The Role of Saving Parameter on Chaotic Dynamics of Distribution of Money, Wealth, and Income

Abstract

In closed economic systems, there exist dual behaviors in the distribution of money, wealth, and income that lack economic justification. Analyzing the fundamental dynamics of these distributions proves useful when studying economic crises. The main purpose was to identify economic distributions exhibiting chaotic gas-like dynamics while incorporating the saving parameter. Computer simulation was employed to reproduce the data representing economic transactions between the participating agents in each transaction. The saving parameter was introduced into the conservation equations of money within the kinetic theory of gases, and chaotic dynamics were utilized to determine the selection of agents and the amounts of money exchange between them. In the simulated distributions, specifically in scenario II, where agent selection was chaotic, and the money exchange was random, a transition from an exponential distribution to a power-law distribution was observed across various saving propensities. Our findings demonstrate that incorporating chaotic dynamics alongside the saving parameter is a suitable approach for modeling economic systems, akin to stochastic dynamics.