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Power Laws of Wealth, Market Order Volumes and Market Returns

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  • Sorin Solomon
  • Peter Richmond

Abstract

Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue that 'fair play' for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent $\alpha \sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $\alpha \sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $\beta \sim \alpha \sim 3/2$. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order $\gamma \sim 2 \alpha \sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for $\beta$ and [Gopikrishnan et al. 1999] for $\gamma$).

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File URL: http://arxiv.org/pdf/cond-mat/0102423
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0102423.

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Date of creation: Feb 2001
Date of revision: Apr 2001
Handle: RePEc:arx:papers:cond-mat/0102423

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Web page: http://arxiv.org/

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Cited by:
  1. G. Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Papers cond-mat/0408227, arXiv.org.
  2. Xavier Gabaix, 2008. "Power Laws in Economics and Finance," NBER Working Papers 14299, National Bureau of Economic Research, Inc.
  3. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
  4. 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.
  5. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
  6. Sorin Solomon & Natasa Golo, 2014. "Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative Agent," Papers 1401.7496, arXiv.org.
  7. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
  8. Victor M. Yakovenko, 2007. "Econophysics, Statistical Mechanics Approach to," Papers 0709.3662, arXiv.org, revised Aug 2008.
  9. Ari Belenkiy, 2001. "Inner Market as a "Black Box"," Papers cond-mat/0106401, arXiv.org.

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