Afriat's Theorem and Samuelson's 'Eternal Darkness'

Matthew Polisson*, Ludovic Renou

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)36-40
Number of pages5
JournalJournal of mathematical economics
Volume65
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Afriat's Theorem
  • Concavity
  • Revealed preference
  • Utility maximization

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