### Abstract

Original language | English |
---|---|

Pages (from-to) | 1142-1163 |

Journal | Journal of Economic Theory |

Volume | 145 |

Issue number | 3 |

Publication status | Published - 2010 |

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### Cite this

*Journal of Economic Theory*,

*145*(3), 1142-1163.

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*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.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - An Afriat theorem for the collective model of household consumption

AU - Cherchye, L.J.H.

AU - de Rock, B.

AU - Vermeulen, F.M.P.

N1 - Appeared earlier as CentER Discussion Paper 2008-72

PY - 2010

Y1 - 2010

N2 - 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.

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.

M3 - Article

VL - 145

SP - 1142

EP - 1163

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 3

ER -