Consider the CES production function $Q = \left[ a L ^ { \frac { \sigma - 1 } { \sigma } } + b K ^ { \frac { \sigma - 1 } { \sigma } } \right] ^ { \frac { \sigma} { \sigma - 1 } }$

. This production function exhibits
A) decreasing returns to scale.
B) constant returns to scale.
C) increasing returns to scale.
D) either decreasing or constant returns to scale, but more information is needed to determine which one.

Question

Consider the CES production function $Q = \left[ a L ^ { \frac { \sigma - 1 } { \sigma } } + b K ^ { \frac { \sigma - 1 } { \sigma } } \right] ^ { \frac { \sigma} { \sigma - 1 } }$

. This production function exhibits
A) decreasing returns to scale.
B) constant returns to scale.
C) increasing returns to scale.
D) either decreasing or constant returns to scale, but more information is needed to determine which one.

Quizplus · Accepted Answer

The CES production function exhibits constant returns to scale because when inputs are increased proportionally, output also increases proportionally with no change in the returns to each factor of production. This can be shown by verifying that the function satisfies the condition of homogeneity of degree 1, i.e., if all inputs are multiplied by a constant factor, the output is multiplied by the same factor.

Consider the CES Production Function Q=[aLσ−1σ+bKσ−1σ]σσ−1Q = \left[ a L ^ { \frac { \sigma - 1 } { \sigma } } + b K ^ { \frac { \sigma - 1 } { \sigma } } \right] ^ { \frac { \sigma} { \sigma - 1 } }Q=[aLσσ−1​+bKσσ−1​]σ−1σ​

Consider the CES Production Function $Q = \left[ a L ^ { \frac { \sigma - 1 } { \sigma } } + b K ^ { \frac { \sigma - 1 } { \sigma } } \right] ^ { \frac { \sigma} { \sigma - 1 } }$