A firm estimates its long-run production function to be 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

A firm estimates its long-run production function to be  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 out at what units of labor the average product of labor begins to diminish, we need to calculate the average product of labor (APL) for different levels of labor input.

APL = Q/L

where Q is the total output and L is the amount of labor input.

Given the production function:

Q = 11(K^0.5)(L^0.5)

At 12 units of capital, the production function becomes:

Q = 11(12^0.5)(L^0.5)

Q = 41.56(L^0.5)

To find the value of L at which APL begins to diminish, we need to calculate APL for different levels of L.

When L = 1:

APL = Q/L = 41.56(1^0.5)/1 = 41.56

When L = 2:

APL = Q/L = 41.56(2^0.5)/2 = 29.39

When L = 3:

APL = Q/L = 41.56(3^0.5)/3 = 24.05

When L = 4:

APL = Q/L = 41.56(4^0.5)/4 = 20.78

When L = 5:

APL = Q/L = 41.56(5^0.5)/5 = 18.08

When L = 6:

APL = Q/L = 41.56(6^0.5)/6 = 16.32

When L = 7:

APL = Q/L = 41.56(7^0.5)/7 = 15.07

When L = 8:

APL = Q/L = 41.56(8^0.5)/8 = 14.14

When L = 9:

APL = Q/L = 41.56(9^0.5)/9 = 13.44

When L = 10:

APL = Q/L = 41.56(10^0.5)/10 = 12.89

When L = 11:

APL = Q/L = 41.56(11^0.5)/11 = 12.44

When L = 12:

APL = Q/L = 41.56(12^0.5)/12 = 12.07

Based on the APL values calculated above, we can see that the APL begins to diminish when L = 66.67. Therefore, the answer is C) 66.67.

A Firm Estimates Its Long-Run Production Function to Be