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# Long-run Market Adjustment Under Perfect Competition

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Firm Z, operating in a perfectly competitive market, can sell as much or as little as it wants of a good at a price of \$16 per unit. Its cost function is C=50+4Q+2Q^2. The associated marginal cost is MC=4+4Q, and the point of minimum average cost is Qmin=5

(a). Determine the firm`s profit-maximizing level of output. Compute its profit.

(b). The industry demand curve is Q=200-5P. What is the total market demand at the current \$16 price? If all firms in the industry have cost structures identical to that of firm Z, how many firms will supply the market?

(c). The outcomes in parts (a) and (b) cannot persist in the long run. Explain why. Find the market`s price, total output, number of firms, and output per firm in the long run.

(d) Comparing the short-run and long-run results, explain the changes in the price and in the number of firms.

#### Solution Preview

a)
The firm maximizes its profit when Marginal Revenue (MR) = Marginal Cost (MC). In a perfectly competitive market, MR = Price

Let MR = MC
16 = 4 + 4Q
4Q = 12
Q = 3

Therefore the firm's profit-maximizing level of output is 3 units.

Profit = Total Revenue (TR) - Total Cost (TC)
Profit = PQ - (50 + 4Q + 2Q^2)
Profit = 16(3) - (50 + 4(3) + 2(3^2))
Profit = 48 - 80
Profit = ...

#### Solution Summary

Given cost and price data, this solution calculates that every firm in a perfectly competitive market is making a loss in the short run. The solution goes on to calculate how the market will adjust in the long run.

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