 Afriat's Theorem and Samuelson's `Eternal Darkness'Matthew Polisson and Ludovic Renou No 16/09, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester 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. Keywords: Afriat's Theorem; concavity; revealed preference; utility maximization (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:lec:leecon:16/09 Ordering information: This working paper can be ordered from Access Statistics for this paper More papers in Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester School of Business, University of Leicester, University Road. Leicester. LE1 7RH. UK Provider-Homepage: https://le.ac.uk/school-of-business. Contact information at EDIRC. |
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