--%>
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 : Problem on prisoners dilemma game Lets

    Lets assume an infinitely repeated prisoner’s dilemma game by two players. The resulting payoffs at each phase by the actions of two players are illustrated below in the table (payoffs are symbolized like (payoff for player 1, payoff for player 2)). Two players

    		•
  • Q : What are the major legal forms of

    What are the major legal forms of business organization?

    		•
  • Q : Describe North American Free Trade

    Describe North American Free Trade Agreement (NAFTA)?

    		•
  • Q : What are the Functions of money Explain

    Explain in short the functions of money? Answer: (A) Medium of exchange: Money can be employed to make payments for all transactions of services and goods.

    		•
  • Q : Problem on utility function Matt’s life

    Matt’s life is divided into two time periods, young and old, and his utility is a function of two “goods”:  consumption when young and consumption whenever old.  Consumption when young and consumption when old are both of normal goods to Ma

    		•
  • Q : Major type of expenditure at the state

    What is the most important source of revenue and the major type of expenditure at the state level?  

    		•
  • Q : Why Public or social goods not be

    Why Public or social goods not be produced through the market?

    		•
  • Q : Importance of rationally optimal

    Economic scarcity is pervasive, that makes choices essential. Therefore, rationally optimal decisions hinge upon tradeoffs which essentially reflect: (i) cooperation to minimize human greed. (ii) opportunity costs. (iii) competitive social behavior. (

    		•
  • 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

    		•
  • Q : Impact of dollar on aspects of

    Question Discuss the impact of dollar depreciation on the various aspects of American Economy. Devaluation of the DollarIntroduction:

    		•