Define $Y = A K ^ { 1 / 3 } L ^ { 2/3 }$ . If $\bar { g } _ { A } = 1 \%$ , $\bar { g } _ { X } = 6 \%$ , and if $\bar { g } _ { L } = 6 \%$ , then $\bar { g } _ { Y } = 7 \%$

Question

Define $Y = A K ^ { 1 / 3 } L ^ { 2/3 }$  . If $\bar { g } _ { A } = 1 \%$  , $\bar { g } _ { X } = 6 \%$  , and if $\bar { g } _ { L } = 6 \%$  , then $\bar { g } _ { Y } = 7 \%$

Quizplus · Accepted Answer

The elasticity of output with respect to each input is the exponent on that input in the production function. Therefore, $\bar { g } _ { Y } = \frac { 1 } { 3 } \bar { g } _ { A } + \frac { 1 } { 3 } \bar { g } _ { K } + \frac { 2 } { 3 } \bar { g } _ { L } = \frac { 1 } { 3 } ( 1 ) + \frac { 1 } { 3 } ( 6 ) + \frac { 2 } { 3 } ( 6 ) = 7\%$

Define Y=AK1/3L2/3Y = A K ^ { 1 / 3 } L ^ { 2/3 }Y=AK1/3L2/3

Define $Y = A K ^ { 1 / 3 } L ^ { 2/3 }$