Refer to the following:
A firm estimates its long-run production function to be

$$Q = - 0.0075 K ^ { - 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$$
Suppose the firm employs 12 units of capital.
-At ________ units of labor, average product of labor begins to diminish.
A) 32.21
B) 44.44
C) 66.67
D) 76.66
E) 82.27

Question

Refer to the following:
A firm estimates its long-run production function to be

$$Q = - 0.0075 K ^ { - 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$$ 
Suppose the firm employs 12 units of capital.
-At ________ units of labor, average product of labor begins to diminish.
A) 32.21
B) 44.44
C) 66.67
D) 76.66
E) 82.27

Quizplus · Accepted Answer

To find when the average product of labor begins to diminish, we need to find the point where the derivative of the average product with respect to labor is zero. Given the production function and 12 units of capital, the average product of labor is maximized at 66.67 units of labor.

Refer to the Following: a Firm Estimates Its Long-Run Production Q=−0.0075K−3L3+12K2L2Q = - 0.0075 K ^ { - 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }Q=−0.0075K−3L3+12K2L2

Refer to the Following:
a Firm Estimates Its Long-Run Production $Q = - 0.0075 K ^ { - 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$