Marginal products of labor and capital (cobb-douglas)

Question

Given the cobb-douglas function $Y=1.01*K^{0.25}L^{0.75}$

$Y=$output; $K=$capital; $L=$labor

How can I determine the marginal products of labor and capital? Not used in this equation. Thanks for the help.

Answer 1

The marginal product is defined as the partial derivative with respect to the respective input.

In your case $\frac{\partial Y}{\partial L}=1.01 * 0.75 * ( \frac{K}{L})^{0.25}$ for labor and $\frac{\partial Y}{\partial K}=1.01 * 0.25 * ( \frac{K}{L})^{0.75}$ for capital.