B = 400. With just two competitors, the market equilibrium level of output is Cournot equilibrium output = Q A + Q B = 400 + 400 = 800 (000) units The Cournot market equilibrium price is $1,250 Q = $1,250 - $1(800) = $450
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P13.7 SOLUTION A. To illustrate Stackelberg first-mover advantages, reconsider the Cournot model but now assume that Firm A , as a leading firm, correctly anticipates the output reaction of Firm B , the following firm. With prior knowledge of Firm B ’s output -reaction curve, Q B = 600 - 0.5 Q A , Firm A ’s total revenue curve becomes TR A = $1,250 Q A - Q A 2 - Q A Q B = $1,250 Q A - Q A 2 - Q A (600 - 0.5Q A ) = $650 Q A - 0.5 Q A 2 With prior knowledge of Firm B ’s output-reaction curve, marginal revenue for Firm A is MR A = ∂TR A /∂Q A = $650 - $1 Q A Because MC A = $50, Firm A’s profit-maximizing output level with prior knowledge of Firm B ’s output -reaction curve is found by setting MR A = MC A = $50 : MR A = MC A $650 - $1 Q A = $50 Q A = 600 After Firm A has determined its level of output, the amount produced by Firm B is calculated from Firm B ’s output -reaction curve Q B = 600 - 0.5 Q A = 600 - 0.5(600) = 300 With just two competitors, the Stackelberg market equilibrium level of output is 900 and price is $350. Notice that market output is greater in Stackelberg equilibrium than in Cournot equilibrium because the first mover, Firm A, produces more output while the follower, Firm B, produces less output. Stackelberg equilibrium also results in a lower market price than that observed in Cournot equilibrium. In this example, Firm A enjoys a significant first-mover advantage. Firm A will produce twice as much output and earn twice as much profit as Firm B so long as Firm B accepts the output decisions of Firm A as given and does not initiate a price war. If Firm A and Firm B cannot agree on which firm is the leader and which firm is the follower, a price war
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