--%>
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 : Cooperative and non-cooperative outcome

    Question: Cineplex and AMC are two rival movie theatre chains. They must each decide whether to set an admission price of $10 or set an admission price of $12; of course, the number of movie goers (and thus their r

    		•
  • Q : Super committee failure Question: Some

    Question: Some commentators have argued that the failure of the "Super committee" is good thing for the economy?  Do you agree? Answer: The Super committe

    		•
  • Q : Market Economy Define the term Market

    Define the term Market Economy and also state its advantages and disadvantages?

    		•
  • 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 are the major legal forms of

    What are the major legal forms of business organization?

    		•
  • Q : Nation’s production possibilities curve

    Suppose that, based on a nation’s production possibilities curve, for 10,000 pizzas domestically an economy must sacrifice to get the one additional industrial robot it desires, but can get that robot from another country in exchange for 9,000 pizzas. To the fol

    		•
  • Q : Historical process by Adam Smith of

    Writings on the historical process by Adam Smith of economic development do not comprise heavy reliance upon: (1) the development of property rights. (2) self interest. (3) divisions of labor in production processes. (4) innovations d

    		•
  • Q : Elucidate Reliance on technology and

    Elucidate Reliance on technology and capital goods of the market system?

    		•
  • Q : Speculation and intermediary operations

    Transaction costs tend to be decreased, prices to consumers are classically stabilized and lowered, and economy-wide efficiency is generally improved through: (1) rigid wage and price controls. (2) central planning that fosters monopo

    		•
  • Q : Barter - Efficiency and the Gains from

    Relative to other systems, economies in that people exchange goods or resources directly along with other people for other goods or resources without using money like a usual denominator rely relatively heavily upon: (i) barter. (ii) specialization. (

    		•