Question

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

Answer 1

A. Additional watches per labor hour= 120000/60000= 2

Marginal cost= $6+$4= $10

P= 28-Q/20000

TR=P*Q= 28Q-Q^2/20000

MR=dTR/dQ= 28-Q/10000

At profit maximizing point MC=MR

28-Q/10000=10

Q*=180,000

But capacity is only 120000

P*=28-120000/20000 = $22

Profit= (P-MC)Q= (22-10)120000=$1440000

B. MC= $12

MC =MR

28-Q/10000=12

Q*=160,000

Produce 120000 at day and 40000 at night

P*=28-160000/20000 = $20

Profit= (20-10)120000+ (20-12)40000

=$1200000+$32000

=$1520000

C. P= 20 - Q/20,000

MR= 20-Q/10000

MC= $10

In the short run, firm should produce output where MR=MC

20-Q/10000=10

Q*= 100000= short run output.

P= 20-100000/10000= $10

In the long run firm will produce only when it earns positive profits i.e total revenue exceeds total cost.

Total revenue= $10*100000=$1000000

Total cost= Total fixed cost+ Total variable cost

= $600000+$6*100000

=$1200000

Since total revenue is less than total cost firm will not produce in the long run.

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