--%>
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 : Qualitative and Quantitative data What

    What is the difference between qualitative data and quantitative data, provide an example of each.

    		•
  • Q : Resource markets in simple circular

    Can someone help me in finding out the right answer from the given options. In resource markets in a simple circular flow model, house-holds exchange their _________ for _________. (1) Resources | income. (2) Goods | profits. (3) Labor | goods. (4) Devotion | enlighte

    		•
  • Q : The market system not only accepts

    Explain the statements: The market system not only accepts self-interest as a fact of human existence.

    		•
  • Q : Introduction of the term net present

    Give a brief introduction of the term net present value? Write down its admittable rules, their merits and demerits?

    		•
  • Q : Speculators decreases price volatility

    Speculators decrease price volatility through, in effect, changing demand curves: (w) out at low prices, and shifting supply curves out at high prices. (x) out at low prices, and shifting supply curves within at low p

    		•
  • Q : Competition is the essential despot of

    Evaluate and explain the statements: “Competition is the essential despot of the market economy”.

    		•
  • Q : Example of self interest to define

    The concept of _____ was demonstrated by _____ along with the quotation, “The defeat of a bit finger would remain the average European from sleeping which night,... but, given he never saw them, he will snore along with the most profound security over the loss o

    		•
  • Q : Illustrate a fundamental characteristic

    Illustrate a fundamental characteristic of demand behavior?

    		•
  • Q : The market system provides such a

    Explain the statements: The market system provides such a variety of desired goods and services precisely.

    		•
  • Q : Reciprocal Trade Agreements Act had

    How Reciprocal Trade Agreements Act had goal of reducing tariffs?

    		•