Ch12 - Monopolistic Competition and Oligopoly

The other way to solve the problem and arrive at the

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The other way to solve the problem and arrive at the same solution is to find the  market supply curve by summing the marginal cost curves, so that Q M =2P-20 is the  market supply.   Setting supply equal to demand results in a quantity of 60 in the  market, or 30 per firm since they are identical. b. Top management in both firms is replaced.   Each new manager independently  recognizes the oligopolistic nature of the light bulb industry and plays Cournot.  What are the equilibrium values of Q E , Q D , and P?  What are each firm’s profits? To determine the Cournot-Nash equilibrium, we first calculate the reaction function  for each firm, then solve for price, quantity, and profit. Profits for Everglow are equal  to  TR E  -  TC E , or  π E = 100 - Q E - Q D ( 29 Q E - 10 Q E + 0.5 Q E 2 ( 29 = 90 Q E - 1.5 Q E 2 - Q E Q D . The change in profit with respect to  Q E  is - - π E E E D Q = Q Q . 90 3 208
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Chapter  12:  Monopolistic Competition and Oligopoly To determine Everglow’s reaction function, set the change in profits with respect to  Q E  equal to 0 and solve for  Q E : 90 - 3 Q E  -  Q D  = 0, or Q E = 90 - Q D 3 . Because Dimlit has the same cost structure, Dimlit’s reaction function is Q D = 90 - Q E 3 . Substituting for  Q D  in the reaction function for Everglow, and solving for  Q E : Q E = 90 - 90 - Q E 3 3 3 Q E = 90 - 30 + Q E 3 Q E = 22.5. By symmetry,  Q D  = 22.5, and total industry output is 45. Substituting industry output into the demand equation gives  P : 45 = 100 -  P , or  P  = $55. Substituting total industry output and  P  into the profit function: c. Suppose   the   Everglow   manager   guesses   correctly   that   Dimlit   has   a   Cournot  conjectural variation, so Everglow plays Stackelberg.   What are the equilibrium  values of Q E , Q D , and P?  What are each firm’s profits? Recall Everglow’s profit function: If Everglow sets its quantity first, knowing Dimlit’s reaction function  we may determine Everglow’s reaction function by substituting for  Q D  in its profit  function. We find π E E E Q Q = - 60 7 6 2 . To determine the profit-maximizing quantity, differentiate profit with respect to  Q E set the derivative to zero and solve for  Q E : = - = = π E E E E Q Q   Q . . 60 7 3 0 257 or 209
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Chapter  12:  Monopolistic Competition and Oligopoly Substituting this into Dimlit’s reaction function, we find  Q D = - = 30 25 7 3 21 4 . . .   Total  industry output is 47.1 and  P  = $52.90.  Profit for Everglow is $772.29 million.  Profit  for Dimlit is $689.08 million.
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