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

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. One, where the exchange occurs between randomly chosen pairs of agents, other where one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest (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) and changes randomly maintaining a fraction of time $\rho(<1)$ of choosing $\lambda = 1$. We also study the nature of distributions $P(m)$ and values of the inequality indices ($g$ and $k$) and the SOPL as $\lambda$ and $\rho$ varies. We find that the inequality decreases with increasing savings ($\lambda$).