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An Afriat Theorem for the collective model of household consumption

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  • Cherchye, Laurens
  • De Rock, Bram
  • Vermeulen, Frederic

Abstract

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 3 (May)
Pages: 1142-1163

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:3:p:1142-1163

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Collective model Consumption Pareto efficiency Revealed preferences Afriat Theorem Collective Axiom of Revealed Preference;

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  3. Bram De Rock & Laurens Cherchye & Frederic Vermeulen, 2008. "Analyzing cost efficient production behavior under economies of scope: a nonparametric methodology," ULB Institutional Repository 2013/7536, ULB -- Universite Libre de Bruxelles.
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Citations

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Cited by:
  1. Laurens CHERCHYE & Bram DE ROCK & Arthur LEWBEL & Frederic VERMEULEN, 2012. "Sharing rule identification for general collective consumption models," Center for Economic Studies - Discussion papers ces12.05, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  2. Ennio Bilancini, 2011. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Journal of Economics, Springer, vol. 102(3), pages 275-286, April.
  3. Per Hjertstrand & James Swofford, 2012. "Revealed preference tests for consistency with weakly separable indirect utility," Theory and Decision, Springer, vol. 72(2), pages 245-256, February.
  4. Ekeland, Ivar & Galichon, Alfred, 2012. "The housing problem and revealed preference theory: duality and an application," Economics Papers from University Paris Dauphine 123456789/10574, Paris Dauphine University.
  5. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2013. "Private versus public consumption within groups: testing the nature of goods from aggregate data," Economic Theory, Springer, vol. 54(3), pages 485-500, November.
  6. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for deciding collectively rational consumption behavior," ULB Institutional Repository 2013/131710, ULB -- Universite Libre de Bruxelles.
  7. Ennio Bilancini, 2010. "On the Rationalizability of Observed Consumers Choise when Prefeerences else," Department of Economics 0636, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".

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