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Stability of Pareto-Zipf Law in Non-Stationary Economies

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  • Sorin Solomon and Peter Richmond

Abstract

Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent a are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent a = 1.4 is related to built-in human social and biological constraints.

Suggested Citation

  • Sorin Solomon and Peter Richmond, 2001. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Computing in Economics and Finance 2001 11, Society for Computational Economics.
    • Handle: RePEc:sce:scecf1:11
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    Cited by:

    1. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.
    2. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    3. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
    4. Alan D. Zimm, 2005. "Derivation of a Logistic Equation for Organizations, and its Expansion into a Competitive Organizations Simulation," Computational and Mathematical Organization Theory, Springer, vol. 11(1), pages 37-57, May.
    5. Ausloos, M. & Bronlet, Ph., 2003. "Strategy for investments from Zipf law(s)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 30-37.
    6. Mimkes, Jürgen, 2010. "Stokes integral of economic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1665-1676.
    7. Smirnov Alexander D., 2018. "Stochastic Logistic Model of the Global Financial Leverage," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-20, January.
    8. Aleksejus Kononovicius & Valentas Daniunas, 2013. "Agent-based and macroscopic modeling of the complex socio-economic systems," Papers 1303.3693, arXiv.org, revised Apr 2013.

    More about this item

    Keywords

    Logistic Equation; Stochastic Multiplicative dynamics; Pareto power laws;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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