A firm produces processed cheese on a single production line during one daily sh

Question

A firm produces processed cheese on a single production line during one daily shift. The maximum capacity of the line is 120,000 boxes of processed cheese per day. To reach this capacity, 60,000 labor-hours are required per day. Each labor-hour costs the firm $8; total fixed costs come to $600,000 and other variable costs average $6 per box. The marketing department estimated the demand to be Q=560,000-20,000P, where P denotes price in dollars and Q is daily demand.

a.) How many additional boxes of processed cheese can be produced by an extra hour of labor?

b.) What is the marginal cost of and additional box of processed cheese?

c.) What price and output should the firm set?

d.) Is production capacity fully utilized?

e.) What contribution does this product line provide?

f.) The firm can increase capacity up to 100% by scheduling night shift. The wage at night averages $12 per hour. Answer a.) to e.) in light of this additional option.

g.) Suppose demand for the firm's processed cheese falls permanently to P=20-Q/20,000. What output should the firm produce in the short run?

Explanation / Answer

a) Q/LH 120,000/60,000 = 2

b) TC = 600,000 + (8/2)L + 6Q MC = 4 + 6 = 10

c,d,e) MR = MC

P = 560,000/20,000 – Q/20,000

P = 28 – 0.00005Q TR = PQ 28(Q) – 0.00005Q(Q)

MR =28 - 0.0001Q 28 – 0.0001Q = 10 0.0001Q = 28 – 10 Q = 180,000

P = 28 – 0.00005(180,000)

P = 19

f) MC = 12/2 + 6 = 12

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