Refer to the following:
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

Refer to the following:
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

Quizplus · Accepted Answer

To find the level of labor usage where the maximum average product occurs, we need to find the derivative of the average product function and set it to zero. The average product (AP) is given by $AP = Q/L = (-0.002L^3 + 0.16L^2)/L = -0.002L^2 + 0.16L$. Taking the derivative of AP with respect to L and setting it to zero gives $d(AP)/dL = -0.004L + 0.16 = 0$. Solving for L gives L = 40.

Refer to the Following: a Short-Run Production Function Was Estimated Q=−0.002L3+0.16L2Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }Q=−0.002L3+0.16L2

Refer to the Following:
a Short-Run Production Function Was Estimated $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$