Template-type: ReDIF-Paper 1.0
Author-Name: Elizabeth Baldwin
Author-Workplace-Name: London School of Economics
Author-Email: e.c.baldwin@lse.ac.uk 
Author-Name: Paul Klemperer
Author-Workplace-Name: Nuffield College, Oxford University
Author-Email: paul.klemperer@economics.ox.ac.uk
Title: Understanding Preferences: “Demand Types”, and the Existence of Equilibrium with Indivisibilities

Abstract: We propose new techniques for understanding agents’ valuations. Our classification
into “demand types”, incorporates existing definitions (such as substitutes, complements,
“strong substitutes”, etc.), and permits additional distinctions. We obtain
an easy-to-check necessary and sufficient condition for the existence of a competitive
equilibrium for indivisible goods. Our condition generalises many existing results, and
provides new insights: contrary to much popular belief, there are more classes of purelycomplements
preferences than classes of purely-substitutes preferences for which competitive
equilibrium always exists. Our techniques are also powerful when equilibrium
cannot be guaranteed from the “demand type”. For a specific set of individual valuations,
we often can check for equilibrium existence by simply counting the number of
intersection points of the geometric objects we study! Our methods also have applications
to matching, and to the Product-Mix Auction, introduced by the Bank of England
in response to the financial crisis.

Classification-JEL: C62; D50; D51; D44; 
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
Length: 71 pages
Creation-Date: 2015-08-15
Number: 2015-W10
File-URL: https://www.nuffield.ox.ac.uk/economics/papers/2015/demandtypes.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:1510