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Envy Minimization In The Optimal Tax Context

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  • Yukihiro Nishimura

    (Yokohama National University and Queen's University)

Abstract

This paper examines the second-best tax policy to minimize envy in the sense of Chaudhuri (1986) and Diamantaras and Thomson (1990). An allocation is $\lambda$-equitable if no agent prefers a proportion $\lambda$ of any other agent's bundle. We study the allocations that maximize $\lambda$ among the second-best Pareto efficient allocations. In the standard two-class economy with identical preferences, the Chaudhuri-Diamantaras-Thomson allocation coincides with the leximin allocation. In many-agent economies, it is possible to order the class of second-best Pareto efficient allocations graded by progressivity in the sense of Hemming and Keen (1983), with respect to the intensity of envy. Envy is then minimized in the most progressive tax system.

Suggested Citation

  • Yukihiro Nishimura, 2008. "Envy Minimization In The Optimal Tax Context," Working Paper 1178, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1178
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    References listed on IDEAS

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    1. Robin Boadway & Katherine Cuff & Maurice Marchand, 2000. "Optimal Income Taxation With Quasi‐Linear Preferences Revisited," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(4), pages 435-460, October.
    2. Bos, Dieter & Tillmann, Georg, 1985. "An 'Envy Tax': Theoretical Principles and Applications to the German Surcharge on the Rich," Public Finance = Finances publiques, , vol. 40(1), pages 35-63.
    3. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    4. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    5. Robin Boadway & Maurice Marchand & Pierre Pestieau & María Del Mar Racionero, 2002. "Optimal Redistribution with Heterogeneous Preferences for Leisure," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(4), pages 475-498, October.
    6. Guesnerie,Roger, 1998. "A Contribution to the Pure Theory of Taxation," Cambridge Books, Cambridge University Press, number 9780521629560, October.
    7. FLEURBAEY, Marc & MANIQUET, François, 1998. "Optimal income taxation: and ordinal approach," LIDAM Discussion Papers CORE 1998065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Stanley L. Winer & Hirofumi Shibata (ed.), 2002. "Political Economy and Public Finance," Books, Edward Elgar Publishing, number 2805, May.
    9. Arnsperger, Christian, 1994. "Envy-Freeness and Distributive Justice," Journal of Economic Surveys, Wiley Blackwell, vol. 8(2), pages 155-186, June.
    10. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
    11. Roemer, John E. & Aaberge, Rolf & Colombino, Ugo & Fritzell, Johan & Jenkins, Stephen P. & Lefranc, Arnaud & Marx, Ive & Page, Marianne & Pommer, Evert & Ruiz-Castillo, Javier, 2003. "To what extent do fiscal regimes equalize opportunities for income acquisition among citizens?," Journal of Public Economics, Elsevier, vol. 87(3-4), pages 539-565, March.
    12. Tuomala, Matti, 1990. "Optimal Income Tax and Redistribution," OUP Catalogue, Oxford University Press, number 9780198286059, Decembrie.
    13. Varian, Hal R., 1976. "Two problems in the theory of fairness," Journal of Public Economics, Elsevier, vol. 5(3-4), pages 249-260.
    14. Georg Tillmann, 2005. "The equity-efficiency trade-off reconsidered," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 63-81, August.
    15. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    16. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 199-209.
    17. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    18. Dixit, Avinash & Seade, Jesus, 1979. "Utilitarian versus egalitarian redistributions," Economics Letters, Elsevier, vol. 4(2), pages 121-124.
    19. Dirk Van de gaer & Marc Fleurbaey & Walter Bossert, 1999. "Responsibility, talent, and compensation: A second-best analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 35-55.
    20. Tarkiainen, Ritva & Tuomala, Matti, 1999. "Optimal Nonlinear Income Taxation with a Two-Dimensional Population; A Computational Approach," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 1-16, February.
    21. Marc Fleurbaey & François Maniquet, 2007. "Help the Low Skilled or Let the Hardworking Thrive? A Study of Fairness in Optimal Income Taxation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(3), pages 467-500, June.
    22. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    23. Boadway, Robin & Keen, Michael, 2000. "Redistribution," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 12, pages 677-789, Elsevier.
    24. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    25. Eytan Sheshinski, 1972. "The Optimal Linear Income-tax," Review of Economic Studies, Oxford University Press, vol. 39(3), pages 297-302.
    26. Guesnerie, Roger & Seade, Jesus, 1982. "Nonlinear pricing in a finite economy," Journal of Public Economics, Elsevier, vol. 17(2), pages 157-179, March.
    27. Stiglitz, Joseph E., 1982. "Self-selection and Pareto efficient taxation," Journal of Public Economics, Elsevier, vol. 17(2), pages 213-240, March.
    28. Edmund S. Phelps, 1973. "Taxation of Wage Income for Economic Justice," The Quarterly Journal of Economics, Oxford University Press, vol. 87(3), pages 331-354.
    29. 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.
    30. Schokkaert, Erik & Van de gaer, Dirk & Vandenbroucke, Frank & Luttens, Roland Iwan, 2004. "Responsibility sensitive egalitarianism and optimal linear income taxation," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 151-182, September.
    31. Hervé Moulin & William Thomson, 1997. "Axiomatic Analysis of Resource Allocation Problems," International Economic Association Series, in: Kenneth J. Arrow & Amartya Sen & Kotaro Suzumura (ed.), Social Choice Re-examined, chapter 5, pages 101-120, Palgrave Macmillan.
    32. Marc Fleurbaey & François Maniquet, 2006. "Fair Income Tax," Review of Economic Studies, Oxford University Press, vol. 73(1), pages 55-83.
    33. Stern, N. H., 1976. "On the specification of models of optimum income taxation," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 123-162.
    34. Boadway, Robin & Cuff, Katherine & Marchand, Maurice, 2000. "Optimal Income Taxation with Quasi-linear Preferences Revisited," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(4), pages 435-460.
    35. Yukihiro Nishimura, 2003. "Optimal commodity taxation for reduction of envy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 501-527, December.
    36. Hemming, R. & Keen, M. J., 1983. "Single-crossing conditions in comparisons of tax progressivity," Journal of Public Economics, Elsevier, vol. 20(3), pages 373-380, April.
    37. Roemer, John E. & Aaberge, Rolf & Colombino, Ugo & Fritzell, Johan & Jenkins, Stephen P. & Lefranc, Arnaud & Marx, Ive & Page, Marianne & Pommer, Evert & Ruiz-Castillo, Javier, 2003. "To what extent do fiscal regimes equalize opportunities for income acquisition among citizens?," Journal of Public Economics, Elsevier, vol. 87(3-4), pages 539-565, March.
    38. Atkinson, A. B. & Stiglitz, J. E., 1976. "The design of tax structure: Direct versus indirect taxation," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 55-75.
    39. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
    40. Moulin, H & Thomson, W, 1995. "Axiomatic Analysis of Resource Allocation," RCER Working Papers 400, University of Rochester - Center for Economic Research (RCER).
    41. 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.
    42. Nishimura, Yukihiro, 2003. "Optimal non-linear income taxation for reduction of envy," Journal of Public Economics, Elsevier, vol. 87(2), pages 363-386, February.
    43. Hellwig, Martin F., 1986. "The optimal linear income tax revisited," Journal of Public Economics, Elsevier, vol. 31(2), pages 163-179, November.
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    More about this item

    Keywords

    Income Taxation; Envy;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

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