The Existence of Equilibrium Flows

TL;DR

This paper establishes conditions for the existence of equilibrium prices in a broad class of equilibrium flow problems, generalizing classical theorems and unifying various economic models.

Contribution

It generalizes Hall's theorem to provide existence conditions for equilibrium prices in equilibrium flow problems, encompassing multiple economic models.

Findings

Established existence conditions for equilibrium prices.

Unified several economic models under a common framework.

Generalized Hall's theorem to broader settings.

Abstract

Galichon, Samuelson and Vernet (2022) introduced a class of problems, equilibrium flow problems, that nests several classical economic models such as bipartite matching models, minimum-cost flow problems and hedonic pricing models. We establish conditions for the existence of equilibrium prices in the equilibrium flow problem, in the process generalizing Hall's theorem.