--%>
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 : Explain how the Circular Flow Model for

    Explain how the Circular Flow Model for a Market-Oriented System?

    		•
  • Q : Cchange in demand and a change in the

    Distinguish between a change in demand and a change in the quantity demanded?

    		•
  • Q : Effects of that depreciation or

    Would a decline in U.S. consumer income or a weakening of U.S. preferences for foreign products cause the dollar to depreciate or appreciate?  Other things equal, what would be the effects of that depreciation or appreciation on U.S. exports and imports?

    		•
  • Q : Explain the term Operating Leverage

    Briefly explain the term Operating Leverage?

    		•
  • Q : Answer the following questions based on

    The dataset used in this question contains data on 180 economics journals for the year 2000. The variable descriptions are as follows: logoclc - log of the number of library subscription loglibcit - log of the library subscription price per citation.

  • Q : Risky forms of production to gain

    Entrepreneurs: (w) undertake risky forms of production to gain uncertain profits. (x) obtain interest payments for their services. (y) are usually overcompensated for their innovations. (z) receive virtually all their wealth by inheritance.

  • Q : Regulate prices to ensure against

    Not between exact activities for government to undertake, according to Adam Smith, would be for the government to: (1) maintain public institutions and public works. (2) protect society by invasion. (3) serves as a medium for law and justice. (4) regu

    		•
  • Q : Explain a refutation of the doctrines

    Adam Smith wrote his Wealth of Nations within part like a refutation of the doctrines: (1) classical liberalism. (2) utilitarianism. (3) mercantilism. (4) physiocracy. (5) laissez faire capitalism.

  • Q : Proper control on capital budgeting

    Write down the steps carried out for proper control on capital budgeting process?

    		•
  • Q : What is the basic principle of

    What is the basic principle of comparative advantage?

    		•