In the Cobb-Douglas production function $Y = \bar { A } K ^ { 1 / 4 } L ^ { 3 / 4 }$ , defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is:
A) $y = \bar { A } k ^ { 3 / 4 }$

B) $y = \bar { A } k ^ { - 1 / 4 }$

C) $y = \bar { A } k ^ { 1 / 4 }$

D) $y = \bar { A } k ^ { 3 / 4 }$.

E) None of these answers are correct.

Question

In the Cobb-Douglas production function $Y = \bar { A } K ^ { 1 / 4 } L ^ { 3 / 4 }$ , defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is:
A) $y = \bar { A } k ^ { 3 / 4 }$

B) $y = \bar { A } k ^ { - 1 / 4 }$

C) $y = \bar { A } k ^ { 1 / 4 }$

D) $y = \bar { A } k ^ { 3 / 4 }$.

E) None of these answers are correct.

Quizplus · Accepted Answer

The per person production function is derived by dividing the original function by L, resulting in $y = \bar{A} (K/L)^{1/4} = \bar{A} k^{1/4}$.

In the Cobb-Douglas Production Function Y=AˉK1/4L3/4Y = \bar { A } K ^ { 1 / 4 } L ^ { 3 / 4 }Y=AˉK1/4L3/4

In the Cobb-Douglas Production Function $Y = \bar { A } K ^ { 1 / 4 } L ^ { 3 / 4 }$