--%>
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 : The market system not only accepts

    Explain the statements: The market system not only accepts self-interest as a fact of human existence.

    		•
  • Q : What is an inverse relationship Briefly

    Briefly explain the use of graphs as a way to present economic relationships. What is an inverse relationship?

    		•
  • Q : Negatively association to probability

    Adam Smith would have agreed mostly along with the concept which wages are: (i) positively associated to physical comfort when working. (ii) negatively related to the cost of learning the business. (iii) positively associated to the s

    		•
  • Q : Advantages rising from division of

    Adam Smith known three advantages rising from divisions of labor which would lead to greater economic wealth that did not include the concept that the division of labor: (w) helps every worker refine specialized skill

    		•
  • 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 : Explain the term Operating Leverage

    Briefly explain the term Operating Leverage?

    		•
  • Q : Need of the Economic Efficiency

    Economic efficiency for society needs which the: (i) opportunity costs of all goods be at their lowest possible values. (ii) maximum probable benefits are acquired for given costs. (iii) greatest possible net benefits are squeezed through available re

    		•
  • Q : Illustrate the 4th role is the

    Illustrate the 4th role is the reallocation of resources?

    		•
  • Q : Define internal rate of return What do

    What do you understand by the term internal rate of return?

    		•
  • Q : Capitalism-Tightly regulate business I

    I have a problem in economics on Capitalism-Tightly regulate business. Please help me in the following question. The govt. in a purely capitalist state would not: (1) Find out the property rights. (2) Enforce contracts among private parties. (3) Offer

    		•