Ideal Gas-Like Distributions in Economics: Effects of Saving Propensity

TL;DR

This paper models economic transactions using an ideal gas analogy, incorporating saving behavior to explain different wealth distribution patterns, including Gibbs-like and Pareto-like distributions, aligning with real-world observations.

Contribution

Introduces a saving propensity parameter into ideal-gas-like market models, revealing how it influences wealth distribution shapes and aligns with empirical data.

Findings

Gibbs-like distribution for zero saving propensity

Non-vanishing most-probable wealth for non-zero savings

Pareto-like distribution when savings are widely distributed

Abstract

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $\lambda$ of agents, such that each agent saves a fraction $\lambda$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $\lambda=0$, has got a non-vanishing most-probable value for $\lambda \ne 0$ and Pareto-like when $\lambda$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.