Abstract
We examine by Monte-Carlo simulations the behavior of a kinetic exchange-trading model for various initial distributions of money in the system of agents. Our goal is to analyze the characteristics of the Pareto laws for the long-time money distribution, in both closed and open systems. We consider three different initial distributions for these two situations. We first briefly summarize the concepts and results of some agent-based money-exchange models. Then, via employing the Monte-Carlo computer simulations, for both types of systems we obtain the long-time money distributions for the initially homogeneous or constant, for positive random, and finally, for both positive and negative random distributions of money among the agents. We conclude that the Pareto laws and their exponents remained nearly the same in all these situations showing little sensitivity to the initial conditions imposed.
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Notes
Inequality is likely to be growing in recent decades due to, i.a., formation of huge corporate conglomerates, overall globalization of economies, rosy tax-evading schemes for ”big global players”, as well as due to other tricks invented by capitalistic magnates via, e.g., their political involvements and lobbying of appropriately ”designed” laws. A 80/20 Pareto-type principle of wealth splitting and the steepness of the firm-size distribution [27, 28] is likely to be even more drastic in modern times. Known as the Matthew effect from biblical times, a pronounced inequality per se is a rather negative factor for a long-term economic development and sustainable growth [29, 30]: it can namely destabilize the ”foundation” of the wealth-distribution pyramid and eradicate the middle-class, the core of many established capitalistic systems.
In a real economic system, the total amount of money is not preserved: a country can lose some of its wealth as a consequence of e.g. inflation, unexpected debt [to cover the costs of war, for example], a big natural catastrophe [drought, etc.], etc. Such a model could, thus, explain an effective decline of the wealth per capita.
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Acknowledgements
We thank two careful referees for their insightful comments which enabled us to improve the manuscript. E. A. is grateful to Humboldt Universität zu Berlin for support and to Potsdam Universität for hospitality. This work was partially supported by DAAD (Project 57588362). R. M. acknowledges financial support by the German Science Foundation (DFG Grant ME 1535/12-1).
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EA performed Monte-Carlo Simulations and analyzed the data; EA, AGC, RM and IMS discussed the results and wrote the manuscript.
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Aydiner, E., Cherstvy, A.G., Metzler, R. et al. Universal Pareto laws in agent-based exchange models: debt and varying initial-money distributions. Eur. Phys. J. B 96, 123 (2023). https://doi.org/10.1140/epjb/s10051-023-00579-y
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DOI: https://doi.org/10.1140/epjb/s10051-023-00579-y