Understanding Preferences: "Demand Types", and the Existence of Equilibrium with Indivisibilities

70 Pages Posted: 18 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: March 2019

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: Competitive Equilibrium, consumer theory, demand type, equilibrium existence, geometry, indivisible goods, Matching, product mix auction, product-mix auction, tropical geometry

JEL Classification: C62, D44, D50, D51

Suggested Citation

Baldwin, Elizabeth and Klemperer, Paul, Understanding Preferences: "Demand Types", and the Existence of Equilibrium with Indivisibilities (March 2019). CEPR Discussion Paper No. DP13586. Available at SSRN: https://ssrn.com/abstract=3354452

Elizabeth Baldwin (Contact Author)

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

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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