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^{45} L^{100}`.
What is the marginal product of labor?
$$
MP_L = \frac{d q \left( K, L \right)}{d L} = \frac{d K^{45} L^{100}}{d L} = 100 K^{45} L^{100 - 1} = 100 K^{45} L^{99}
$$