--%>
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 : National currencies of foreign exchange

    Elucidate various national currencies of foreign exchange market?

    		•
  • Q : Elucidate how to maintain competition

    Elucidate how to maintain competition?

    		•
  • Q : Explain the following from Hull Explain

    Explain the following from Hull, England a news dispatch: “The fish market here slumped today to what local commentators called a ‘disastrous level’—all because of a shortage of potatoes”.

    		•
  • Q : Laffer curve & Tax rate Question: Do

    Question: Do raising tax rates necessarily raise tax revenue? What factors affect how tax revenue changes when tax rates change? Using the 'human capital' investment model,

    		•
  • 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

    		•
  • Q : Economic bailout of Spain and Greece

    Question: Conduct an analysis on the following topic and prepare an Executive Summary-style report with supporting exhibits (Insightful Graphs, tables etc. from quality expert analyst references used to write the r

    		•
  • Q : Illustrations of opportunity costs

    Illustrations of opportunity costs which you might or will have incurred would comprise: (i) severe injuries suffered within an accident since you failed to buckle up. (ii) the income you could earn when you were not in school. (iii) time spent studyi

    		•
  • Q : Explain how women expanded production

    Explain how women expanded production possibilities?

    		•
  • Q : Illustrate Rational Behaviour of

    Illustrate Rational Behaviour of Economic Perspective?

    		•
  • Q : The supply curve when each of these

    What happens to the supply curve when each of these determinants changes?

    		•