Power Law Distribution of Wealth in a Money-Based Model

TL;DR

This paper introduces a money-based model for wealth distribution that captures the power law distribution across a wide parameter range, extending previous models by providing exact calculations of the Zipf exponent.

Contribution

It presents a novel wealth distribution model focusing on capital movements, extending the EZ model, with exact calculation of the Zipf exponent over a broad parameter range.

Findings

The model reproduces the power law distribution of wealth.

The Zipf exponent depends nontrivially on model parameters.

Exact calculation of the Zipf exponent is achieved.

Abstract

A money-based model for the power law distribution (PLD) of wealth in an economically interacting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro behaviors of individuals. It is proposed as an extension of the Equiluz and Zimmermann's (EZ) model for crowding and information transmission in financial markets. Still, we must emphasize that in EZ model the PLD without exponential correction is obtained only for a particular parameter, while our pattern will give it within a wide range. The Zipf exponent depends on the parameters in a nontrivial way and is exactly calculated in this paper.