The steady-state level of output per worker in the Solow model, with the production function $Y = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }$ , is given by:
A) $y ^ { * } = \bar { A } \left( \frac { \bar { s } } { \bar { d } } \right) ^ { 1 / 2 }$
B) $$y ^ { * } = \bar { A } ^ { 3 / 2 } \left( \frac { \bar { d } } { \bar { s } } \right) ^ { 1 / 2 } \bar { L }$$
C) $y ^ { * } = \bar { A } ^ { 3 / 2 } \left( \frac { \bar { s } } { \bar { d } } \right) ^ { 1 / 2 } \bar { L }$
D) $y ^ { * } = \bar { A } ^ { 3 / 2 } \left( \frac { \bar { s } } { \bar { d } } \right) ^ { 1 / 2 }$
E) $y ^ { * } = \bar { A } \left( \frac { \bar { s } } { \bar { d } } \right) ^ { 1 / 3 }$

Question

Quizplus · Accepted Answer

In the Solow model, the steady-state output per worker is derived from the production function and the capital accumulation equation. The correct formula is $y^* = \bar{A}^{3/2} \left( \frac{\bar{s}}{\bar{d}} \right)^{1/2}$, which matches choice D.

The Steady-State Level of Output Per Worker in the Solow Y=AˉKt1/3Lˉ2/3Y = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }Y=AˉKt1/3​Lˉ2/3

The Steady-State Level of Output Per Worker in the Solow $Y = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }$