Kinetic Exchange Income Distribution Models with Saving Propensities: Inequality Indices and Self-Organised Poverty Level

TL;DR

This paper investigates how different saving behaviors and trade dynamics in kinetic exchange models influence income distribution and inequality, revealing that higher savings reduce inequality and promote a self-organized poverty level.

Contribution

It introduces a detailed analysis of inequality measures in kinetic exchange models with varying saving propensities and trade rules, highlighting the emergence of a self-organized poverty level.

Findings

Inequality decreases as saving propensity increases.

Higher savings lead to increased self-organized poverty levels.

Different trade dynamics significantly affect income distribution.

Abstract

We report the numerical results for the steady state income or wealth distribution $P(m)$ and the resulting inequality measures (Gini $g$ and Kolkata $k$ indices) in the kinetic exchange models of market dynamics. We study the variations of $P(m)$ and of the indices $g$ and $k$ with the saving propensity $\lambda$ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviors. One, where each agent has the same value of $\lambda$ (constant over time) and the other where $\lambda$ for each agent can take two values (0 and 1), changing randomly over a fraction of time $\rho(<1)$ of choosing $\lambda = 1$. We find that the inequality decreases with increasing savings ($\lambda$); inequality indices ($g$ and $k$) decrease and SOPL increases with increasing $\lambda$, indicating possible applications in economic policy making.