Firm z, operating in a perfectly competitive market, can sell as much or as litt
ID: 1234568 • Letter: F
Question
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 ou tcomes in parts a and b cannot persisit in the long run. Explain why. Find the market's price, total output, number of firms, and o utput 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.
Explanation / Answer
a) Profit is maximum when Marginal Revenue = Marginal Cost.
Hence 4+4Q = 16
Hence, Q = 3 units.
Profit at this point = 16*3 - C = 48 - (50 + 4Q +2Q^2) = - $32
ie loss of $32
b) Q = 200 -5P
Hence current market demand at $16 = 200 - 5*16 = 120 units.
If all of the companies have the same cost structure, (hence, each company manufactures 3 units), the total number of suppliers is 120/3 = 40.
c) The outcomes of a and b cannot last in long term because there is a net loss in the process.
The price will be at lowest average cost: Q = 5 units. Hence, Market price = 4+4Q = $24, total output = 200-24*5 = 80 units, and output per firm = 80/5 = 16 units
d) In the short run, the marginal cost is the driving parameter, while in long term, the average cost is to be minimized. Hence, the optimal price changes and so does the number of firms.
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