You were recently hired to replace the manager of the Roller

You were recently hired to replace the manager of the Roller Division at a major conveyor-manufacturing firm, despite the manager’s strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company’s production information, you learn that labor is paid $9 per hour and the last worker hired produced 110 rollers per hour. The company rents roller cutters and crimping machines for $14 per hour, and the marginal product of capital is 120 rollers per hour. Should you change the mix of capital and labor, and if so, how should it change?

A. You should increase labor and decrease capital.

B. You should not change the mix of capital and labor.

C. You should increase capital and decrease labor.

Solution

Option (C).

Input mix is optimal when (Marginal product of labor / Cost of labor) = (Marginal product of capital / Cost of capital)

Marginal product of labor / Cost of labor = 110/9 = 12.22

Marginal product of capital / Cost of capital = 120/14 = 8.57

Since (Marginal product of labor / Cost of labor) > (Marginal product of capital / Cost of capital), input mix is not optimal and you should decrease labor and increase capital.