Ch12 - Monopolistic Competition and Oligopoly

D if the managers of the two companies collude what

Info icon This preview shows pages 20–22. Sign up to view the full content.

View Full Document Right Arrow Icon
d. If the managers of the two companies collude, what are the equilibrium values of  Q E , Q D , and P?  What are each firm’s profits? If   the   firms   split   the   market   equally,   total   cost   in   the   industry   is   10 2 2 Q Q T T + therefore,  MC Q T = + 10 .  Total revenue is  100 Q T - Q T 2 ; therefore,  MR = 100 - 2 Q T .   To determine the profit-maximizing quantity, set  MR = MC  and solve for  Q T : 100 - 2 Q T = 10 + Q T , or Q T = 30. This means  Q E  = Q D  = 15. Substituting  Q T  into the demand equation to determine price: P  = 100 - 30 = $70. The profit for each firm is equal to total revenue minus total cost: π i = 70 ( 29 15 ( 29 - 10 ( 29 15 ( 29 + 15 2 2 = $787.50 million. 10.   Two firms produce luxury sheepskin auto seat covers, Western Where (WW) and  B.B.B. Sheep (BBBS).  Each firm has a cost function given by: ( q )  =  30 q +  1.5 q 2 The market demand for these seat covers is represented by the inverse demand equation: P =  300  -  3 Q, where  Q  =  q 1  +  q 2  , total output. a. If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the  firms behave as Cournot oligopolists), what will be the equilibrium quantities  selected by each firm?  What is total output, and what is the market price?  What  are the profits for each firm? We are given each firm’s cost function  C(q) = 30q + 1.5q 2  and the market demand  function P = 300 - 3Q where total output Q is the sum of  each firm’s output q 1  and  q 2.   We find the best response functions for both firms by setting marginal revenue  equal to marginal cost (alternatively you can set up the profit function for each firm  and differentiate with respect to the quantity produced for that firm): R 1  = P q 1  = (300 - 3(q 1  + q 2 )) q 1  = 300q 1  - 3q 1 2  - 3q 1 q 2 . MR 1  = 300 - 6q 1  - 3q 2 MC 1  = 30 + 3q 1 300 - 6q 1  - 3q 2  = 30 + 3q 1   210
Image of page 20

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

View Full Document Right Arrow Icon
Chapter  12:  Monopolistic Competition and Oligopoly q 1  = 30 - (1/3)q 2 . By symmetry, BBBS’s best response function will  be: q 2  = 30 - (1/3)q 1 . Cournot equilibrium occurs at the intersection of these two best response functions,  given by: q 1  = q 2  = 22.5. Thus, Q = q 1  + q 2  = 45 P = 300 - 3(45) = $165. Profit for both firms will be equal and given by: R - C = (165) (22.5) - (30(22.5) + 1.5(22.5 2 )) = $2278.13. b. It occurs to the managers of WW and BBBS that they could do a lot better by  colluding.  If the two firms collude, what would be the profit-maximizing choice of  output?  The industry price?  The output and the profit for each firm in this case?
Image of page 21
Image of page 22
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern