--%>
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 : Heterodox cost theory Is Eiteman &

    Is Eiteman & Guthrie’s empirical evidence on the shape of the average total cost curve consistent along with heterodox cost theory?  Discuss it out.

    		•
  • Q : Exchange is the necessary consequence

    Explain: “Exchange is the necessary consequence of specialization.”

    		•
  • Q : Describe Traditional approach of

    Briefly describe Traditional approach of capital structure?

    		•
  • Q : Invisible hand Describe the meaning of

    Describe the meaning of the term “invisible hand.”

    		•
  • Q : Explain producers in an industry

    Explain producers in an industry are receiving pure or economic profits?

    		•
  • Q : Determine the clearest illustration of

    The clearest illustration of economic inefficiency would be: (w) maintaining a warehouse full of pet rocks within hopes such that someday the fad will return. (x) pet rocks being unavailable to people willing to pay a price that exceeds the marginal s

    		•
  • Q : When productive resources are utilized

    While productive resources are utilized efficiently: (w) prices greatly exceed production costs for current outputs. (x) opportunity costs are at their minimums for all goods. (y) domestic production exceeds the value of foreign output. (z) the value

    		•
  • Q : Describe the Slope of a nonlinear curve

    Describe the Slope of a nonlinear curve?

    		•
  • Q : Demand often exceeds supply and supply

    “In the corn market, demand often exceeds supply and supply sometimes exceeds demand.” “The price of corn rises and falls in response to changes in supply and demand.” Among these 2 statements used correctly which in the terms “supply&rdq

    		•
  • Q : When are transaction costs to ultimate

    Transaction costs to ultimate consumers are reduced if: (w) consumers travel long distances to buy directly from manufacturers quite than buying the goods at local retail stores. (x) intermediaries generate income while conveying goods from manufactur

    		•