Ch12 - Monopolistic Competition and Oligopoly

To determine how much american would be willing to

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To determine how much American would be willing to spend to reduce its average  costs, we must calculate the difference in profits, assuming Texas Air’s average cost  is 25.  First, without investment, American’s profits would be: (55)(15) - (40)(15) = $225. Second, with investment by both firms, the reaction functions would be: Q 1  = 37.5 - 0.5 Q 2     and       Q 2  = 37.5 - 0.5 Q 1 . To determine  Q 1 , substitute for  Q 2  in the first reaction function and solve for  Q 1 : Q 1  = 37.5 - (0.5)(37.5 - 0.5Q 1 ) = 25. Substituting for  Q 1  in the second reaction function to find  Q 2 : Q 2  = 37.5 - 0.5(37.5 - 0.5 Q 2 ) = 25. Substituting industry output into the demand equation to determine price: P  = 100 - 50 = $50. Therefore, American’s profits if  Q 1  =  Q 2  = 25 (when both firms have  MC = AC  = 25)  are π 2  = (100 - 25 - 25)(25) - (25)(25) = $625. 206
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Chapter  12:  Monopolistic Competition and Oligopoly The difference in profit with and without the cost-saving investment for American is  $400.  American would be willing to invest up to $400 to reduce its marginal cost to  25 if Texas Air also has marginal costs of 25. 207
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Chapter  12:  Monopolistic Competition and Oligopoly *9.  Demand for light bulbs can be characterized by Q = 100 - P, where Q is in millions of  lights sold, and P is the price per box.  There are two producers of lights:  Everglow and  Dimlit.  They have identical cost functions: C i = 10Q i + 1/ 2Q i 2 i = E, D ( 29 Q = Q E  + Q D . a. Unable to recognize the potential for collusion, the two firms act as short-run  perfect competitors.  What are the equilibrium values of Q E , Q D , and P?  What are  each firm’s profits? Given that the total cost function is  C Q Q i i i = + 10 1 2 2 / , the marginal cost curve for  each firm is  MC Q i i = + 10 .   In the short run, perfectly competitive firms determine  the  optimal level of output  by taking  price  as given  and setting  price  equal  to  marginal cost.  There are two ways to solve this problem.  One way is to set price  equal to marginal cost for each firm so that: P = 100 - Q 1 - Q 2 = 10 + Q 1 P = 100 - Q 1 - Q 2 = 10 + Q 2 . Given we now have two equations and two unknowns, we can solve for Q 1  and Q 2 Solve the second equation for Q 2  to get Q 2 = 90 - Q 1 2 , and substitute into the other equation to get 100 - Q 1 - 90 - Q 1 2 = 10 + Q 1 . This yields a solution where Q 1 =30, Q 2 =30, and P=40.  You can verify that P=MC for  each firm.  Profit is total revenue minus total cost or Π = 40 * 30 - (10 *30 + 0.5 *30 * 30) = $450 million.
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