Assume a Cobb-Douglas production function in which the share of capital is a = 0.25 and the share of labor is b = 0.75.If the rental cost of capital is rc = 10%, the desired capital stock of a cost-minimizing firm should be equal to

Question

Quizplus · Accepted Answer

The cost-minimizing firm chooses the amount of capital such that the marginal product of capital equals the rental cost of capital.

The marginal product of capital is the partial derivative of the production function with respect to capital:

MPK = aY/K

Setting this equal to the rental cost of capital:

rc = 0.1 = MPK

Substituting in the given values of a and b:

0.1 = 0.25Y/K

K = 2.5Y

Therefore, the optimal choice for the desired capital stock is K* = 2.5Y.

Assume a Cobb-Douglas Production Function in Which the Share of Capital