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Nonlocal Reaction–Diffusion Models of Heterogeneous Wealth Distribution

Author

Listed:
  • Malay Banerjee

    (Department of Mathematics & Statistics, IIT Kanpur, Kanpur 208016, India)

  • Sergei V. Petrovskii

    (School of Mathematics & Actuarial Science, University of Leicester, Leicester LE1 7RH, UK)

  • Vitaly Volpert

    (Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
    Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In this work we study an economic–demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources, the homogeneous-in-space wealth–population distribution is replaced by a periodic-in-space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy.

Suggested Citation

  • Malay Banerjee & Sergei V. Petrovskii & Vitaly Volpert, 2021. "Nonlocal Reaction–Diffusion Models of Heterogeneous Wealth Distribution," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:351-:d:496942
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    2. Vincenzo Quadrini & José-Víctor Ríos-Rull, 1997. "Understanding the U.S. distribution of wealth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 21(Spr), pages 22-36.
    3. Davies, James B. & Shorrocks, Anthony F., 2000. "The distribution of wealth," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 11, pages 605-675, Elsevier.
    4. 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.
    5. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    6. Wang, Neng, 2007. "An equilibrium model of wealth distribution," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1882-1904, October.
    7. Crelis F. Rammelt & Maarten Van Schie & Fredu Nega Tegabu & Maggi Leung, 2017. "Vaguely Right or Exactly Wrong: Measuring the (Spatial) Distribution of Land Resources, Income and Wealth in Rural Ethiopia," Sustainability, MDPI, vol. 9(6), pages 1-19, June.
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