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Universal patterns of inequality


  • Anand Banerjee
  • Victor M. Yakovenko


Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures between different systems generates net fluxes of money and population. To describe income distribution, a stochastic process with additive and multiplicative components is introduced. The resultant distribution interpolates between exponential at the low end and power law at the high end, in agreement with the empirical data for USA. We show that the increase of income inequality in USA originates primarily from the increase of the income fraction going to the upper tail, which now exceeds 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world can be approximately described by the exponential function. Comparing the data for 1990, 2000, and 2005, we discuss the effect of globalization on the inequality of energy consumption.

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  • Anand Banerjee & Victor M. Yakovenko, 2009. "Universal patterns of inequality," Papers 0912.4898,, revised Apr 2010.
  • Handle: RePEc:arx:papers:0912.4898

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    References listed on IDEAS

    1. Fujiwara, Yoshi & Souma, Wataru & Aoyama, Hideaki & Kaizoji, Taisei & Aoki, Masanao, 2003. "Growth and fluctuations of personal income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 598-604.
    2. Fiaschi, Davide & Marsili, Matteo, 2012. "Distribution of wealth and incomplete markets: Theory and empirical evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 243-267.
    3. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518,, revised Dec 2009.
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    2. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    3. Newby, Michael & Behr, Adam & Feizabadi, Mitra Shojania, 2011. "Investigating the distribution of personal income obtained from the recent U.S. data," Economic Modelling, Elsevier, vol. 28(3), pages 1170-1173, May.
    4. Caticha, Ariel & Golan, Amos, 2014. "An entropic framework for modeling economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 149-163.
    5. Elvis Oltean, 2016. "Modelling income, wealth, and expenditure data by use of Econophysics," Papers 1603.08383,
    6. Costas Efthimiou & Adam Wearne, 2016. "Household Income Distribution in the USA," Papers 1602.06234,
    7. Chatterjee, Arnab & Chakrabarti, Anindya S. & Ghosh, Asim & Chakraborti, Anirban & Nandi, Tushar K., 2016. "Invariant features of spatial inequality in consumption: The case of India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 169-181.
    8. repec:eee:phsmap:v:490:y:2018:i:c:p:278-288 is not listed on IDEAS
    9. Park, Ji-Won & Kim, Chae Un & Isard, Walter, 2012. "Permit allocation in emissions trading using the Boltzmann distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4883-4890.
    10. Alberto Russo, 2017. "An Agent Based Macroeconomic Model with Social Classes and Endogenous Crises," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 3(3), pages 285-306, November.
    11. Soriano-Hernández, P. & del Castillo-Mussot, M. & Campirán-Chávez, I. & Montemayor-Aldrete, J.A., 2017. "Wealth of the world’s richest publicly traded companies per industry and per employee: Gamma, Log-normal and Pareto power-law as universal distributions?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 733-749.
    12. 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.
    13. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.

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