Given a Production Function $Y _ { t } = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }$

Essay

Given a production function $Y _ { t } = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }$ , if $\bar { A } = 2 , \bar { L } = 4 , \bar { s } = 0.2$ , and $\bar { d } = 0.05$ :
(a) Calculate the steady-state level of capital and output.
(b) Does the above production function exhibit constant returns to scale, or does it exhibit diminishing marginal returns? Explain, and define the difference between these two concepts.