Let $Y = A K ^ { \frac { 1 } { 3 } } L ^ { - \frac { 2 } { 3 } }$ If $\bar { g } _ { A } = 1 \%$, $\bar { g } _ { X } = 3 \%$, and if $\bar { g } _ { L } = 6 \% ,$ then $\bar { g } _ { Y } = 6 \%$,

Question

Let $Y = A K ^ { \frac { 1 } { 3 } } L ^ { - \frac { 2 } { 3 } }$  If $\bar { g } _ { A } = 1 \%$,   $\bar { g } _ { X } = 3 \%$,  and if $\bar { g } _ { L } = 6 \% ,$  then $\bar { g } _ { Y } = 6 \%$,

Quizplus · Accepted Answer

The growth rate of $Y$ is calculated using the growth rates of $A$, $K$, and $L$ with their respective exponents: $\bar{g}_Y = \bar{g}_A + \frac{1}{3}\bar{g}_K - \frac{2}{3}\bar{g}_L$. Substituting the given values, $\bar{g}_Y = 1\% + \frac{1}{3}(3\%) - \frac{2}{3}(6\%) = 1\% + 1\% - 4\% = -2\%$.

Let Y=AK13L−23Y = A K ^ { \frac { 1 } { 3 } } L ^ { - \frac { 2 } { 3 } }Y=AK31​L−32​

Let $Y = A K ^ { \frac { 1 } { 3 } } L ^ { - \frac { 2 } { 3 } }$