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The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process

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  • Bouleau, Nicolas
  • Chorro, Christophe

Abstract

In this paper we consider some elementary and fair zero-sum games of chance in order to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties. In particular, we emphasize that randomness plays a key role in concentrating wealth in the extreme, in the hands of a single player. From a mathematical perspective, we interestingly adopt some diffusion limits for small and high-frequency transactions which are otherwise extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms. We show that taxation of income is not sufficient to overcome this extreme concentration process in contrast to the uniform taxation of capital which stabilizes the economy and prevents agents from being ruined.

Suggested Citation

  • Bouleau, Nicolas & Chorro, Christophe, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 379-395.
    • Handle: RePEc:eee:phsmap:v:479:y:2017:i:c:p:379-395
    DOI: 10.1016/j.physa.2017.03.017
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    More about this item

    Keywords

    Wealth distribution; Fair zero-sum games; Wright–Fisher diffusions; Inequalities; Impact of modes of taxation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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