Question

A firm produces sunglasses on a single production line served during one daily shift. The total output of glasses depends directly on the number of labor-hours employed on the line. Maximum capacity of the line is 100,000 glasses per month; this output requires 50,000 labor-hours per month. Total fixed costs come to $600,000 per month; the wage rate averages $12 per hour; and other variable costs (materials, etc.)  average $6 per set of glasses. The marketing department’s estimate of demand is P = 26–Q / 20,000 where P denotes price in dollars and Q is monthly demand.

a) How many additional sunglasses can be produced by an extra hour of labor? What is the marginal cost of an additional set of glasses? As a profit maximizer, what price and output should the firm set? Is production capacity fully utilized? What contribution to paying fixed costs does this product line provide?

b) The firm can increase capacity up to 100 percent by scheduling a night shift. The wage rate at night averages $16 per hour. Answer the questions in part (a) in light of this additional option.

c) Suppose demand for the firm's sunglasses falls permanently to P=20-Q/20,000. In view of this fall in demand, what output should the firm produce in the short run? Explain.

Answer 1

irm 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 + 2Q². The associated marginal cost function is MC = 4 + 4Q and the point of minimum average cost is Q min = 5.
Answer-A. Determine the firm's profit-maximizing level of output. Compute its profit.
MC=MR MR =$16
4 + 4Q = 16 4Q = 12 Q= 3
Profit maximizing output is 3

TR-TC
TR = P*Q = 16 x 3 = 48
TC = 50+4Q + 2Q²
TC = 50+12 + 18 = 80
Profit = TR - TC = 48 - 80 = -32
Answer-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?
Q = 200 - 5p = 200 - 5*16
Q = 200 - 80 = 120
The number of firms supplying the market would be the Q 120 / 3 (profit maximizing output) = 40

Answer C. The outcomes in part 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.

Answer D. Comparing the short-run and long-run results, explain the changes in the price and in the number of firms.
As the industry under perfect competition and in the short run are earning profits. Therefore, in the long run this will give encouragement for the new firms to enter in to the market leading to increase in the overall supply and causing the normal price to fall which results in normal profits in the long run. So, in the long run the price will come down due to increase in the number of firms in the long run. P = AR = MR = AC = MC