Suppose you are given the following information about a particular industry: Q_D

Question

Suppose you are given the following information about a particular industry: Q_D = 45,000 - 5,000P Market demand Q_s = 25,000P Market supply C(q) = 400 + q^2/400 Firm total cost function MC(q) = q/200 Firm marginal cost function Assume that all firms are identical and that the market is characterized by perfect competition. c. What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain. d. What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain.

Explanation / Answer

In the long run the firm will not sell products at a price that is below minimum average cost. At any price below minimum average cost, profit is negative and the firm is better off selling its fixed resources and producing zero output. To find the minimum average cost, set marginal cost(MC) equal to average cost(AC) and solve for q.

Thus,

q/200= 400/q+q/400

q/400=400/q

q2 =400*400

q=400

Average cost at q=400 is 2. (400/400+ 400/400)

Therefore, the firm will not sell for any price less than 2 in the long run.

d:

In short run, the firm will sell for any positive price, because at this price marginal cost will be above AVC(average variable cost). Profit willl be negative if price is below minimum average cost, or if it is below 2.

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