Afriat's Theorem and Samuelson's 'Eternal Darkness'
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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.
Polisson , M & Renou , L 2016 , ' Afriat's Theorem and Samuelson's 'Eternal Darkness' ' Journal of Mathematical Economics , vol 65 , pp. 36-40 . DOI: 10.1016/j.jmateco.2016.05.003
Journal of Mathematical Economics
© 2016 Elsevier B.V. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jmateco.2016.05.003
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