Forges, Françoise and Iehlé, Vincent (2012): Essential Data, Budget Sets and Rationalization.

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Abstract
According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An ”essential experiment” consists of observed consumption bundles (x1,xn) and a feasibility matrix α. Starting with a standard experiment, in which the economist has speciﬁc budget sets in mind, we show that the necessary and suﬃcient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full speciﬁcation of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment (x1,...,xn;α), we show that the cyclical consistency of α, together with a further consistency condition involving both (x1,...,xn) and α, guarantees that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with (x1,...,xn;α). The conditions are also trivially necessary.
Item Type:  MPRA Paper 

Original Title:  Essential Data, Budget Sets and Rationalization 
Language:  English 
Keywords:  Afriat’s theorem, budget sets, cyclical consistency, rational choice, revealed preference 
Subjects:  D  Microeconomics > D1  Household Behavior and Family Economics > D11  Consumer Economics: Theory C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology; Computer Programs > C81  Methodology for Collecting, Estimating, and Organizing Microeconomic Data 
Item ID:  36519 
Depositing User:  Vincent Iehlé 
Date Deposited:  08. Feb 2012 16:16 
Last Modified:  12. Feb 2013 04:07 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/36519 