An Afriat theorem for the collective model of household consumption

L.J.H. Cherchye, B. de Rock, F.M.P. Vermeulen

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)1142-1163
JournalJournal of Economic Theory
Volume145
Issue number3
Publication statusPublished - 2010

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Collective model
Household consumption
Revealed preference
Concavity
Rationality
Consumption externalities
Household behavior
Utility function
Monotonicity
Individual preferences
Externalities
Intra-household allocation
Axiom
Rational behavior

Cite this

Cherchye, L.J.H. ; de Rock, B. ; Vermeulen, F.M.P. / An Afriat theorem for the collective model of household consumption. In: Journal of Economic Theory. 2010 ; Vol. 145, No. 3. pp. 1142-1163.
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Cherchye, LJH, de Rock, B & Vermeulen, FMP 2010, 'An Afriat theorem for the collective model of household consumption', Journal of Economic Theory, vol. 145, no. 3, pp. 1142-1163.

An Afriat theorem for the collective model of household consumption. / Cherchye, L.J.H.; de Rock, B.; Vermeulen, F.M.P.

In: Journal of Economic Theory, Vol. 145, No. 3, 2010, p. 1142-1163.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Cherchye, L.J.H.

AU - de Rock, B.

AU - Vermeulen, F.M.P.

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AB - 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.

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