Suppose k, l, and A grow at constant rates given by $\bar { g } _ { k }$ $\bar { g } _ { y }$,
And $\bar { g } _ { A }$`
What is the growth rate of y if $y = A k ^ { a } l ^ { 1 - a } , a 0 ?$
A) $g _ { y } = \bar { g } _ { A } + a \left( \bar { g } _ { k } + \bar { g } _ { t } \right)$
B) $g _ { y } = \bar { g } _ { A } + a \bar { g } _ { k } + ( 1 - a ) \bar { g } _ { l }$
C) $g _ { y } = a \bar { g } _ { A } + a \bar { g } _ { k } + a \bar { g } _ { l }$
D) $g _ { y } = \bar { g } _ { A } + \bar { g } _ { l } ^ { a } + \bar { g } _ { l } ^ { ( 1 - a ) }$
E) $g _ { y } = \bar { g } _ { A } \times a \bar { g } _ { k } \times ( 1 - a ) \bar { g } _ { l }$

Question

Suppose k, l, and A grow at constant rates given by $\bar { g } _ { k }$ $\bar { g } _ { y }$,
And $\bar { g } _ { A }$`
What is the growth rate of y if $y = A k ^ { a } l ^ { 1 - a } , a > 0 ?$
A) $g _ { y } = \bar { g } _ { A } + a \left( \bar { g } _ { k } + \bar { g } _ { t } \right)$
B) $g _ { y } = \bar { g } _ { A } + a \bar { g } _ { k } + ( 1 - a ) \bar { g } _ { l }$
C) $g _ { y } = a \bar { g } _ { A } + a \bar { g } _ { k } + a \bar { g } _ { l }$
D) $g _ { y } = \bar { g } _ { A } + \bar { g } _ { l } ^ { a } + \bar { g } _ { l } ^ { ( 1 - a ) }$
E) $g _ { y } = \bar { g } _ { A } \times a \bar { g } _ { k } \times ( 1 - a ) \bar { g } _ { l }$

Quizplus · Accepted Answer

The growth rate of y is the sum of the growth rates of its components, weighted by their respective elasticities: $\bar { g } _ { A }$ for A, $a \bar { g } _ { k }$ for k, and $(1 - a) \bar { g } _ { l }$ for l.

Suppose K, L, and a Grow at Constant Rates Given gˉk\bar { g } _ { k }gˉ​k​

Suppose K, L, and a Grow at Constant Rates Given $\bar { g } _ { k }$