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A mathematical theory for wealth distribution

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Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Summary

We review a qualitative mathematical theory of kinetic models for wealth distribution in simple market economies. This theory is a unified approach that covers a wide class of such models which have been proposed in the recent literature on econophysics. Based on the analysis of the underlying homogeneous Boltzmann equation, a qualitative description of the evolution of wealth in the large-time regime is obtained. In particular, the most important features of the steady wealth distribution are classified, namely the fatness of the Pareto tail and the tails’ dynamical stability. Most of the applied methods are borrowed from the kinetic theory of rarefied gases. A concise description of the moment hierarchy and suitable metrics for probability measures are employed as key tools.

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Acknowledgements

Bertram Düring is supported by the Deutsche Forschungsgemeinschaft, grant JU 359/6 (Forschergruppe 518). Daniel Matthes is supported by the Deutsche Forschungsgemeinschaft, grant JU 359/7.

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Authors and Affiliations

  1. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040, Wien, Austria

    Bertram Düring & Daniel Matthes

Authors
  1. Bertram Düring
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  2. Daniel Matthes
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Corresponding author

Correspondence to Bertram Düring .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, Via Saldini 50, Milano, 20133, Italy

    Giovanni Naldi

  2. Dipartimento di Matematica, Università di Ferrara, Via Machiavelli, 35, Ferrara, 44100, Italy

    Lorenzo Pareschi

  3. Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, Pavia, 27100, Italy

    Giuseppe Toscani

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Dedicated to Prof. Giuseppe Toscani, on the occasion of his 60th birthday

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Düring, B., Matthes, D. (2010). A mathematical theory for wealth distribution. In: Naldi, G., Pareschi, L., Toscani, G. (eds) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4946-3_4

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