N firms compete in a perfectly competitive industry. Market demand Q, for a good

Question

N firms compete in a perfectly competitive industry. Market demand Q, for a good is given by Q=3000-50P, where P is the market price. For each firm I, the long run total cost function , C(qi) is:

C(qi) = 0 if qi = 0

C(qi) = 100 + qi2    for qi > 0

a. What is the long-run supply curve for an individual firm? Explain

b. Assume that there is freen entry and exit. What is the level of output of each firm, total market output and the market price in the long-run equilibrium? If we measure welfare as the sum of profits and consumers’ surplus, what is the level of welfare associated with long run equilibrium?

Explanation / Answer

MC(qi) = 2qi

AC(qi) = 100/qi + qi

a. The long run supply curve will be the rising portion of the MC curve after MC equals AC at its minimum point.

2qi = 100/qi + qi

or, qi = 10

b. Level of output per firm = 10

P = MC = 2*10 = 20

Market demand = 3000-(50*20) = 2000

Number of firms = 2000/10 = 200

CS = 1/2(60 - 20)*10 = 200

Profit = 0

Welfare = 200

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