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# Power Laws of Wealth, Market Order Volumes and Market Returns

## Author

Listed:
• 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 $\gamma$).

## Suggested Citation

• Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423, arXiv.org, revised Apr 2001.
• Handle: RePEc:arx:papers:cond-mat/0102423
as

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

## Citations

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Cited by:

1. Sorin Solomon & Nataša Golo, 2015. "Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 5-30, April.
2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
3. Ari Belenkiy, 2001. "Inner Market as a "Black Box"," Papers cond-mat/0106401, arXiv.org.
4. Geoff Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Microeconomics 0408003, University Library of Munich, Germany.
5. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 461-504.
6. Alex Kindler & Michael Golosovsky & Sorin Solomon, 2019. "Early prediction of the outcome of Kickstarter campaigns: is the success due to virality?," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-6, December.
7. Victor M. Yakovenko, 2007. "Econophysics, Statistical Mechanics Approach to," Papers 0709.3662, arXiv.org, revised Aug 2008.
8. Pierpaolo Andriani & Bill McKelvey, 2009. "Perspective ---From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations," Organization Science, INFORMS, vol. 20(6), pages 1053-1071, December.
9. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
10. 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.
11. 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.
12. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
13. 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.
14. Zoltan Neda & Istvan Gere & Tamas S. Biro & Geza Toth & Noemi Derzsy, 2019. "Scaling in Income Inequalities and its Dynamical Origin," Papers 1911.02449, arXiv.org.
15. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
16. 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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