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On growth-optimal tax rates and the issue of wealth inequalities

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  • Jean-Philippe Bouchaud

    (Capital Fund Management and Ecole Polytechnique)

Abstract

We introduce a highly stylized, yet non trivial model of the economy, with a public and private sector coupled through a wealth tax and a redistribution policy. The model can be fully solved analytically, and allows one to address the question of optimal taxation and of wealth inequalities. We find that according to the assumption made on the relative performance of public and private sectors, three situations are possible. Not surprisingly, the optimal wealth tax rate is either 0% for a deeply dysfunctional government and/or highly productive private sector, or 100 % for a highly efficient public sector and/or debilitated/risk averse private investors. If the gap between the public/private performance is moderate, there is an optimal positive wealth tax rate maximizing economic growth, even -- counter-intuitively -- when the private sector generates more growth. The compromise between profitable private investments and taxation however leads to a residual level of inequalities. The mechanism leading to an optimal growth rate is related the well-known explore/exploit trade-off.

Suggested Citation

  • Jean-Philippe Bouchaud, 2015. "On growth-optimal tax rates and the issue of wealth inequalities," Papers 1508.00275, arXiv.org, revised Aug 2015.
    • Handle: RePEc:arx:papers:1508.00275
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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).
    2. Seroussi, Inbar & Sochen, Nir, 2020. "Localization phase transition in stochastic dynamics on networks with hub topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    3. Liu, Z. & Serota, R.A., 2017. "Correlation and relaxation times for a stochastic process with a fat-tailed steady-state distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 301-311.
    4. Stojkoski, Viktor & Karbevski, Marko & Utkovski, Zoran & Basnarkov, Lasko & Kocarev, Ljupco, 2021. "Evolution of cooperation in networked heterogeneous fluctuating environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    5. Ole Peters & Alexander Adamou, 2018. "The sum of log-normal variates in geometric Brownian motion," Papers 1802.02939, arXiv.org.
    6. Zhiyuan Liu & R. A. Serota, 2017. "On absence of steady state in the Bouchaud-M\'ezard network model," Papers 1704.02377, arXiv.org.
    7. Liebmann, Thomas & Kassberger, Stefan & Hellmich, Martin, 2017. "Sharing and growth in general random multiplicative environments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 193-206.
    8. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distributions of Historic Market Data -- Relaxation and Correlations," Papers 1907.05348, arXiv.org, revised Feb 2020.
    9. Jean-Philippe Bouchaud, 2020. "How Much Income Inequality Is Too Much?," Papers 2004.09835, arXiv.org.

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