--%>
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 : Single seller not sell at a price lower

    An individual seller within perfect competition will not sell at a price lower than the market price since: w) demand for the product will exceed supply.  x) the seller would begin a price war. y) the seller can sell any quantity she desires at the prevailing mar

    		•
  • Q : Question 7 Question 7: You are given

    Question 7: You are given the following data about two firms: FIRM A Quantity 0 1 2 3 4 5 6 Total revenue ($) 0 10 20 30 40 50 60 Average revenue ($) ___ ___ ___ ___ ___ ___ ___ Marginal revenue ($) ___ ___ ___ ___ ___ ___ Total cost ($) 30 42 50 60 76 100 14

    		•
  • Q : Distinguish clearly between a plant

    Distinguish clearly between a plant, a firm, and an industry?

    		•
  • Q : Eco Quantity TR TC 0 $0.00 $10.00 1

    Quantity TR TC 0 $0.00 $10.00 1 $150.00 $30.00 2 $290.00 $50.00 3 $420.00 $80.00 4 $540.00 $120.00 5 $650.00 $170.00 6 $750.00 $230.00 7 $840.00 $300.00 8 $920.00 $

    		•
  • Q : Ambrose’s budget constraint Question:

    Question: Ambrose consumes two goods, peanuts (x1 ) and a composite good (x2). He has a utility functionU = 4 √x1 + x2. This means his MU1 = 2/ √x1 an

    		•
  • Q : Banking crisis on checkable deposits

    Question: Some developing countries have suffered banking crises in which depositors lost part or all of their deposits (in some countries there is no deposit insurance). This type of crisis decreases depositors' confidence in the banking syst

    		•
  • Q : Requirement of building blocks for a

    Building blocks for a capitalist system consist of: (1) supplies and demands. (2) private property rights. (3) laissez-faire policies. (4) market-determined outputs and prices. (5) All of the above. Please guys hel

    		•
  • Q : Introduction of the term capital

    Give brief introduction of the term capital structure? And also write down its principles?

    		•
  • Q : Affects the location of the production

    Explain how, if at all, each of the following affects the location of the production possibilities curve?

    		•
  • Q : Distribution of income and wealth in a

    Of the given options, the economist whose theories pivoted least upon the distribution of income and wealth (class conflict) in a capitalist system would have been: (1) Adam Smith. (2) David Ricardo. (3) Karl Marx. (4

    		•