Part $II.$ Problems

Consider $an$ economy where the production function $is$

$y=k^{\frac{1}{2}}$

where $yis$ output per effective worker and $kis$ capital per effective worker. The

depreciation rate $is=0\mathrm{.}04,$ the savings rate $iss=0\mathrm{.}2,$ the population growth

rate $isn=0\mathrm{.}03$ and technology growth rate $isg=0\mathrm{.}03.$

$a.$ Find the steady state level $of$ capital per effective worker $(k^{*})$ and the

steady state consumption per effective worker $(c^{*}).$

$b.$ Find the golden rule level $of$ capital per effective worker $(k_g^{*})$ and the

golden rule level $of$ consumption per effective worker $(c_g^{*}).$

$c.$ Find $s_g,$ that $is$ the level $of$ the savings rate that would lead the econ$-$

omy $to$ the golden rule steady state.

Consider $an$ economy where technology growth $isg=0,$ but population

growth $is$ positive and equal $ton.$ Use graphs $to$ illustrate how the steady state

capital and the golden rule capital change $in$ response $to$:

$a.an$ increase $in$ the depreciation rate

$b.$ a decrease $in$ population growth rate

Explain what governments can $doto$ reduce frictional unemployment.