Given a production function $Y_t\frac{?}{b}=ar(A)\frac{K_t^{\frac{1}{3}}}{b}ar(L{)}^{\frac{2}{3}},$ if $\frac{?}{\text{b}\text{a}\text{r}}(A)=2\frac{,}{b}ar(L)=4\frac{,}{b}ar(s)=0\mathrm{.}2,$ and $\frac{?}{\text{b}\text{a}\text{r}}(d)=0\mathrm{.}05$ :

$($a$)$ Calculate the steady$-$state level of capital and output. Show your work.

$($b$)$ Does this production function exhibit constant returns to scale or does it exhibit diminishing marginal

returns? Explain, and define the difference between these two concepts.