Working Paper: CEPR ID: DP13586
Authors: Elizabeth Baldwin; Paul Klemperer
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; Demand Type; Matching; Geometry; Tropical Geometry
JEL Codes: C62; D50; D51; D44
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| demand types (C69) | competitive equilibrium (D41) |
| unimodular set of vectors (C29) | competitive equilibrium (D41) |
| purely complements (D10) | competitive equilibrium (D41) |
| intersection count theorem (C62) | equilibrium existence (C62) |
| classification of demand types (R22) | equilibrium existence (C62) |