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^{56} L^{84}`.
What is the marginal product of labor?
$$
MP_L = \frac{d q \left( K, L \right)}{d L} = \frac{d K^{56} L^{84}}{d L} = 84 K^{56} L^{84 - 1} = 84 K^{56} L^{83}
$$