Ans_HW10

Ans_HW10 - Answer to Practice Homework 10 13.1 a) b) c) P =...

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Answer to Practice Homework 10 13.1 a) P = MC implies 70 – 2 Q = 10, or Q = 30 and P = 10. b) A monopolist produces until MR = MC yielding 70 – 4 Q = 10 so Q m = 15 and P m = 40. Thus π m = (40 – 10)*15 = 450. c) For Amy, MR A = MC implies 70 – 4 q A 2 q B = 10. We could either calculate Beau’s profit-maximization condition (and solve two equations in two unknowns), or, inferring that the equilibrium will be symmetric since each seller has identical costs, we can exploit the fact that q A = q B in equilibrium. (Note: You can only do this after calculating marginal revenue for one Cournot firm, not before.) Thus 70 – 6 q A = 10 or q A = 10. Similarly, q B = 10. Total market output under Cournot duopoly is Q d = q A + q B = 20, and the market price is P d = 70 – 2*20 = 30. Each duopolist earns π d = (30 – 10)*10 = 200. 13.2 a) With two firms, demand is given by 1 2 300 3 3 P Q Q = - - . If 2 50 Q = , then 1 300 3 150 P Q = - - or 1 150 3 P Q = - . Setting MR MC = implies 1 1 150 6 100 8.33 Q Q - = = If 2 20 Q = , then 1 240 3 P Q = - . Setting MR MC = implies 1 1 240 6 100 23.33 Q Q - = = b) For Firm 1, 2 1 (300 3 ) 3 P Q Q = - - . Setting MR MC = implies 2 1 1 2 (300 3 ) 6 100 33.33 0.5 Q Q Q Q - - = = - Since the marginal costs are the same for both firms, symmetry implies 2 1 33.33 0.5 Q Q = - . Graphically, these reaction functions appear as
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0 20 40 60 0 20 40 60 Firm 1 Quantity Firm 2 Quantity Firm 1 Reaction Function Firm 2 Reaction Function 22.22 22.22 c) Because of symmetry, in equilibrium both firms will choose the same level of output. Thus, we can set 1 2 Q Q = and solve 2 2 2 33.33 0.5 22.22 Q Q Q = - = Since both firms will choose the same level of output, both firms will produce 22.22 units. Price can be found by substituting the quantity for each firm into market demand. This implies price will be 300 3(44.44) 166.67 P = - = . d) If this market were perfectly competitive, then equilibrium would occur at the point where 100 P MC = = . e) If the firms colluded to set the monopoly price, then 300 6 100 33.33 Q Q - = = At this quantity, market price will be 200 6 300 3( ) 200 P = - = . f)
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Ans_HW10 - Answer to Practice Homework 10 13.1 a) b) c) P =...

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