The Cobb–Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities

By defining the Variable Output Elasticities Cobb–Douglas function, this article shows that a large class of production functions can be written as a Cobb–Douglas function with non-constant output elasticity. Compared to standard flexible functions such as the Translog function, this framework has several advantages. [1] It does not require the use of a second order approximation. [2] This greatly facilitates the deduction of linear input demands function without the need of involving the duality theorem. [3] It allows for a tractable generalization of the CES function to the case where the elasticity of substitution between each pair of inputs is not necessarily the same. [4] This provides a more general and more flexible framework compared to the traditional nested CES approach while facilitating the analyze of the substitution properties of nested CES functions. The case of substitutions between energy, capital and labor is provided.