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On the qualitative properties of the optimal income tax

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  • Ruiz del Portal, X.

Abstract

We explore the precise requirements for the qualitative results on optimum income taxation to hold, with the aim of extending their application to a larger space of solutions than that of continuous, piecewise differentiable functions assumed in the literature. In particular, properties (R1)-(R8) in Ebert (1992) are shown to hold when the endogenous variables of the problem are defined by non-smooth or even discontinuous functions, provided consumption is supposed to be normal and leisure non-inferior. Moreover, the referred properties continue to hold, without assuming the normality of consumption, if it is supposed that the function descriptive of gross income becomes absolutely continuous. In addition, a characterization of the set of potential solutions stemming from Lebesgue's Decomposition Theorem has been used to analyze the relevance of properties (R1)-(R8), vis-à-vis other possible features of optimal tax schedules. The conclusion is that, even assuming the normality of consumption, the case for regressivity should be viewed, on the lines suggested by Kaneko (1982) within a somehow different model, as an exceptional outcome versus other income tax structures that may arise at the optimum.

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  • Ruiz del Portal, X., 2010. "On the qualitative properties of the optimal income tax," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 288-298, May.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:288-298
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    References listed on IDEAS

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    1. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 175-208.
    2. Seade, J. K., 1977. "On the shape of optimal tax schedules," Journal of Public Economics, Elsevier, vol. 7(2), pages 203-235, April.
    3. Brunner, Johann K., 1993. "A note on the optimum income tax," Journal of Public Economics, Elsevier, vol. 50(3), pages 445-451, March.
    4. Ruiz del Portal, X., 2008. "Is the optimal income tax regressive?," Economics Letters, Elsevier, vol. 100(3), pages 402-404, September.
    5. Efraim Sadka, 1976. "On Income Distribution, Incentive Effects and Optimal Income Taxation," Review of Economic Studies, Oxford University Press, vol. 43(2), pages 261-267.
    6. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    7. Jesus Seade, 1982. "On the Sign of the Optimum Marginal Income Tax," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 637-643.
    8. Brito, Dagobert L & Oakland, William H, 1977. "Some Properties of the Optimal Income-Tax," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 407-423, June.
    9. Tuomala, Matti, 1984. "On the optimal income taxation : Some further numerical results," Journal of Public Economics, Elsevier, vol. 23(3), pages 351-366, April.
    10. Mamoru Kaneko, 1981. "On the Existence of an Optimal Income Tax Schedule," Review of Economic Studies, Oxford University Press, vol. 48(4), pages 633-642.
    11. X. RUIZ del PORTAL, 2007. "The Problem of Optimum Income Taxation: A Remark on Its Monotonicity Constraint," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 265-283, April.
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