Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities

Elizabeth Baldwin and Paul Klemperer

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We propose new techniques for understanding agents' valuations. Our classification 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" for indivisible goods. 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 (search for similar items in EconPapers)
JEL-codes: C62 D44 D50 D51 (search for similar items in EconPapers)
Pages: 68 pages
Date: 2016-10-09
New Economics Papers: this item is included in nep-mic
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Citations: View citations in EconPapers (3)

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http://eprints.lse.ac.uk/63198/ Open access version. (application/pdf)

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 (2019)
Working Paper: Understanding Preferences: “Demand Types”, and the Existence of Equilibrium with Indivisibilities (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:63198

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