Ch12 - Monopolistic Competition and Oligopoly

Iii given that the good is homogeneous both will

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(iii)   Given  that the good is homogeneous, both will produce  where price equals  marginal cost.  Firm A will increase price to $80 and firm B will keep its price at $50.  Assuming firm B can produce enough output, they will supply the entire market. b. The marginal cost of both firms increases. (i)  Again refer to figure 12.4.  The increase in the marginal cost of both firms will shift  both reaction functions inwards.  Both firms will decrease quantity produced and price  will increase. (ii)  When marginal cost increases, both firms will produce less and price will increase,  as in the monopoly case. (iii)  As in the above cases, price will increase and quantity produced will decrease. c.   The demand curve shifts to the right. (i)   This is the opposite of the above case in part b.   In this case, both reaction  functions will shift outwards and both will produce a higher quantity.  Price will tend  to increase. (ii)  Both firms will increase the quantity produced as demand and marginal revenue  increase.  Price will also tend to increase. (iii)  Both firms will supply more output.  Given that marginal cost is constant, the  price will not change. 8.  Suppose the airline industry consisted of only two firms: American and Texas Air Corp.  Let the two firms have identical cost functions, C(q) = 40q.  Assume the demand curve for  the industry is given by P = 100 - Q and that each firm expects the other to behave as a  Cournot competitor. a. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses  the output level that maximizes its profits when taking its rival’s output as given.  What are the profits of each firm? To determine the Cournot-Nash equilibrium, we first calculate the reaction function  for each firm, then solve for price, quantity, and profit. Profit for Texas Air,   π 1 , is  equal to total revenue minus total cost: 204
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Chapter  12:  Monopolistic Competition and Oligopoly π 1  = (100 -  Q 1  -  Q 2 ) Q 1  - 40 Q 1 , or π π 1 1 1 2 1 2 1 1 1 1 2 1 2 100 40 60 = - - - = - - Q Q Q Q Q Q Q Q Q , .  or  The change in  π 1  with respect to  Q 1  is = - - 1 1 1 2 60 2 π Q Q Q . Setting the derivative to zero and solving for  Q 1  in terms of  Q 2  will give Texas Air’s  reaction function: Q 1  = 30 - 0.5 Q 2 . Because American has the same cost structure, American’s reaction function is Q 2  = 30 - 0.5 Q 1 .
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