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Gini and Optimal Income Taxation by Rank

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  • Laurent Simula
  • Alain Trannoy

Abstract

We solve the non-linear income tax program for a rank-dependent social welfare function à la Yaari, expressing the trade-off between size and inequality using the Gini or related families of positional indices. The key idea is that when agents optimize and absent bunching, ranks in the actual and optimal allocations become an invariant dimension. This allows us to obtain optimal marginal tax rates as a function of ranks, and numerically illustrate the relationship between ranks and taxes. For singles without children, the actual US tax schedule seems to indicate a distaste for differences in the upper part of the distribution.

Suggested Citation

  • Laurent Simula & Alain Trannoy, 2020. "Gini and Optimal Income Taxation by Rank," CESifo Working Paper Series 8141, CESifo.
    • Handle: RePEc:ces:ceswps:_8141
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    1. Boadway, Robin & Jacquet, Laurence, 2008. "Optimal marginal and average income taxation under maximin," Journal of Economic Theory, Elsevier, vol. 143(1), pages 425-441, November.
    2. Emmanuel Saez & Joel Slemrod & Seth H. Giertz, 2012. "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 50(1), pages 3-50, March.
    3. Thomas Piketty & Emmanuel Saez & Stefanie Stantcheva, 2014. "Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities," American Economic Journal: Economic Policy, American Economic Association, vol. 6(1), pages 230-271, February.
    4. Etienne Lehmann & Laurent Simula & Alain Trannoy, 2014. "Tax me if you can! Optimal Nonlinear Income Tax Between Competing Governments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1995-2030.
    5. Thomas Piketty & Emmanuel Saez, 2012. "Optimal Labor Income Taxation," NBER Working Papers 18521, National Bureau of Economic Research, Inc.
    6. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    7. Thomas Piketty & Emmanuel Saez, 2013. "Optimal Taxation of Labor Income," PSE-Ecole d'économie de Paris (Postprint) halshs-00944881, HAL.
    8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    9. Emmanuel Saez & Stefanie Stantcheva, 2016. "Generalized Social Marginal Welfare Weights for Optimal Tax Theory," American Economic Review, American Economic Association, vol. 106(1), pages 24-45, January.
    10. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    11. Bastani, Spencer & Selin, Håkan, 2014. "Bunching and non-bunching at kink points of the Swedish tax schedule," Journal of Public Economics, Elsevier, vol. 109(C), pages 36-49.
    12. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    13. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    14. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    15. Alain Trannoy, 2019. "Talent, equality of opportunity and optimal non-linear income tax," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(1), pages 5-28, March.
    16. Salanié, Bernard, 2011. "The Economics of Taxation," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262016346, December.
    17. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    18. Bernard Salanié, 2005. "The Economics of Contracts: A Primer, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262195259, December.
    19. Emmanuel Saez, 2001. "Using Elasticities to Derive Optimal Income Tax Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(1), pages 205-229.
    20. Laurent Simula, 2010. "Optimal nonlinear income tax and nonlinear pricing: optimality conditions and comparative static properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 199-220, July.
    21. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    22. Weymark, John A, 1987. "Comparative Static Properties of Optimal Nonlinear Income Taxes," Econometrica, Econometric Society, vol. 55(5), pages 1165-1185, September.
    23. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    24. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    25. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1553-1623.
    26. Sen, Amartya, 1974. "Informational bases of alternative welfare approaches : Aggregation and income distribution," Journal of Public Economics, Elsevier, vol. 3(4), pages 387-403, November.
    27. Diamond, Peter A, 1998. "Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates," American Economic Review, American Economic Association, vol. 88(1), pages 83-95, March.
    28. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    29. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
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    Cited by:

    1. Laurent Simula & Alain Trannoy, 2020. "Bunching and Rank-Dependent Optimal Income Taxation," CESifo Working Paper Series 8443, CESifo.
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    3. Mikhail Lvovitch Dorofeev, 2021. "Does Income Inequality Create Excessive Threats to the Sustainable Development of Russia? Evidence from Intercountry Comparisons via Analysis of Inequality Heatmaps," Economies, MDPI, vol. 9(4), pages 1-17, November.

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    More about this item

    Keywords

    Gini; optimal taxation; income taxation; ranks;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

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