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From microscopic taxation and redistribution models to macroscopic income distributions

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  • Bertotti, Maria Letizia
  • Modanese, Giovanni

Abstract

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modeling of taxation and redistribution in a closed society. This framework allows one to describe the evolution of income distribution over the population and to explain the emergence of collective features based on 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.

Suggested Citation

  • Bertotti, Maria Letizia & Modanese, Giovanni, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3782-3793.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3782-3793
    DOI: 10.1016/j.physa.2011.06.008
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    Cited by:

    1. M. L. Bertotti & G. Modanese, 2016. "Mathematical models describing the effects of different tax evasion behaviors," Papers 1701.02662, arXiv.org.
    2. Maria Letizia Bertotti & Giovanni Modanese, 2015. "Economic inequality and mobility in kinetic models for social sciences," Papers 1504.03232, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    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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