Question

A firm’s production function is as follows: Q = 240K^(1/2) L^(1/4). If the firm uses 25 units of capital, what is the firm’s MPL?

Answer 1

To find the firm's MPL (marginal product of labor), differentiate the production function with respect to labor and substitute the given value of capital. The firm's MPL is given by MPL = 30 * L^(-3/4).

Step-by-step explanation:

The firm's production function is given by Q = 240K^(1/2) L^(1/4), where Q represents the output, K represents the amount of capital, and L represents the amount of labor. To find the firm's MPL (marginal product of labor), we need to find the derivative of the production function with respect to labor, which is MPL = (dQ/dL).

Let's differentiate the production function with respect to L:

dQ/dL = (1/4) * 240 * K^(1/2) * L^(-3/4)

Now, substituting the given value of K as 25 units, we get:

MPL = (1/4) * 240 * 25^(1/2) * L^(-3/4) = 30 * L^(-3/4)

Therefore, the firm's MPL is given by MPL = 30 * L^(-3/4).