The statistical distribution of money and the rate of money transference

TL;DR

This paper explores the statistical distribution of money among agents, showing it follows a Gamma function similar to energy distribution in molecules, and reaches equilibrium through pairwise transactions.

Contribution

It demonstrates that money distribution in economies can be modeled using statistical mechanics principles, specifically the Gamma distribution, independent of initial conditions.

Findings

Money distribution fits a Gamma function across countries.

Equilibrium is achieved through pairwise transactions.

Distribution is independent of initial conditions and transaction details.

Abstract

The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma function, confirming the validity of the statistical distribution at equilibrium. The equilibrium state is reached through pair wise money transference processes, independently of the shape of the initial distribution and also of the detailed nature of the money transactions between the economic agents.