Ch12 - Monopolistic Competition and Oligopoly

In the cournot model firm 1 takes firm 2s output as

Info icon This preview shows pages 6–8. Sign up to view the full content.

View Full Document Right Arrow Icon
In the Cournot model, Firm 1 takes Firm 2’s output as given and maximizes profits.  The profit function derived in 2.a becomes π 1  = (50 - 5 Q 1  - 5 Q ) Q 1  - (20 + 10 Q ), or π = 40 Q 1 - 5 Q 1 2 - 5 Q 1 Q 2 - 20 . Setting the derivative of the profit function with respect to  Q 1  to zero, we find Firm  1’s reaction function: π 1 Q = 40 - 10 1 Q -5 2 Q= 0 , o r 1 Q= 4 - Q 2 2 . Similarly, Firm 2’s reaction function is Q 2 = 3 .8 - Q 1 2 . To find the Cournot equilibrium, we substitute Firm 2’s reaction function into Firm  1’s reaction function: Q 1 = 4 - 1 2 3 .8 - Q 1 2 , or Q 1 = 2 .8 . Substituting this value for  Q 1  into the reaction function for Firm 2, we find  Q 2  = 2.4. Substituting the values for   Q 1   and   Q 2   into the demand function to determine the  equilibrium price: P  = 50 – 5(2.8+2.4) = $24. The profits for Firms 1 and 2 are equal to π 1  = (24)(2.8) - (20 + (10)(2.8)) = 19.20 and        π 2  = (24)(2.4) - (10 + (12)(2.4)) = 18.80. c. How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal  but the takeover is not? In order to determine how much Firm 1 will be willing to pay to purchase Firm 2, we  must compare Firm 1’s profits in the monopoly situation versus those in an oligopoly.  The difference between the two will be what Firm 1 is willing to pay for Firm 2.  From part a, profit of firm 1 when it set marginal revenue equal to its marginal cost  was $60.  This is what the firm would earn if it was a monopolist.  From part b, profit  was $19.20 for firm 1.  Firm 1 would therefore be willing to pay up to $40.80 for firm  2.   196
Image of page 6

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 3.  A monopolist can produce at a constant average (and marginal) cost of AC = MC = 5.  It  faces a market demand curve given by Q = 53 - P. a. Calculate   the   profit-maximizing   price   and   quantity   for   this   monopolist.     Also  calculate its profits. The monopolist wants to choose quantity to maximize its profits: max  π  =  PQ  -  C ( Q ), π  = (53 -  Q )( Q ) -  5 Q , or  π  = 48 Q  -  Q 2 . To determine the profit-maximizing quantity, set the change in  π  with respect to the  change in  Q  equal to zero and solve for  Q : d dQ Q Q π = - + = = 2 48 0 24 , .  or  Substitute the profit-maximizing quantity,  Q  = 24, into the demand function to find  price: 24 = 53 -  P , or  P  = $29. Profits are equal to π  =  TR  -  TC  = (29)(24) - (5)(24) = $576.
Image of page 7
Image of page 8
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