Question# $3(3*5=15$ points$)$

Suppose that you have two different countries, $i=1ori=2,$ which are characterized $by$ the

Solow model. These countries are identical except for their saving rates. The central equation

$of$ the Solow model $is$:

$K_{i,t+1}=s_{i}A{K}_{i,t}^{}+(1-)K_{i,t},i=1,2$

$K_{i,t}is$ capital $in$ country $i.$ The countries have the same $A,,$ and $.$ They only differ $in$

their saving rates. Suppose that $A=1,=0\mathrm{.}33,$ and $=0\mathrm{.}1.$ Suppose that the saving rate

$in$ country $1is{s}_i=0\mathrm{.}2.$ Suppose that both economies have converged $to$ their steady states.

Suppose that steady state output $in$ country $1is$ twice $as$ big $asin$ country $2,i.e.\frac{Y_1^{*}}{Y_2^{*}}=2.$

$(a)$ What would the saving rate $in$ country $2$ have $tobe$ for this $tobe$ true?

$(b)$ Calculate the steady state values $ofRkin$ the classr $in$ the class