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Title: Afriat's Theorem and Samuelson's 'Eternal Darkness'
Authors: Polisson, Matthew
Renou, Ludovic
First Published: 20-May-2016
Publisher: Elsevier
Citation: Journal of Mathematical Economics, 2016, 65, pp. 36-40
Abstract: Suppose that we have access to a finite set of expenditure data drawn from an individual consumer, i.e., how much of each good has been purchased and at what prices. Afriat (1967) was the first to establish necessary and sufficient conditions on such a data set for rationalizability by utility maximization. In this note, we provide a new and simple proof of Afriat’s Theorem, the explicit steps of which help to more deeply understand the driving force behind one of the more curious features of the result itself, namely that a concave rationalization is without loss of generality in a classical finite data setting. Our proof stresses the importance of the non-uniqueness of a utility representation along with the finiteness of the data set in ensuring the existence of a concave utility function that rationalizes the data.
DOI Link: 10.1016/j.jmateco.2016.05.003
ISSN: 0304-4068
Embargo on file until: 20-May-2019
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2016 Elsevier B.V. After embargo this will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: The file associated with this record is under a 36-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Economics

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