The Economy's Potential: Duality and Equilibrium

TL;DR

This paper introduces the concept of the economy's potential as a duality measure between social welfare and utility, providing new insights into Walrasian equilibria, their existence, and welfare implications.

Contribution

It presents a novel duality framework linking social welfare and utility, offering a new perspective on equilibrium conditions and price interpretation in economics.

Findings

Walrasian equilibria correspond to roots of the potential function

Prices at equilibrium minimize weighted indirect utility

The potential framework clarifies welfare theorems and equilibrium existence

Abstract

I introduce a concave function of allocations and prices -- the economy's potential -- which measures the difference between utilitarian social welfare and its dual. I show that Walrasian equilibria correspond to roots of the potential: allocations maximize weighted utility and prices minimize weighted indirect utility. Walrasian prices are "utility clearing" in the sense that the utilities consumers expect at Walrasian prices are just feasible. I discuss the implications of this simple duality for equilibrium existence, the welfare theorems, and the interpretation of Walrasian prices.