Question $2$: Solow Model with Labor Efficiency $(30$ Marks$)$

As studied in class, the neoclassical aggregate production function is at the center of the Solow growth model. Suppose that an economy$$s aggregate production function is given by:

Y $=$ K$($EL$)1$

where E is the efficiency of labor.

Assume that economy is closed, has a zero population growth rate, n $=0,$ and zero rate of capital depreciation, $=0.$ The savings rate is s $=16\%,$ the rate of labour productivity, E$$ is $4\%,$ and $=1/3.$

$($A$)$i$)$

ii$)$Derive the marginal product of effective workers, MPEL $($i$.$e$.$ the derivative of Y with respect

of EL$).$

iii$)$Find the growth rates of MPK and MPEL, and interpret your answers.

$($B$)$Write an expression for the law of motion $($capital accumulation equation$)$ of capital per effective worker. I want to see every steps. We did this in class, this time I want you to do it $($to start, try without your notes, a good preparation for your Final Exam$).$