Essential Data, Budget Sets and Rationalization

Francoise Forges and Vincent Iehlé

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Afriat’s theorem; budget sets; cyclical consistency; rational choice; revealed preference (search for similar items in EconPapers)
JEL-codes: C81 D11 (search for similar items in EconPapers)
Date: 2012-02-07
New Economics Papers: this item is included in nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/36519/1/MPRA_paper_36519.pdf original version (application/pdf)

Related works:
Journal Article: Essential data, budget sets and rationalization (2013)
Working Paper: Essential Data, Budget Sets and Rationalization (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:36519

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().