DP13586 Understanding Preferences: "Demand Types", and the Existence of Equilibrium with Indivisibilities

Author(s):	Elizabeth Baldwin, Paul Klemperer
Publication Date:	March 2019
Keyword(s):	Competitive Equilibrium, consumer theory, demand type, equilibrium existence, geometry, indivisible goods, Matching, product mix auction, product-mix auction, tropical geometry
JEL(s):	C62, D44, D50, D51
Programme Areas:	Industrial Organization
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=13586

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.