Suppose the short-run production function is q = L^0.5.If the marginal cost of producing the tenth unit is $5,what is the wage per unit of labor? A)$1 B)5¢ C)25¢ D)It cannot be determined without more information.

Question

Quizplus · Accepted Answer

The marginal cost (MC) is the change in total cost from producing one more unit of output. Given MC = $5 for the tenth unit and the production function q = L^0.5, the marginal product of labor (MPL) is 0.5L^(-0.5). For the tenth unit, L = 100 (since 10 = 100^0.5). MPL at L = 100 is 0.5/10 = 0.05. MC = wage/MPL, so $5 = wage/0.05, thus wage = $5 * 0.05 = $0.25 or 25¢.

Suppose the Short-Run Production Function Is Q = L0

Suppose the Short-Run Production Function Is Q = L⁰