--%>
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 : Variation of wages in inverse proportion

    This wages vary within inverse proportion to the agreeableness and constancy of the employment was a perception first explicitly stated through: (i) Adam Smith. (ii) Karl Marx. (iii) Thomas Malthus. (iv) John Stuart Mill. (v) David Ricardo.

  • Q : Consumer purchase decision If the price

    If the price of a good is given, how does a consumer choose/decide as to how much of that good to purchase?

    		•
  • Q : Describe four important areas to

    Describe four important areas to emphasize Expenditures?

    		•
  • Q : Fruit Question: Read the following

    Question: Read the following excerpts from the article "Fruit, veg costs surge' by Todd, Dagwell, published in the Herald on January 25th 2011 and answer questions below:

    Q : Describe the output effects of Inflation

    Describe the output effects of Inflation?

    		•
  • Q : An Inquiry in the Nature and Causes The

    The first comprehensive work upon economics written within English was authored through Adam Smith in 1776 year and entitled that “An Inquiry within the Nature and Causes of: (1) Laws of Supply and Demand.” (2) Wealth of Nations.” (3

    		•
  • Q : Decreases in opportunity costs of

    The opportunity costs of production and consumption for most resources and goods tend to be decreased by: (w) private monopoly power. (x) price floors. (y) intense competition. (z) price ceilings. Hey friends pleas

    		•
  • Q : Economic efficiency enhancement as

    Transaction costs are decreased and economic efficiency is enhanced by: (1) long-term wage and price controls. (2) monopolies which cooperate with central planners. (3) blacklists and yellow dog contracts. (4) bureaucratic tendencies

    		•
  • Q : Explain how an increase in state

    Use two market diagrams to explain how an increase in state subsidies to public colleges might affect tuition and enrollments in both public and private colleges.

    		•
  • Q : Use of human and material resources

    What are the merits of speciality in the use of human and material resources?

    		•