A Constructive Proof of the Existence of a Utility in Revealed Preference Theory
Abstract: 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.
Keywords: Problem of revealed preferences, pseudo-mononicity, variational limits
Category 1: Applications -- OR and Management Sciences (Finance and Economics )
Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )
Category 3: Combinatorial Optimization (Approximation Algorithms )
Citation: RMIT University, SMGS, GPO Box2476V, Melbourne, Victoria, 3001. Date: 13/01/2012.
Entry Submitted: 02/10/2012
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