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Kinetic models for optimal control of wealth inequalities

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  • Bertram During
  • Lorenzo Pareschi
  • Giuseppe Toscani

Abstract

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker-Planck based models and taxation-redistribution policies and the present approach are also discussed.

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  • Bertram During & Lorenzo Pareschi & Giuseppe Toscani, 2018. "Kinetic models for optimal control of wealth inequalities," Papers 1803.02171, arXiv.org, revised Jul 2018.
    • Handle: RePEc:arx:papers:1803.02171
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    1. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
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    6. Düring, Bertram & Matthes, Daniel & Toscani, Giuseppe, 2008. "Kinetic equations modelling wealth redistribution: A comparison of approaches," CoFE Discussion Papers 08/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    7. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
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    Cited by:

    1. Giacomo Dimarco & Giuseppe Toscani & Mattia Zanella, 2024. "A multi-agent description of the influence of higher education on social stratification," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 19(3), pages 493-521, July.
    2. Neñer, Julian & Laguna, María Fabiana, 2021. "Optimal risk in wealth exchange models: Agent dynamics from a microscopic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    3. Düring, Bertram & Georgiou, Nicos & Merino-Aceituno, Sara & Scalas, Enrico, 2022. "Continuum and thermodynamic limits for a simple random-exchange model," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 248-277.
    4. Tian, Songtao & Liu, Zhirong, 2020. "Emergence of income inequality: Origin, distribution and possible policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Max Greenberg & H. Oliver Gao, 2024. "Twenty-five years of random asset exchange modeling," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-27, June.
    6. Wang, Lingling & Lai, Shaoyong & Sun, Rongmei, 2022. "Optimal control about multi-agent wealth exchange and decision-making competence," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    7. G. Dimarco & L. Pareschi & G. Toscani & M. Zanella, 2020. "Wealth distribution under the spread of infectious diseases," Papers 2004.13620, arXiv.org.
    8. Desogus, Marco & Casu, Elisa, 2022. "Chaos, granularity, and instability in economic systems of countries with emerging market economies: relationships between GDP growth rate and increasing internal inequality," MPRA Paper 115744, University Library of Munich, Germany, revised 2022.
    9. Hongjing Chen & Chong Lai & Hanlei Hu, 2024. "Kinetic Models for the Exchange of Production Factors in a Multi-agent Market," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2559-2584, June.
    10. Xia Zhou & Shaoyong Lai, 2023. "The mutual influence of knowledge and individual wealth growth," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-22, June.

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