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.