Concave Preferences Over Bundles and the First Fundamental Theorem of Welfare Economics
12 Pages Posted: 28 Aug 2015 Last revised: 19 Sep 2015
Date Written: September 8, 2015
Abstract
In this paper we are concerned with numerical representation of preferences over bundles. Specifically, we provide an axiomatic characterization of preferences that have a numerical representation that look similar to a concave function defined on a convex set. We call such preferences concave. We also show that the concept of a super-gradient is inherent to rational choice. We discuss additively separable preferences and their axiomatization due to Fishburn (1970) since they are an important example of concave preferences. Using the same methods that we use to prove earlier results we show that the first fundamental theorem of welfare economics holds for combinatorial assignment problems.
Keywords: preferences over bundles, concave, first fundamental theorem, welfare economics
JEL Classification: D00
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