Ch12 - Monopolistic Competition and Oligopoly

Profits for firm 1 are p 1 q 1 400 and by symmetry

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Profits for Firm 1 are  P 1 Q 1  = $400, and, by symmetry, profits for Firm 2 are also $400. b. Suppose Firm 1 sets its price  first  and then Firm 2 sets its price.  What price will  each firm charge, how much will it sell, and what will its profit be? If Firm 1 sets its price first, it takes Firm 2’s reaction function into account.  Firm 1’s  profit function is: 213
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Chapter  12:  Monopolistic Competition and Oligopoly π 1 = P 1 20 - P 1 + 20 + P 1 2 = 30 P 1 - P 1 2 2 . To determine the profit-maximizing price, find the change in profit with respect to a  change in price: d π 1 dP 1 = 30 - P 1 . Set this expression equal to zero to find the profit-maximizing price: 30 -  P 1  = 0, or  P 1  = $30. Substitute  P 1  in Firm 2’s reaction function to find  P 2 : P 2 20 30 2 = + = $25. At these prices, Q 1  = 20 - 30 + 25 = 15   and       Q 2  = 20 + 30 - 25 = 25. Profits are π 1  = (30)(15) = $450   and π 2  = (25)(25) = $625. If Firm 1 must set its price first, Firm 2 is able to undercut Firm 1 and gain a larger  market share. 214
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Chapter  12:  Monopolistic Competition and Oligopoly c. Suppose you are one of these firms, and there are three ways you could play the  game: (i) Both firms set price at the same time.  (ii) You set price first.  (iii)  Your  competitor sets price first.  If you could choose among these options, which would  you prefer?  Explain why. Your first choice should be (iii), and your second choice should be (ii).  (Compare the  Nash profits in part 11.a, $400, with profits in part 11.b., $450 and $625.)  From the  reaction functions, we know that the price leader provokes a price increase in the  follower.  By being able to move second, however, the follower increases price by less  than the leader, and hence undercuts the leader.  Both firms enjoy increased profits,  but the follower does best. *12.  The dominant firm model can help us understand the behavior of some cartels.  Let’s  apply this model to the OPEC oil cartel.  We shall use isoelastic curves to describe world  demand   W   and noncartel (competitive) supply   S .   Reasonable numbers  for the price  elasticities of world demand and non-cartel supply are -1/2 and 1/2, respectively.  Then,  expressing  W  and  S  in millions of barrels per day (mb/d), we could write W = 160 P - 1 2 and S = 3 1 3 P 1 2 . Note that OPEC’s net demand is D = W - S. a. Sketch the world demand curve   W , the non-OPEC supply curve   S , OPEC’s net  demand   curve   D,   and   OPEC’s   marginal   revenue   curve.     For   purposes   of  approximation, assume OPEC’s production cost is zero.  Indicate OPEC’s optimal  price,   OPEC’s   optimal   production,   and  non-OPEC   production   on   the   diagram. 
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