Question

A bottling company uses two inputs to produce bottles of the soft drink​ Sludge: bottling machines​ (K) and workers​ (L). The isoquants have the usual smooth shape. The machines cost​ $1,000 per day to run​ (r), and the workers earn​ $200 per day​ (w). At the current level of​ production, the marginal product of machines ​(MP Subscript Upper K​) is an additional 316 bottles per​ day, and the marginal product of labor ​(MP Subscript Upper L​) is 39 more bottles per day. Is this firm producing at minimum​ cost? If it is minimizing​ cost, explain why. If it is not minimizing​ cost, explain how the firm should change the ratio of inputs it uses to lower its cost.

Answer 1

Answer:

No.

Explanation:

In order to minimizing the cost for a given level of output, the firm should equate the weighted marginal product of capital with the weighted marginal product of labor.

$\frac{MP_{K} }{r}= \frac{MP_{L} }{w}$

Put the value in the above equation, we get

$\frac{316}{1,000}= \frac{39}{200}$

0.316 > 0.195

Now, $\frac{MP_{K} }{r}>\frac{MP_{L} }{w}$, so the firm is not minimizing its cost in producing the bottles of the soft drink​ Sludge.

Hence, in order to minimize cost the firm should substitute labor with more of capital, so that MP 'K' falls and become equal to MP 'L'.