Question

A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $12 per hour and capital is rented at $8 per hour. Currently, the marginal product of labor is 60 units of output per hour and the marginal product of capital is 45 units of output per hour is the firm using the cost minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process?

Answer 1

Step-by-step explanation:

According to the rule of cost minimization, a firm should should employ that quantity f labor and capital for which the marginal rate of technical substitution between capital and labor (MRTSkl) equals the wage rental ratio (w/r). Hence, the cost minimization rules becomes:

(MRTSkl) = w/r

MPl / MPk = w / r

MPl / w = MPk / r

In the case given, substitute the values of the variables and find that

MPl / w = MPk / r

60 / 12 < 45 / 8

5 < 5.625

Since the ratio is not equal, the firm is not using the optimum mix of inputs. On last dollar spent basis, capital is a better deal than labor, and the firm should use less labor and increase the amount of capital in order to minimize costs.