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Exponential wealth distribution: a new approach from functional iteration theory

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  • Ricardo Lopez-Ruiz
  • Jose-Luis Lopez
  • Xavier Calbet

Abstract

Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $ f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.

Suggested Citation

  • Ricardo Lopez-Ruiz & Jose-Luis Lopez & Xavier Calbet, 2011. "Exponential wealth distribution: a new approach from functional iteration theory," Papers 1103.1501, arXiv.org.
    • Handle: RePEc:arx:papers:1103.1501
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    References listed on IDEAS

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    1. J. Gonzalez-Estevez & M. G. Cosenza & R. Lopez-Ruiz & J. R. Sanchez, 2008. "Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system," Papers 0801.0969, arXiv.org.
    2. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 213-221.
    3. Ricardo Lopez-Ruiz, 2010. "Exponential wealth distribution in different discrete economic models," Papers 1009.3550, arXiv.org.
    4. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    5. 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. R. Lopez-Ruiz & E. Shivanian & S. Abbasbandy & J. L. Lopez, 2011. "A Generalized Continuous Model for Random Markets," Papers 1104.2187, arXiv.org, revised May 2011.

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