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Essential Data, Budget Sets and Rationalization

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  • Forges, Françoise
  • Iehlé, Vincent

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36519.

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Date of creation: 07 Feb 2012
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Handle: RePEc:pra:mprapa:36519

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Keywords: Afriat’s theorem; budget sets; cyclical consistency; rational choice; revealed preference;

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  1. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1779-86, November.
  2. Teo Chung Piaw & Rakesh V. Vohra, 2003. "Afrait's Theorem and Negative Cycles," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1377, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Donald J. Brown & Caterina Calsamiglia, 2005. "The Nonparametric Approach to Applied Welfare Analysis," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1507, Cowles Foundation for Research in Economics, Yale University.
  4. M.J. Todd & A. Fostel & H.E. Scarf, 2004. "Two New Proofs of Afriat's Theorem," Econometric Society 2004 North American Summer Meetings, Econometric Society 632, Econometric Society.
  5. Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers, University of Brescia, Department of Economics ubs0609, University of Brescia, Department of Economics.
  6. Christopher Chambers & Federico Echenique, 2009. "Profit maximization and supermodular technology," Economic Theory, Springer, Springer, vol. 40(2), pages 173-183, August.
  7. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 945-73, July.
  8. Yatchew, Adonis John, 1985. "A note on non-parametric tests of consumer behaviour," Economics Letters, Elsevier, Elsevier, vol. 18(1), pages 45-48.
  9. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  10. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer, Springer, vol. 45(1), pages 349-378, October.
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Cited by:
  1. Francoise Forges & Vincent Iehlé, 2013. "Afriat's Theorem for Indivisible Goods," CESifo Working Paper Series 4498, CESifo Group Munich.
  2. Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer, Springer, vol. 54(3), pages 463-484, November.
  3. Alfred Galichon & John Quah, 2013. "Symposium on revealed preference analysis," Economic Theory, Springer, Springer, vol. 54(3), pages 419-423, November.

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