Perturbation theory in a pure exchange non-equilibrium economy

TL;DR

This paper introduces a formalism using mean field theory to analyze linear perturbations in a pure exchange economy, revealing that wealth distribution depends only on initial conditions if preferences are static and homogeneous.

Contribution

It develops a novel perturbation theory framework for non-equilibrium economies, showing the independence of wealth distribution from interaction networks under certain conditions.

Findings

Wealth distribution is determined solely by initial conditions.

Network structure influences relaxation time but not final wealth distribution.

Static, homogeneous preferences lead to network-independent equilibrium outcomes.

Abstract

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the non-equilibrium theory. In particular, it is completely determined in terms of the initial conditions, and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.