A geometric approach to the transfer problem for a finite number of traders

TL;DR

This paper provides a geometric characterization of the transfer problem in finite-trader exchange economies, linking it to equilibrium stability and extending previous two-trader results.

Contribution

It introduces a geometric method to characterize the transfer problem for any finite number of traders, generalizing earlier two-trader findings.

Findings

Transfer problem occurs iff the equilibrium index is -1

Regular equilibrium implies transfer problem if index is -1

Stable Walras tatonnement equilibria do not have the transfer problem

Abstract

We present a complete characterization of the classical transfer problem for an exchange economy with an arbitrary finite number of traders. Our method is geometric, using an equilibrium manifold developed by Debreu, Mas-Colell, and Balasko. We show that for a regular equilibrium the transfer problem arises if and only if the index at the equilibrium is $-1$. This implies that the transfer problem does not happen if the equilibrium is Walras tatonnement stable. Our result generalizes Balasko's analogous result for an exchange economy with two traders.