The Cobb-Douglas function for a continuum model

Javier Humberto Ospina-Holguín ()

Revista Cuadernos de Economia, 2017, vol. 36, issue 70, 1-18

Abstract: This paper introduces two formal equivalent definitions of the Cobb-Douglas function for a continuum model based on a generalization of the Constant Elasticity of Substitution (CES) function for a continuum under not necessarily constant returns to scale and based on principles of product calculus. New properties are developed, and to illustrate the potential of using the product integral and its functional derivative, it is shown how the profit maximization problem of a single competitive firm using a continuum of factors of production can be solved in a manner that is completely analogous to the one used in the discrete case. ***** Este artículo introduce dos definiciones formales equivalentes de la función CobbDouglas para un modelo continuo basadas en una generalización de la función de elasticidad de sustitución constante (CES) para un continuo bajo rendimientos a escala no necesariamente constantes y con base en principios del cálculo de producto. Se desarrollan propiedades nuevas; y para ilustrar el potencial de usar la integral producto y su derivada funcional, se muestra cómo el problema de maximización de beneficios de una única empresa competitiva que usa un continuo de factores de producción se puede solucionar de una manera completamente análoga a la utilizada en el caso discreto.

Keywords: CES function; Cobb-Douglas function; continuum; product integral; functional derivative. (search for similar items in EconPapers)
JEL-codes: D11 D21 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:col:000093:015064

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