Identities for Homogeneous Utility Functions

22 Pages Posted: 9 Nov 2010

See all articles by Miguel Andrés Espinosa

Miguel Andrés Espinosa

Universidad de los Andes, Colombia - Department of Economics

Juan David Prada Sarmiento

Central Bank of Colombia

Date Written: September 2, 2010

Abstract

Using a homogeneous and continuous utility function that represents a household's preferences, this paper proves explicit identities between most of the different objects that arise from the utility maximization and the expenditure minimization problems. The paper also outlines the homogeneity properties of each object. Finally, we show explicit algebraic ways to go from the indirect utility function to the expenditure function and from the Marshallian demand to the Hicksian demand and vice versa, without the need of any other function, thus simplifying the integrability problem avoiding the use of differential equations.

Keywords: Identities, Homogeneous Utility Functions and Household Theory

JEL Classification: D10, D11

Suggested Citation

Espinosa, Miguel Andrés and Prada Sarmiento, Juan David, Identities for Homogeneous Utility Functions (September 2, 2010). Documento CEDE No. 2010-26, Available at SSRN: https://ssrn.com/abstract=1705480 or http://dx.doi.org/10.2139/ssrn.1705480

Miguel Andrés Espinosa (Contact Author)

Universidad de los Andes, Colombia - Department of Economics ( email )

Carrera 1a No. 18A-10
Santafe de Bogota, AA4976
Colombia

Juan David Prada Sarmiento

Central Bank of Colombia ( email )

Carrera 7 #14-78
Bogota
Colombia

HOME PAGE: http://www.banrep.gov.co

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