Kinetic exchange income distribution models with saving propensities: inequality indices and self-organized poverty level

Abstract

We report the numerical results for the steady-state income or wealth distribution [Formula: see text] and the resulting inequality measures (Gini [Formula: see text] and Kolkata [Formula: see text] indices) in the kinetic exchange models of market dynamics. We study the variations of [Formula: see text] and of the indices [Formula: see text] and [Formula: see text] with the saving propensity [Formula: see text] 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 behaviours. One, where each agent has the same value of [Formula: see text] (constant over time) and the other where [Formula: see text] for each agent can take two values (0 and 1), changing randomly over a fraction of time [Formula: see text] of choosing [Formula: see text]. We find that the inequality decreases with increasing savings ([Formula: see text]); inequality indices ([Formula: see text] and [Formula: see text]) decrease and SOPL increases with increasing [Formula: see text], indicating possible applications in economic policy making. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.