Ch12 - Monopolistic Competition and Oligopoly

Firm 2s revenue function is symmetric to that of firm

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Firm 2’s revenue function is symmetric to that of Firm 1 and hence Profit maximization implies MR 2  = MC 2 , or 201
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Chapter  12:  Monopolistic Competition and Oligopoly which is Firm 2’s best response function. Cournot equilibrium occurs at the intersection of best response functions.  Substituting for  Q 1  in the response function for Firm 2 yields: Thus Q 2 =0 and Q 1 =15.  P = 30 - Q 1  + Q 2  = 15, which is the monopoly price. 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 π 1 = 300 Q 1 - Q 1 2 - Q 1 Q 2 - 60 Q 1 = 240 Q 1 - Q 1 2 - Q 1 Q 2 . Therefore, 1 p 1 Q = 240 - 2 1 Q - 2 Q . 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, π 1  = (140)(80) - (60)(80) = $6,400   and π 2  = (140)(80) - (60)(80) = $6,400. Therefore, profit is $6,400 for both firms in Cournot-Nash equilibrium. b. Suppose the two firms form a cartel to maximize joint profits.  How many widgets  will be produced?  Calculate each firm’s profit. 202
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Chapter  12:  Monopolistic Competition and Oligopoly Given the demand curve is P=300-Q, the marginal revenue curve is MR=300-2Q.  Profit will be maximized by finding the level of output such that marginal revenue is  equal to marginal cost: 300-2Q=60 Q=120. When output is equal to 120, price will be equal to 180, based on the demand curve.  Since both firms have the same marginal cost, they will split the total output evenly  between themselves so they each produce 60 units.  Profit for each firm is: π  = 180(60)-60(60)=$7,200.
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