An Axiom for Concavifiable Preferences in View of Alt's Theory

TL;DR

This paper establishes necessary and sufficient conditions for representing Alt's preference system with continuous, concave, and differentiable utility functions, extending classical economic laws with formal mathematical criteria.

Contribution

It introduces a new axiom characterizing concavifiable preferences within Alt's framework, linking economic intuition with mathematical representation.

Findings

Characterizes when Alt's preferences have a continuous utility representation.

Provides conditions for the utility to be concave, extending Gossen's first law.

Determines when the utility function is continuously differentiable.

Abstract

We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can be seen as an extension of Gossen's first law, and thus has an economic interpretation. Together with the above results, we provide a necessary and sufficient condition for Alt's utility to be continuously differentiable.