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From microscopic taxation and redistribution models to macroscopic income distributions

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  • Maria Letizia Bertotti
  • Giovanni Modanese

Abstract

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution of the income distribution over the population and to explain the emergence of collective features based on the knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.

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  • Maria Letizia Bertotti & Giovanni Modanese, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Papers 1109.0606, arXiv.org.
    • Handle: RePEc:arx:papers:1109.0606
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    References listed on IDEAS

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    Cited by:

    1. Bertotti, M.L. & Chattopadhyay, A.K. & Modanese, G., 2017. "Stochastic effects in a discretized kinetic model of economic exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 724-732.
    2. Yuliya Tyurina, 2014. "Harmonization of the relations between the state and individuals in the context of taxation theory," Review of Applied Socio-Economic Research, Pro Global Science Association, vol. 8(2), pages 207-218, June.
    3. M. L. Bertotti & G. Modanese, 2016. "Mathematical models describing the effects of different tax evasion behaviors," Papers 1701.02662, arXiv.org.
    4. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.
    5. Maria Letizia Bertotti & Giovanni Modanese, 2015. "Economic inequality and mobility in kinetic models for social sciences," Papers 1504.03232, arXiv.org.
    6. Maria Letizia Bertotti & Amit K Chattopadhyay & Giovanni Modanese, 2017. "Economic inequality and mobility for stochastic models with multiplicative noise," Papers 1702.08391, arXiv.org.
    7. M. L. Bertotti & G. Modanese, 2018. "Mathematical models describing the effects of different tax evasion behaviors," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(2), pages 351-363, July.

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