A firm produces digital watches on a single production line serviced during one daily shift. The total output of watches depends directly on the number of labor-hours employed on the line. Maximum capacity of the line is 120,000 watches per month; this output requires 60,000 hours of labor per month. Total fixed costs come to $600,000 per month, the wage rate averages $8 per hour, and other variable costs (e.g., materials) average $6 per watch. The marketing department’s estimate of demand is P = 28 - Q/20,000, where P denotes price in dollars and Q is monthly demand.
a. How many additional watches can be produced by an extra hour of labor? What is the marginal cost of an additional watch? As a profit maximizer, what price and output should the firm set? Is production capacity fully utilized? What contribution 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 $12 per hour. Answer the questions in part (a) in light of this additional option.
c. Suppose that demand for the firm’s watches 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? In the long run? Explain.