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^{38} L^{47}`.

What is the marginal product of labor?

$$ MP_L = \frac{d q \left( K, L \right)}{d L} = \frac{d K^{38} L^{47}}{d L} = 47 K^{38} L^{47 - 1} = 47 K^{38} L^{46} $$