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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.

Suggested Citation

  • 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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    File URL: http://arxiv.org/pdf/1109.0606
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    References listed on IDEAS

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    1. M. Patriarca & E. Heinsalu & A. Chakraborti, 2010. "Basic kinetic wealth-exchange models: common features and open problems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 145-153, January.
    2. Clementi, F. & Gallegati, M., 2005. "Power law tails in the Italian personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 427-438.
    3. A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 135-149, November.
    4. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2009. "Microeconomics of the ideal gas like market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4151-4158.
    5. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
    6. Ben-Naim, E & Krapivsky, P.L & Vazquez, F & Redner, S, 2003. "Unity and discord in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 99-106.
    7. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    8. Grabowski, A. & Kosiński, R.A., 2006. "Ising-based model of opinion formation in a complex network of interpersonal interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 651-664.
    9. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
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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. repec:eee:phsmap:v:490:y:2018:i:c:p:278-288 is not listed on IDEAS
    3. Maria Letizia Bertotti & Amit K Chattopadhyay & Giovanni Modanese, 2017. "Economic inequality and mobility for stochastic models with multiplicative noise," Papers 1702.08391, arXiv.org.
    4. M. L. Bertotti & G. Modanese, 2016. "Mathematical models describing the effects of different tax evasion behaviors," Papers 1701.02662, arXiv.org.

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