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Breakdown of the mean-field approximation in a wealth distribution model

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  • Matus Medo

Abstract

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.

Suggested Citation

  • Matus Medo, 2008. "Breakdown of the mean-field approximation in a wealth distribution model," Papers 0809.4139, arXiv.org, revised Nov 2008.
    • Handle: RePEc:arx:papers:0809.4139
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    File URL: http://arxiv.org/pdf/0809.4139
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    Cited by:

    1. Kemp, Jordan T. & Bettencourt, Luís M.A., 2022. "Statistical dynamics of wealth inequality in stochastic models of growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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