# Short-Run Production and Marginal and Average Product

Consider the following short-run production function (where L = variable input, Q = Output): Q = 6L2 - 0.4L3

a. Determine the marginal product function (MPL)

b. Determine the average product function (APL)

c. Find the value of L that maximizes Q

d. Find the value of L at which the marginal product function takes on its maximum value

e. Find the value of L at which the average product function takes on its maximum value

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#### Solution Preview

Q1. Consider the following short-run production function (where L = variable input, Q = Output): Q = 6L2 - 0.4L3

a. Determine the marginal product function (MPL)

Q=6L^2-0.4L^3

Marginal product of L=MPL=dQ/dL=12L-1.2L^2

b. Determine the average product ...

#### Solution Summary

This solution determines the marginal product function, the average product function, the value of L that maximizes quantity, the value of L at which the marginal product function takes on its maximum value, and the value of L at which the average product function takes on its maximum value.