Distribution Of Wealth In A Network Model Of The Economy

TL;DR

This paper demonstrates that wealth distribution in a networked economic model follows a generalized inverse gamma distribution, simplifying to an inverse gamma distribution in the mean-field limit, supported by analytical and numerical evidence.

Contribution

It introduces a generalized inverse gamma distribution to describe wealth in the Bouchaud-Mézard network model, extending previous mean-field results.

Findings

Wealth distribution follows a three-parameter generalized inverse gamma distribution.

In the mean-field limit, it simplifies to an inverse gamma distribution.

Analytical and numerical methods confirm the distribution's applicability.

Abstract

We show, analytically and numerically, that wealth distribution in the Bouchaud-M\'ezard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.