Which of the following represents a short-run cubic production function?
A) $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$
B) $Q = 3 A L ^ { 2 } + 2 B L \left( \text { where } A = a \bar { K } ^ { 3 } , B = b \bar { K } ^ { 2 } \right)$
C) $Q = A L ^ { 3 } + B L ^ { 2 } \left( \text { where } A = a \bar { K } ^ { 3 } , B = b \bar { K } ^ { 2 } \right)$
D) $Q = A L ^ { 2 } + B L \left( \text { where } A = a \overline { K ^ { - 3 } } , B = b \bar { K } ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

A short-run production function is one where at least one input is fixed in the short run. A cubic production function implies that the highest degree of either input is 3. Option C meets both criteria as it has a fixed input, 'L', and has the highest degree of an input at 3. The other options have either a fixed input with a lower maximum degree or have degrees higher than 3, making them not cubic in nature.

Which of the Following Represents a Short-Run Cubic Production Function Q=aK3L3+bK−2L2Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }Q=aK3L3+bK−2L2

Which of the Following Represents a Short-Run Cubic Production Function $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$