--%>
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 regarding supplies-demands and

    The new supply and demand curves within University City are S0 and D0. But after the county commission imposed a $3 per six-pack excise tax upon beer: (1) demand fell to D1 from the perspectives of beer dealers. (2) co

    		•
  • Q : Explain the term leverages Briefly

    Briefly explain the term leverages?

    		•
  • 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 : 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 : Define the for whom query in market

    The market system responses the “for whom?” query with: (i) distributing goods on the basis of require. (ii) using central planning to coordinate production decisions. (iii) catering to consumers with adequate resources to demand goods. (i

    		•
  • Q : How can we calculate Price earnings

    How can we calculate Price earnings ratio?

    		•
  • Q : Determine relative price when two

    When the prices for doughnuts and croissants are $.50 and $1 correspondingly: (w) the opportunity cost for one doughnut is two croissants. (x) this is better to buy two doughnuts than one croissant. (y) one croissant will make Pierre twice as happy as one doughnut. (z

    		•
  • Q : Consumer purchase decision If the price

    If the price of a good is given, how does a consumer choose/decide as to how much of that good to purchase?

    		•
  • Q : Divide of the study of economics MOST

    The study of economics is MOST frequently divided within: (1) positive economics and negative economics. (2) macroeconomics and microeconomics. (3) subjective economics and objective economics. (4) supply side and demand side economics. (5) conservative economics and

    		•
  • Q : Elucidate reallocation of resources

    Elucidate reallocation of resources?

    		•