A production function is given as below

$=1$

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 $()$ 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 $,,,$ and $.$

$[5$ 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$]$