Ch12 - Monopolistic Competition and Oligopoly

# Becomes large the market price approaches the price

This preview shows pages 8–11. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 = - - + - .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern