A production function is given as below

$Y=K^{}{L}^{1-}$

where Y is output, K is capital and L is effective worker. Suppose $$ is $0\mathrm{.}6,$ growth rate of population $(n)$ is $1\%,$ depreciation rate of capital $()$ is $2\%$ and growth rate of effective worker $(g)$ is $4\%.$

$($a$)$ If saving rate $(s)$ is $30\%,$ find steady states for capital per effective worker $(k),$ output per effective worker $(y)$ and consumption per effective worker $(c)$ in term of parameters used in the model namely $,s,n,$ and $g.$

$[5$ marks$]$

$($b$)$ What is the golden rule value for $k?$

$[3$ marks$]$

$($c$)$ What is the level of saving rate in order to obtain a golden rule capital stock?

$[2$ marks$]$