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

Paul Klemperer and Elizabeth Baldwin

No 13586, CEPR Discussion Papers from C.E.P.R. Discussion Papers

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; Competitive equilibrium; Indivisible goods; Product mix auction; Product-mix auction; Demand type; Matching; Geometry; Tropical geometry (search for similar items in EconPapers)
JEL-codes: C62 D44 D50 D51 (search for similar items in EconPapers)
Date: 2019-03
New Economics Papers: this item is included in nep-des, nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (28)

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Related works:
Journal Article: Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities (2019)
Working Paper: Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities (2016)
Working Paper: Understanding Preferences: “Demand Types”, and the Existence of Equilibrium with Indivisibilities (2015)
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