https://hal-sciencespo.archives-ouvertes.fr/hal-03582829Reynés, FrédéricFrédéricReynésOFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences PoThe Cobb-Douglas function as a flexible functionThe Cobb-Douglas function as a flexible functionHAL CCSD2017Flexible production functionsCobb-Douglas functionCES functionSubstitution capital-labor-energy[SHS.ECO] Humanities and Social Sciences/Economics and FinanceSciences Po Institutional Repository, Spire2022-02-21 14:32:592022-03-25 03:58:332022-03-24 14:26:07enPreprints, Working Papers, ...https://hal-sciencespo.archives-ouvertes.fr/hal-03582829/documentapplication/pdf1By defining the Variable Output Elasticities Cobb-Douglas function, this article shows that a large class of production functions can be written as 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 requires 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 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.