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

Quizplus · Accepted Answer

The CES production function exhibits constant returns to scale because if we scale up inputs by a factor k, then the output will also increase by a factor of k as the exponent of the function remains the same. Hence, the ratio of output to input remains constant, and we have constant returns to scale. In the CES production function, the exponent in the outermost bracket is equal to $\frac{\sigma}{\sigma-1}>1$. Therefore, the function exhibits constant returns to scale.

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