--%>
Assignment Help - homework help

Firms operating under Cournot competition or Cournot market

Question:

Suppose three identical firms are engaged in Cournot competition in quantities. They all have marginal costs equal to 40.

Market demand is given by:

P(X) = 200 - X = 200 - (x1 + x2 + x3), where P denotes price, X total quantity demanded, and xi individual demand for firms i = 1,2, and 3.

a) Explain in what type of markets Cournot type competition can occur. Write down the demand curve and marginal revenue curve for firm 1.

b) What is the first order condition for profit maximization for firm 1? Compute the optimum quantity x1* for firm 1 as a function of quantities x2 and x3.

c) Since the firms are identical, symmetrical solutions exist also for the two other firms. Use this to compute the optimum quantity produced (and sold) for each firm.

d) Compute total demand, X, and market price, P. Compute each firm's profit, πi, and the sum total of all profits.

Summary:

The details about three identical firms operating in Cournot competition are given. The demand curve with marginal revenue, profit maximization, optimum quantity, total demand and market price related questions are answered.

Answer:

(a)    Cournot competition happens when firms in market compete over the quantity they can sell. Also, the output decisions must be made simultaneously.

P = 200 - x1 - x2 - x3

ð  Px1 = 200x1 - x12 - x1x2- x1x3 = Total revenue curve for firm 1

ð  MR = 200 -2x1 - x2 - x3 = Marginal revenue curve of firm 1

(b)   The FOC is:

MR = MC

ð  200- 2x1 - x2 - x3 = 40

ð  x1 = (160 - x2 - x3)/2

(c)    Symmetry means that in the end result, x1 = x2 = x3

Using the above condition,

x1 = (160 - x1 - x1)/2

ð  4x1 = 160

ð  x1 = 40 = x2 = x3

(d)   Total demand = x1 + x2 + x3 = 120

Price = 200 - 120 = 80

π1 = π2 = π3 = 40*80 - 40*40 = 40*40 = 1600

Therefore, π1 +π2 +π3 = 3*1600 = 4800

   Related Questions in Business Economics

  • Q : Factor Price Equalization theorem

    Please answer each of the exercises below. While you may work together on the homework, you must turn in your own work (in your own words). Homework must be handed in at the beginning of class on the due date unless other arrangements have been made. No late homework will be accepted. Homework wi

    		•
  • Q : Theories of capital structure Write

    Write down the theories of capital structure?

    		•
  • Q : Market structure and pricing decision

    Just need help to see if I am in the right direction if there any think wrong need help with it.

    		•
  • Q : Question 7 Question 7: You are given

    Question 7: You are given the following data about two firms: FIRM A Quantity 0 1 2 3 4 5 6 Total revenue ($) 0 10 20 30 40 50 60 Average revenue ($) ___ ___ ___ ___ ___ ___ ___ Marginal revenue ($) ___ ___ ___ ___ ___ ___ Total cost ($) 30 42 50 60 76 100 14

    		•
  • Q : Contestable Markets The least probable

    The least probable of the given industries to be a contestable market is: (1) video rentals. (2) pizza delivery. (3) cable television. (4) trucking. Can someone explain/help me with best solution about problem of <

    		•
  • Q : Increase the overall effectiveness of

    How the government can increase the overall effectiveness of the market system?

    		•
  • Q : Regression Your firm is worried about

    Your firm is worried about being sued for gender discrimination. There is a growing perception that males are being paid more than females in your department. Using the data in the SALARY tab in the Excel file provided, please complete the following using a = .05 a). Do the men appear to earn mo

    		•
  • Q : Describe Spillovers and externalities

    Describe Spillovers and externalities?

    		•
  • Q : Introduction of the term Cost of capital

    Give a brief introduction of the term Cost of capital?

    		•
  • Q : Wealth of Nations academic

    By the perspective of nowadays academic standards, Adam Smith must have more evidently acknowledged that several the analyses and insights for that he took credit within his Wealth of Nations had really been gleaned from the writings

    		•