--%>
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 Federal corporate income tax Use

    Use the circular flow model to confirm this assertion for a 2% reduction in the Federal corporate income tax.

    		•
  • Q : Who define economics as a subset of

    Economists who viewed economics like a subset of jurisprudence combined: (1) John Stuart Mill. (2) Alfred Marshall. (3) Karl Marx. (4) William Stanley Jevons. (5) Adam Smith. Hey friends please give your opinion fo

    		•
  • Q : Gross domestic product Question Would

    Question Would "Victory Points" be a measure of player's "GDP"? If not, then how would you calculate a player's GDP?

  • Q : Production Possibility Curve Production

    Production Possibility Curve: Similar to the individuals, a society as entire has restricted resources. It has to decide what to manufacture with restricted resource

    		•
  • Q : Supply and demand at tax burdens and

    The new supply and demand curves within University City are S0 and D0. But after the county commission imposed at $3 per six-pack excise tax upon beer: (w) beer sellers' revenue after taxes decreases by $60,000 monthly. (x) buyers and sellers eac

    		•
  • Q : Important source of revenue and major

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

  • 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 : U.S. exports create a demand for

    True or false? “U.S. exports create a demand for foreign currencies; foreign imports of U.S. goods generate supplies of foreign currencies.”  Explain.

    		•
  • Q : Self-interest theory demonstration by

    The model of _____ was demonstrated by _____ along with the quote, “The loss of a small finger would remain the average European by sleeping which night, ... but, given he never observed them, he will snore with the most profound security over the loss of millio

    		•
  • 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

    		•