Question

Assume that the aggregate production of an economy is Yt= √Kt Lt , where Kt+1 =( 1-d) Kt+ It, St= sYt and Lt= L( i.e., the notation and meanings is to correspond the setting for the allow model with constant population. Then the savings rate s that maximizes the steady rate of consumption equals ?

Answer 1

$ct=(1-s)\times Y t$

$s=\frac{St}{Yt}$

$Yt=\sqrt{Kt}\times Lt$

$Kt + 1 = (1-d)\times Kt + It$

$Kt = (1-d)\times Kt+It-1$

Lt = L

$Yt=\sqrt{((1-d) Kt + It-1)}\times L$

$ct=(1-\frac{St}{Yt})\times Yt=Yt-St=\sqrt{(1-d) Kt + It-1)}\times L-St$