Differentiability of preferences without derivatives

Michael Richter (), Ariel Rubinstein () and Áron Tóbiás ()
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Michael Richter: Department of Economics, Baruch College, CUNY and Department of Economics, Royal Holloway, University of London
Ariel Rubinstein: School of Economics, Tel Aviv University and Department of Economics, New York University
Áron Tóbiás: Maxwell School of Citizenship and Public Affairs, Syracuse University

Theoretical Economics, Forthcoming

Abstract: A new definition of differentiable convex preferences is proposed for spaces that require no algebraic structure. Given a set of primitive orderings Λ, preferences are Λ-convex-differentiable if, at each non-maximal alternative, there is a unique ordering in Λ whose advancement is necessary for preference improvement and whose reduction is sufficient for preference deterioration. As an application, it is shown that differentiability of preferences guarantees the second welfare theorem in a two-agent exchange economy with a finite set of distinct indivisible goods.

Keywords: Preferences; differentiable preferences; convex preferences (search for similar items in EconPapers)
JEL-codes: C6 D1 D6 (search for similar items in EconPapers)
Date: 2026-09-10
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