Question

Suppose that a firms production function is Q=F(L)=L^3-200L^2+10,000L. it's marginal product of labor is Mpl=3L^2-400L+10,000. at what amount of labor input are the firms average and marginal product of labor equal confirm that the average and marginal product curves satisfy the relationship discussed in the text.

Answer 1

The amount of labor input at which the firm's average and marginal product of labor are equal is 200.

Step-by-step explanation:

To find the amount of labor input at which the firm's average and marginal product of labor are equal, we need to set the average product of labor (APL) equal to the marginal product of labor (MPL).

Mathematically, APL is calculated as Q/L and MPL is the derivative of the production function, which is 3L^2-400L+10,000.

Setting APL = MPL, we get (L^3-200L^2+10,000L) / L = 3L^2-400L+10,000.

Simplifying the equation and solving for L, we find that at L = 200, the average and marginal product of labor are equal.

This confirms the relationship discussed in the text, where the average and marginal product curves intersect.