--%>
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 : Variation of wages in inverse proportion

    This wages vary within inverse proportion to the agreeableness and constancy of the employment was a perception first explicitly stated through: (i) Adam Smith. (ii) Karl Marx. (iii) Thomas Malthus. (iv) John Stuart Mill. (v) David Ricardo.

  • Q : Summary of what can cause an increase

    Illustrate a summary of what can cause an increase in demand?

    		•
  • Q : Illustrate Economics for citizenship

    Illustrate Economics for citizenship?

    		•
  • Q : Introduction of the term Financial

    Give a brief introduction of the term Financial Leverage?

    		•
  • Q : Absolute advantage in international

    One early involvement of Adam Smith to the theory of gains by international trade, although later thoroughly revised and refined through David Ricardo, was the conception of: (1) mercantilism. (2) absolute advantage. (3) comparative a

    		•
  • Q : Higher opportunity costs of attendance

    Economics professors would attribute students’ higher rates of attendance on days while examinations are administered to the: (w) intensified needs to learn valuable material. (x) higher opportunity costs of missing set relative to other schedul

    		•
  • Q : Exploit consumers in highly competitive

    This is difficult for firms within highly competitive markets to exploit consumers since: (i) consumer advocates organize boycotts that generate bad publicity. (ii) market pressures force fair distributions of products. (iii) the government sets price

    		•
  • Q : Describe redistributive effects of

    Describe redistributive effects of inflation?

    		•
  • Q : Eco Quantity TR TC 0 $0.00 $10.00 1

    Quantity TR TC 0 $0.00 $10.00 1 $150.00 $30.00 2 $290.00 $50.00 3 $420.00 $80.00 4 $540.00 $120.00 5 $650.00 $170.00 6 $750.00 $230.00 7 $840.00 $300.00 8 $920.00 $

    		•
  • Q : How might government correct this

    What divergences arise between equilibrium and an efficient output spillover benefits are present?  How might government correct this divergence?

    		•