A Constructive Proof of the Existence of a Utility in Revealed Preference Theory

  • J-P Crouzeix
  • Andrew C. Eberhard
  • Daniel Ralph
    • Categories Approximation Algorithms, Finance and Economics, Generalized Convexity/Monoticity Tags , , Short URL: https://optimization-online.org/?p=11915

    Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which are closely related to a number of established axioms in preference theory. The proof establishes the existence of a limit of a sequences of indirect utilities that rationalise finite data sets, where the sample size increases to infinity. This limiting utility provides a rationalisation of the demand relation. Up to a rescaling this limiting indirect utility is unique and continuous on a set of full measure.

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    RMIT University, SMGS, GPO Box2476V, Melbourne, Victoria, 3001. Date: 13/01/2012.

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