Suppose that the production function for the economy is: Y = AK¹/⁴ᴸ³/⁴.Assume that real GDP is $8000 billion,capital stock is $32 000 billion,and the labour supply is 120 million (or 0.120 billion)workers.The value of the marginal product of capital is ________ per dollar of capital.

Question

Quizplus · Accepted Answer

The marginal product of capital (MPK) is derived from the production function Y = AK¹/⁴L³/⁴. The MPK is given by the partial derivative of Y with respect to K, which is (1/4)AK⁻³/⁴L³/⁴. Substituting the given values (Y = 8000, K = 32000, L = 0.120), we find that MPK = (1/4)(8000/32000) = 0.0625 per dollar of capital.

Suppose That the Production Function for the Economy Is: Y