Oligopoly_PQ - Oligopoly:Chapter12...

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Oligopoly: Chapter 12 Practice Questions for Mid Term 6.  Suppose that two identical firms produce widgets and that they are the only firms in the  market.  Their costs are given by C 1  = 60Q 1  and C 2  = 60Q 2 , where Q 1  is the output of Firm 1  and Q 2  the output of Firm 2.  Price is determined by the following demand curve: P = 300 - Q where Q = Q 1  + Q 2 . a. Find the Cournot-Nash equilibrium.  Calculate the profit of each firm at this equilibrium. To determine the Cournot-Nash equilibrium, we first calculate the reaction function for  each firm, then solve for price, quantity, and profit. Profit for Firm 1,  TR 1  -  TC 1 , is equal to Therefore, Setting this equal to zero and solving for  Q 1  in terms of  Q 2 : Q 1  = 120 - 0.5 Q 2 . This is Firm 1’s reaction function.  Because Firm 2 has the same cost structure, Firm 2’s  reaction function is Q 2  = 120 - 0.5 Q 1  . Substituting for  Q 2  in the reaction function for Firm 1, and solving for  Q 1 , we find Q 1  = 120 - (0.5)(120 - 0.5 Q 1 ), or  Q 1  = 80. By symmetry,  Q 2  = 80.  Substituting  Q 1  and  Q 2  into the demand equation to determine the  price at profit maximization: P  = 300 - 80 - 80 = $140. Substituting the values for price and quantity into the profit function,
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This note was uploaded on 04/19/2011 for the course ECON 101 taught by Professor Gul during the Spring '11 term at Lahore School of Economics.

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Oligopoly_PQ - Oligopoly:Chapter12...

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