Understanding Preferences: 'Demand Types', and The Existence of Equilibrium with Indivisibilities

68 Pages Posted: 4 Sep 2015 Last revised: 15 Mar 2019

See all articles by Elizabeth Baldwin

Elizabeth Baldwin

University of Oxford - Department of Economics; Hertford College, Oxford

Paul Klemperer

University of Oxford - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: October 2, 2018

Abstract

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into "Demand Types" incorporates existing definitions (substitutes, complements, "strong substitutes", etc.) and permits new ones. Our Unimodularity Theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a "demand type". Contrary to popular belief, equilibrium is guaranteed for more classes of purely-complements, than of purely-substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition-formation, and the "Product-Mix Auction" introduced by the Bank of England in response to the financial crisis.

Keywords: consumer theory; equilibrium existence; general equilibrium; competitive equilibrium; duality; indivisible goods; geometry; tropical geometry; convex geometry; auction; product mix auction; product-mix auction; substitute; complement; demand type; matching

JEL Classification: C62, D50, D51, D44

Suggested Citation

Baldwin, Elizabeth and Klemperer, Paul, Understanding Preferences: 'Demand Types', and The Existence of Equilibrium with Indivisibilities (October 2, 2018). Available at SSRN: https://ssrn.com/abstract=2643086 or http://dx.doi.org/10.2139/ssrn.2643086

Elizabeth Baldwin

University of Oxford - Department of Economics ( email )

10 Manor Rd
Oxford, OX1 3UQ
United Kingdom

Hertford College, Oxford ( email )

Hertford College
Catte Street
Oxford, OX1 3BW
United Kingdom

HOME PAGE: http://elizabeth-baldwin.me.uk/

Paul Klemperer (Contact Author)

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom
+44 1865 278 588 (Phone)
+44 1865 278 557 (Fax)

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

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