Marginal Product of Labor

The marginal product of labor tells how many additional products the firm makes with a tiny bit more labor. $$MP_L = \frac{d q \left( K, L \right)}{d L}$$

Example

In the cookie factory, the production function is

$$ q \left( K, L \right) = K L^2 $$

The marginal product of labor is

$$ MP_L = \frac{d q \left( K, L \right)}{d L} = 2 K L $$

Question

In the cookie factory, the production function is `q \left( K, L \right) = K^{30} L^{26}`.

What is the marginal product of labor?

$$ MP_L = \frac{d q \left( K, L \right)}{d L} = \frac{d K^{30} L^{26}}{d L} = 26 K^{30} L^{26 - 1} = 26 K^{30} L^{25} $$