Optimization Online


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

A Eberhard(andy.eb***at***rmit.edu.au)
D Ralph(d.ralph***at***jbs.cam.ac.uk)
J-P Crouzeix(crouzeix***at***isima.fr)

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.

Download: [PDF]

Entry Submitted: 02/10/2012
Entry Accepted: 02/11/2012
Entry Last Modified: 02/10/2012

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society