--%>
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 Economics Of Property And

    There are THREE questions in this assignment. The overall word length for this assignment should be in the range of 2,000-2,500 words. You may incur a penalty if you exceed the upper value. You must state the total number of words

    		•
  • Q : Advantage in production of two products

    Explain by giving example of an absolute advantage in production of two products?

    		•
  • Q : Labour economic Can someone help me in

    Can someone help me in finding out the right answer from the given options. The Taft Hartley Act of 1946 made it illegal to encompass a: (1) Right-to-work law passed by the state legislature. (2) Conviction for the misdemeanor and serve as union officer. (3) Union for the agricultural migrants or go

    		•
  • Q : Problem on opportunity cost buying a

    After agonizing regarding whether to buy a hot dog or a hamburger along with his last dollar while he goes to the fair, Jeeter at last chooses the hot dog. The hamburger shows Jeeter's: (i) normative choice, because it would be more nutritious. (ii) opportunity cost o

    		•
  • Q : Theories of capital structure Write

    Write down the theories of capital structure?

    		•
  • Q : Distinguish clearly between a plant

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

    		•
  • Q : Define Benefit Cost Ratio or

    Briefly describe the term Benefit Cost Ratio (or B/C Ratio) or Profitability Index (or PI)?

    		•
  • Q : What is the opportunity cost of your

    Suppose you arrive at a store expecting to pay $100 for an item, but learn that a store two miles away is charging $50 for it.  Would you drive there and buy it?  How does your decision benefit you?  What is the opportunity cost of your decision?  Now suppose you arrive at a s

    		•
  • Q : Consumer and producer surplus in the

    In perfectly competitive market, the market demand and market supply curves are provided by Qd = 1000 −10Pd and Qd = 30Ps. Assume that the government gives a subsidy of $20 per unit to each and every seller in the mark

    		•
  • 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

    		•