Specialty Steel has carefully measured production in its new plant to determine

Question

Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production. It has found that, for its two inputs K and L, it has the following marginal products: MP_K = 12 units and MP_L = 20 units. The inputs are hired in perfectly competitive markets, and the firm faces input costs of P_K = $8.50 and P_L = $11 per unit. You have been hired as a consultant to assist Specialty in increasing profitability. What do you recommend about production planning? Explain. Assuming MP_K and input costs remain constant, at what MP_L will the firm be operating efficiently?

Explanation / Answer

The firm maximizes profit when the ratios of marginal products to input costs are equal across all inputs.

This requires that MPk/Pk = MPL/PL.

MPk/Pk = 12 / 8.5 = 1.41

MPL/PL = 20 /11 = 1.81

Here, the respective ratios are 1.41 and 1.81 and are not equal.

Therefore, the firm is not maximizing profit.

It can increase profit by hiring more labor and/or less capital to bring this ratio into equality.

Assuming MPk and input costs remain constant, the firm operates efficiently when MPk/Pk = MPL/PL

So, 12 / 8.5 = MPL / 11

MPL = 11 * 12 / 8.5 = 15.53 = 16 (Approx)

So, at MPL = 16 units the firm will be operating efficiently.

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