If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$
, the marginal product of capital is (1/3)(Y/K).

Question

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ 
, the marginal product of capital is (1/3)(Y/K).

Quizplus · Accepted Answer

The marginal product of capital (MPK) is the partial derivative of the production function with respect to capital $K$. Differentiating $Y = K^{1/3}L^{2/3}$ with respect to $K$ gives $\frac{\partial Y}{\partial K} = \frac{1}{3}K^{-2/3}L^{2/3}$. Simplifying, this is $\frac{1}{3}\left(\frac{Y}{K}\right)$.

If the Production Function Is Given By Y=K1/3L2/3Y = K ^ { 1 / 3 } L ^ { 2 / 3 }Y=K1/3L2/3

If the Production Function Is Given By $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$