An Afriat Theorem for the Collective Model of Household Consumption

CentER Discussion Paper Series No. 2008-72

31 Pages Posted: 9 Sep 2008

See all articles by L. Cherchye

L. Cherchye

KU Leuven; Erasmus Research Institute of Management (ERIM)

Bram De Rock

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES)

Frederic Vermeulen

Tilburg University - CentER; IZA Institute of Labor Economics

Multiple version iconThere are 2 versions of this paper

Date Written: September 3, 2008

Abstract

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a 'collective' version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

Keywords: Collective model, consumption, Pareto efficiency, revealed preferences, Afriat theorem, Collective Axiom of Revealed Preferences

JEL Classification: D11, D12, D13, C14

Suggested Citation

Cherchye, Laurens and De Rock, Bram and Vermeulen, Frederic, An Afriat Theorem for the Collective Model of Household Consumption (September 3, 2008). CentER Discussion Paper Series No. 2008-72, Available at SSRN: https://ssrn.com/abstract=1264971 or http://dx.doi.org/10.2139/ssrn.1264971

Laurens Cherchye (Contact Author)

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Bram De Rock

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Av. F. D. Roosevelt, 50
CP 114
Brussels, B-1050
Belgium

Frederic Vermeulen

Tilburg University - CentER ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands
+31 13 466 3196 (Phone)

HOME PAGE: http://center.uvt.nl/staff/vermeulen/

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

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