Economic Segregation Under the Action of Trading Uncertainties

Chiara Bardelli,Giuseppe Toscani,Elena Ballante,Silvia Figini,Mattia Zanella

doi:10.3390/sym12091390

Abstract

We study the distribution of wealth in a market economy in which the trading propensity of the agents is uncertain. Our approach is based on kinetic models for collective phenomena, which, at variance with the classical kinetic theory of rarefied gases, has to face the lack of fundamental principles, which are replaced by empirical social forces of which we have at most statistical information. The proposed kinetic description allows recovering emergent wealth distribution profiles, which are described by the steady states of a Fokker–Planck-type equation with uncertain parameters. A statistical study of the stationary profiles of the Fokker–Planck equation then shows that the wealth distribution can develop a multimodal shape in the presence of observable highly stressful economic situations.

Highlights

The mathematical modeling of elementary interactions among agents leading to the correct description of the emerging wealth distribution in Western societies has attracted both applied mathematicians and physicists in the last few decades
A significant part of this research activity applied the methodology of statistical mechanics to build kinetic-type equations [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] able to reproduce at best the typical features of economies, including the formation of fat-tailed distributions observed by Pareto in capitalistic societies [19]
We studied in this paper the consequences of stressful situations in the wealth distribution profile by considering a random saving propensity in the form of a Beta distribution

Summary

Introduction

The mathematical modeling of elementary interactions among agents leading to the correct description of the emerging wealth distribution in Western societies has attracted both applied mathematicians and physicists in the last few decades. Besides the kinetic models able to produce, in agreement with the discoveries of the Italian economist Vilfredo Pareto, the fat-tailed behavior of the stationary profile [26,28], a class of Fokker–Planck-type equations has a distinguished role.

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Conclusion