A bottling company uses two inputs to produced bottles of the soft drink Sludge:

Question

A bottling company uses two inputs to produced bottles of the soft drink Sludge: bottling machines (K) and and workers (L). The isoquants have the usual smooth shape. The machines cost $1000 per day to run (r), and the workers earn $200 per day (w). At the current level of production, the marginal product of machines (MPm) is an additional 457 bottles per day, and the marginal product of labor (MPL) is 38 more bottles per day.

The bottling company

A. is not minimizing the cost of production because MPm/r < MPL/w and should use more labor and fewer machines.

B. is minimizing the cost of production because MPM/r = MPL/w

C. is not minimizing the cost of production becuase MPm?r > MPL/w and should use less labor and more machines

D. is not mminimizing the cost of production because MPm/r > MPL/w and should use more labor and fewer machines

E. is not minimizing the cost of production because MPm/MPL = r/w and we should use more labor and fewer machines.

Explanation / Answer

D. is not mminimizing the cost of production because MPm/r > MPL/w and should use more labor and fewer machines

Explanation:

To minimize costs the firm should set the marginal product per dollar equal for each factor. For labour, MP/w = 38/200 = .19. For capital MP/r = 457/1000 = .457. In this case the firm is not minimizing cost because these ratios are not equal. The firm should use more labor and less capital.

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