--%>
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 : Mixed Economy Define the term Mixed

    Define the term Mixed Economy and also state their advantages and disadvantages?

    		•
  • Q : State of good or service at last unit

    Which of the given describes a situation in which each good or service is produced up to the point where the last unit gives a marginal benefit to consumers equivalent to the marginal cost of producing this? w) productive efficiency.

    		•
  • 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 : What are the determinants of demand

    What are the determinants of demand?

    		•
  • 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 : Illustrate the complex cases when both

    Illustrate the complex cases when both supply and demand shift?

    		•
  • Q : Characteristic of an oligopolistic

    Which of the given is a quality of an oligopolistic market structure? w) There are only some dominant sellers. x) every firm sells a unique product. y) this is easy for new firms to enter the industry. z) Each firm require not react to the actions of

    		•
  • Q : External factors which influencing the

    Write down the external factors which influencing the capital structure?

    		•
  • Q : Government expenditures on goods and

    Explain Government expenditures on goods and services and transfer payments?

    		•
  • Q : Founder of modern economics The person

    The person along with, arguably, the top claim to the name “founder of modern economics”: (1) John Stuart Mill. (2) Karl Marx. (3) John Maynard Keynes. (4) Joan Robinson. (5) Adam Smith. Hello guys I wa

    		•