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

question 15

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.

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Definitions:

Underapplied Manufacturing Overhead

A scenario in which the assigned manufacturing overhead expenses fall short of the real overhead costs experienced.

Overapplied Manufacturing Overhead

Refers to a situation where the estimated manufacturing overhead cost allocated to products is more than the actual overhead costs incurred.

Work in Process Inventory

The value of materials and products that are partially completed in the manufacturing process.

Overapplied Manufacturing Overhead

A scenario in which the assigned costs for manufacturing overhead are greater than the overhead expenses actually encountered.