A firm produces output using capital and labor. The firm's marginal product of labor (MP Subscript Upper L) is 40 and its marginal product of capital (MP Subscript Upper K) is 28. Suppose the wage per unit of labor (w) is $6.00 and the cost per unit of capital (r) is $3.00. Is the firm minimizing the cost of production? What should the firm do, if anything, to produce the same level of output at lower cost? The firm

b. The firm should continue to increase the units of labor by reducing the unit of capital until when the ratio of Marginal product of labor to Marginal product of capital of is equal to the ratio of w to r.

Explanation:

a. Is the firm minimizing the cost of production?

The firm minimizing the cost of production where:

Marginal product of labor / Marginal product of capital = w / r

From the question, we have:

40 / 28 = 6 / 3

1.43 = 2

Since the ratio of Marginal product of labor to Marginal product of capital of 1.43 is not equal to the ratio of w to r, the firm is not minimizing the cost of production.

b. What should the firm do, if anything, to produce the same level of output at lower cost?

The firm should continue to increase the units of labor by reducing the unit of capital until when the ratio of Marginal product of labor to Marginal product of capital of is equal to the ratio of w to r.

The closest point at which this will happen is when the Marginal product of labor is 45 and Marginal product of capital is 23 where we have:

45 / 23 = 1.96, or 2 approximately.