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Gini and Optimal Income Taxation by Rank

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  • Laurent Simula

    (ENS de Lyon - École normale supérieure de Lyon, GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Alain Trannoy

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We solve the nonlinear income tax program for rank-dependent social welfare functions, expressing the trade-off between size and inequality using the Gini and related families of positional indices. Absent bunching, ranks in the actual and optimal allocations are invariant. Exploiting this feature, we provide new, simple, and intuitive tax formulas for both the quasilinear and additive cases and new comparative static results. Our approach makes insights from optimal taxation more widely accessible. In some of our simulations the actual US tax policy is close to being optimal—except at the top, where optimal rates are much higher than in actuality.

Suggested Citation

  • Laurent Simula & Alain Trannoy, 2022. "Gini and Optimal Income Taxation by Rank," Post-Print hal-04000868, HAL.
    • Handle: RePEc:hal:journl:hal-04000868
    DOI: 10.1257/pol.20200272
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    Cited by:

    1. Støstad, Morten Nyborg & Cowell, Frank, 2024. "Inequality as an externality: consequences for tax design," LSE Research Online Documents on Economics 123752, London School of Economics and Political Science, LSE Library.

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