Distributions of money in model markets of economy

TL;DR

This paper investigates how different transaction rules affect money distribution in simple economic models, revealing transitions from Gibbs to power-law and eventual concentration of wealth.

Contribution

It introduces a new investment-based model and analyzes the resulting money distributions, including power-law behavior and long-term wealth concentration.

Findings

Money distribution follows Gibbs law under random sharing.

Investment model yields power-law distribution with exponent near one.

Long-term dynamics lead to wealth condensation among few agents.

Abstract

We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing but locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-periods, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.