Abstract
This paper deals with the modeling of wealth distribution considering a society with non-constant population and non-conservative wealth trades. The modeling approach is based on the kinetic theory of active particles, where individuals are distinguished by a scalar variable (the activity) which expresses their social state. A qualitative analysis of the model focusing on asymptotic behaviors and measurement of inequality through the Gini coefficient is presented. Finally, some specific case-studies are proposed in order to carry out numerical experiments to validate our model, characterize societies and investigate emerging behaviors.
Highlights
Worldwide inequality constitutes a major and increasing global problem
The Organization for Economic Cooperation and Development (OECD) noted that within member countries, the richest 10% of the population earn more than nine times the income of the poorest 10%
In the first social dynamics models [14,15] γ was taken as a constant parameter, while [16] introduced a further development in which γ depends on the instantaneous distribution of active particles over the wealth classes
Summary
Worldwide inequality constitutes a major and increasing global problem. While booming stock markets, giant mergers and financial speculation provide huge rewards to a tiny minority, a great part of the world’s population does not benefit from economical systems of growth and development. The evolution of the probability distribution is obtained by a balance of particles within elementary volumes of the space of the microscopic states, where the dynamics of inflow and outflow of particles is related to interactions at the microscopic scale This approach has so far been applied to derive a variety of models of complex systems in life sciences, such as opinion formation [9,10], collective learning [11,12], and behavioral economy [13], among many others. In [27] an agent-based network model is presented in order to study interactions “hosts” and “guests”, identifying conditions under which cooperative or uncooperative societies arise In this present paper we consider a spatially homogeneous population divided into functional subsystems or social classes, characterized by their wealth.
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