Question

Q=6L^2-0.4L^3 is the function of short run production
Find the value of L that maximumes the out put

Answer 1

We have the production function as:

$$Q=6L^2-0.4L^3$$

From the production function, the marginal product of labor is:

$$MPL = 12L - 0.12L^2$$

At the optimal production, the marginal product is zero. Therefore:

$$MPL = 12L - 0.12L^2 = 0\\[0.3cm] 12L - 0.12L^2 = 0\\[0.3cm] 12 = 0.12L\\[0.3cm] L = \dfrac{12}{0.12}\\[0.3cm] \color{red}{L^* = 100}$$