A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At what level of labor usage does the maximum average product occur?
A)20
B)30
C)40
D)50
E)60

Question

Quizplus · Accepted Answer

The average product of labor (APL) is given by:
$$APL = Q/L = (-0.002L^3 + 0.16L^2)/L = -0.002L^2 + 0.16L$$
To maximize APL, we take the derivative of APL with respect to L and set it equal to zero:
$$dAPL/dL = -0.004L + 0.16 = 0$$
Solving for L, we get:
$$L = 40$$
Therefore, the maximum average product occurs when the level of labor usage is 40.

A Short-Run Production Function Was Estimated As Q=−0.002L3+0.16L2Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }Q=−0.002L3+0.16L2

A Short-Run Production Function Was Estimated As $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$