The Cobb-Douglas function as a flexible function:Analysing the sustitution between capital, labor and energy

摘要

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