If the production function is given by
, the marginal product of capital is (1/3)(Y/K).

Question

If the production function is given by  
, the marginal product of capital is (1/3)(Y/K).

Quizplus · Accepted Answer

This is because the formula for marginal product of capital in a production function with constant returns to scale is MPK = ∂Y/∂K, where ∂ denotes partial derivative. Taking the partial derivative of the given production function with respect to K gives Y/K, which means MPK = Y/K. Since it is given that (1/3)(Y/K) = MPK, this statement is true.

If the Production Function Is Given by