Ch12 - Monopolistic Competition and Oligopoly

Becomes large the market price approaches the price

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 becomes large the market price approaches the price that would  prevail under perfect competition. If there are  N  identical firms, then the price in the market will be  P = 53 - Q 1 + Q 2 + L + Q N ( 29 . Profits for the  i ’th firm are given by π i = PQ i - C Q i ( 29 , π i = 53 Q i - Q 1 Q i - Q 2 Q i - L - Q i 2 - L - Q N Q i - 5 Q i . Differentiating to obtain the necessary first-order condition for profit maximization, d dQ Q Q Q i i N π = - - - - - - = 53 2 5 0 1 L L . Solving for  Q i , Q i = 24 - 1 2 Q 1 + L + Q i - 1 + Q i + 1 + L + Q N ( 29 . 198
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Chapter  12:  Monopolistic Competition and Oligopoly If all firms face the same costs, they will all produce the same level of output, i.e., Q i  =  Q *.  Therefore, Q * = 24 - 1 2 N - 1 ( 29 Q *, or 2 Q * = 48 - N - 1 ( 29 Q *, or We may substitute for  Q = NQ *, total output, in the demand function: P = 53 - N 48 N + 1 . Total profits are π T  =  PQ  -  C ( Q ) =  P ( NQ *) - 5( NQ *) or π T   = 53 - N 48 N + 1 N ( 29 48 N + 1 - 5 N 48 N + 1 or π T   or π T   Notice that with  firms and that, as  N  increases (N    ) Q  = 48. Similarly, with as N    , P  = 53 - 48 = 5. With  P  = 5,  Q  = 53 - 5 = 48. Finally, so as N    , π T   = $0. 199
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Chapter  12:  Monopolistic Competition and Oligopoly In perfect competition, we know that profits are zero and price equals marginal cost.  Here,   π T   = $0 and   P = MC   = 5.   Thus, when   N   approaches infinity, this market  approaches a perfectly competitive one. 4.  This exercise is a continuation of Exercise 3.  We return to two firms with the same  constant  average and marginal cost, AC = MC  = 5, facing the market  demand  curve Q 1  + Q 2  = 53 - P.  Now we will use the Stackelberg model to analyze what will happen if one  of the firms makes its output decision before the other. a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before  Firm 2).   Find the reaction curves that tell each firm how much to produce in  terms of the output of its competitor. Firm 1, the Stackelberg leader, will choose its output,   Q 1 , to maximize its profits,  subject to the reaction function of Firm 2: max  π 1  =  PQ 1  -  C ( Q 1 ), subject to Q 2 = 24 - Q 1 2 . Substitute for  Q 2  in the demand function and, after solving for  P , substitute for  P  in  the profit function: max π 1 = 53 - Q 1 - 24 - Q 1 2 Q 1 ( 29 - 5 Q 1 . To   determine   the   profit-maximizing   quantity,   we   find   the   change   in   the   profit  function with respect to a change in  Q 1 : d dQ Q Q π 1 1 1 1 53 2 24 5 = - - + - .
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