Minimal entropy and uniqueness of price equilibria in a pure exchange economy

TL;DR

This paper explores how minimal entropy relates to the uniqueness of price equilibria in pure exchange economies, proposing a conjecture and validating it under specific conditions.

Contribution

It introduces a novel connection between Shannon's differential entropy and equilibrium uniqueness, extending the understanding in economic theory.

Findings

Entropy is minimal if and only if the price is unique, under certain conditions.

The conjecture is validated for economies with two consumers and any number of goods.

Partial validation for economies with two goods and multiple consumers.

Abstract

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.