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Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

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  • Eliazar, Iddo
  • Cohen, Morrel H.

Abstract

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance–poor fractality, rich fractality, and middle-class fractality–and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality–amalgamated into a composite hierarchical structure–underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

Suggested Citation

  • Eliazar, Iddo & Cohen, Morrel H., 2014. "Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 30-40.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:30-40
    DOI: 10.1016/j.physa.2014.01.059
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    References listed on IDEAS

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    1. Chakrabarti,Bikas K. & Chakraborti,Anirban & Chakravarty,Satya R. & Chatterjee,Arnab, 2013. "Econophysics of Income and Wealth Distributions," Cambridge Books, Cambridge University Press, number 9781107013445, November.
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    2. Iddo Eliazar & Giovanni M. Giorgi, 2020. "From Gini to Bonferroni to Tsallis: an inequality-indices trek," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 119-153, August.
    3. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    4. Eliazar, Iddo, 2024. "From Zipf to Price and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 647(C).
    5. Luckstead, Jeff & Devadoss, Stephen, 2017. "Pareto tails and lognormal body of US cities size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 573-578.
    6. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    7. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    8. 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.

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