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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.
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