Understanding Preferences: 'Demand Types', and The Existence of Equilibrium with Indivisibilities
68 Pages Posted: 4 Sep 2015 Last revised: 15 Mar 2019
Date Written: October 2, 2018
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: Suggested Citation