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From microscopic taxation and redistribution models to macroscopic income distributions

  • Maria Letizia Bertotti
  • Giovanni Modanese
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    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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    Paper provided by in its series Papers with number 1109.0606.

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    Date of creation: Sep 2011
    Publication status: Published in Physica A 390 (2011) 3782-3793
    Handle: RePEc:arx:papers:1109.0606
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    1. Fabio Clementi & Mauro Gallegati, 2005. "Power Law Tails in the Italian Personal Income Distribution," Microeconomics 0505005, EconWPA.
    2. 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.
    3. 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.
    4. Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543,, revised Nov 2007.
    5. 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.
    6. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518,, revised Dec 2009.
    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. 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.
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