--%>
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 : Which type of maximization required in

    Productive (technical) efficiency needs maximization of the: (i) opportunity cost of a specified value of output. (ii) resources used to produce a specified value of output. (iii) value of output produced for a given total cost. (iv) satisfaction atta

    		•
  • Q : Business Strategies Cingular and Alltel

    Cingular and Alltel involve in aggressive and expensive advertising for cell-phones. A reason for this advertising may be: (1) attempts to increase market share. (2) predatorily drive other firms by the market. (3) to increase the use of cell phones.

    		•
  • Q : David Hume statement regarding money in

    In modern parlance, David Hume statement regarding money which is Tis none of the wheels of trade. And tis the oil, was referring to the notion that money: (i) is relatively costly to produce. (ii) facilitates divisions of labor and specialization and

    		•
  • Q : Advantage and disadvantage of Sole

    Illustrate the advantage and disadvantage of Sole proprietorship?

    		•
  • Q : Elucidate the various trade which

    Elucidate the various trade which enacted by governments?

    		•
  • Q : Decentralized a virtue of capitalism

    The idea which a virtue of capitalism is decentralized its decision making emerged while: (1) social philosophers looked for alternatives to feudal kings like economic regulators. (2) Russian imperialism fostered anti-communist sentiment after World W

    		•
  • Q : What is the opportunity cost of

    What is the opportunity cost of attending college?  In 2000, nearly 80% of college-educated Americans held jobs, whereas only about 40% of those who did not finish high school held jobs.  How might this difference relate to opportunity costs?

    		•
  • Q : Introduction of the term Financial

    Give a brief introduction of the term Financial Leverage?

    		•
  • Q : Calculate Equilibrium Quantity and Price

    1. The owner of a firm calculates that next year's profit will be $1,000. Each successive year profit will increase by 10% (i.e. year 2: $1100; year 3: $1210 and so on.) At the end of the 5th year the firm could be sold for $20,000. A) if the appropriate di

    		•
  • Q : What is American made in today’s global

    Illustrates how hard it is to define what is “American made” in today’s global economy?

    		•