IDEAS home Printed from https://ideas.repec.org/p/qed/wpaper/1178.html
   My bibliography  Save this paper

Envy Minimization In The Optimal Tax Context

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1178.pdf
    File Function: First version 2008
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Marc Fleurbaey & François Maniquet, 2006. "Fair Income Tax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 55-83.
    5. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    6. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    7. 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.
    8. Guesnerie,Roger, 1998. "A Contribution to the Pure Theory of Taxation," Cambridge Books, Cambridge University Press, number 9780521629560, September.
    9. 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.
    10. 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).
    11. repec:bla:jpbect:v:2:y:2000:i:4:p:435-60 is not listed on IDEAS
    12. Stanley L. Winer & Hirofumi Shibata (ed.), 2002. "Political Economy and Public Finance," Books, Edward Elgar Publishing, number 2805.
    13. 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.
    14. Arnsperger, Christian, 1994. "Envy-Freeness and Distributive Justice," Journal of Economic Surveys, Wiley Blackwell, vol. 8(2), pages 155-186, June.
    15. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
    16. Tuomala, Matti, 1990. "Optimal Income Tax and Redistribution," OUP Catalogue, Oxford University Press, number 9780198286059.
    17. 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.
    18. 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.
    19. Varian, Hal R., 1976. "Two problems in the theory of fairness," Journal of Public Economics, Elsevier, vol. 5(3-4), pages 249-260.
    20. 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.
    21. 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.
    22. 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.
    23. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    24. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    25. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    26. 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.
    27. Dixit, Avinash & Seade, Jesus, 1979. "Utilitarian versus egalitarian redistributions," Economics Letters, Elsevier, vol. 4(2), pages 121-124.
    28. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    29. 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.
    30. Moulin, H & Thomson, W, 1995. "Axiomatic Analysis of Resource Allocation," RCER Working Papers 400, University of Rochester - Center for Economic Research (RCER).
    31. Guesnerie, Roger & Seade, Jesus, 1982. "Nonlinear pricing in a finite economy," Journal of Public Economics, Elsevier, vol. 17(2), pages 157-179, March.
    32. 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.
    33. 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.
    34. 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.
    35. Efraim Sadka, 1976. "On Income Distribution, Incentive Effects and Optimal Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 261-267.
    36. 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.
    37. Ebert, Udo, 1992. "A reexamination of the optimal nonlinear income tax," Journal of Public Economics, Elsevier, vol. 49(1), pages 47-73, October.
    38. Eytan Sheshinski, 1972. "The Optimal Linear Income-tax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(3), pages 297-302.
    39. Stiglitz, Joseph E., 1982. "Self-selection and Pareto efficient taxation," Journal of Public Economics, Elsevier, vol. 17(2), pages 213-240, March.
    40. Edmund S. Phelps, 1973. "Taxation of Wage Income for Economic Justice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 331-354.
    41. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nishimura, Yukihiro, 2003. "Optimal non-linear income taxation for reduction of envy," Journal of Public Economics, Elsevier, vol. 87(2), pages 363-386, February.
    2. LUTTENS, Roland Iwan & OOGHE, Erwin, 2006. "Is it fair to ‘make work pay’ ?," LIDAM Discussion Papers CORE 2006026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Roland Iwan Luttens & Erwin Ooghe, 2007. "Is it Fair to ‘Make Work Pay’?," Economica, London School of Economics and Political Science, vol. 74(296), pages 599-626, November.
    4. Obara Takuya & Tsugawa Shuichi, 2019. "Public Good Provision Financed by Nonlinear Income Tax Under Reduction of Envy," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 19(4), pages 1-16, October.
    5. Jacquet, Laurence & Van de Gaer, Dirk, 2011. "A comparison of optimal tax policies when compensation or responsibility matter," Journal of Public Economics, Elsevier, vol. 95(11), pages 1248-1262.
    6. Stefan Homburg, 2001. "The Optimal Income Tax: Restatement and Extensions," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 58(4), pages 363-395, November.
    7. Obara, Takuya & 小原, 拓也 & Tsugawa, Shuichi & Managi, Shunsuke, 2019. "Envy-free Pricing for Impure Public Good," CCES Discussion Paper Series 69, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    8. Erwin Ooghe & Andreas Peichl, 2015. "Fair and Efficient Taxation under Partial Control," Economic Journal, Royal Economic Society, vol. 125(589), pages 2024-2051, December.
    9. Ooghe, Erwin & Peichl, Andreas, 2010. "Fair and Efficient Taxation under Partial Control: Theory and Evidence," IZA Discussion Papers 5388, Institute of Labor Economics (IZA).
    10. Stiglitz, Joseph E., 2018. "Pareto efficient taxation and expenditures: Pre- and re-distribution," Journal of Public Economics, Elsevier, vol. 162(C), pages 101-119.
    11. 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.
    12. Laurence Jacquet & Dirk Van de Gaer, 2015. "Politiques fiscales optimales pour les bas revenus et principe de compensation," Revue économique, Presses de Sciences-Po, vol. 66(3), pages 579-600.
    13. 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.
    14. Oztek, Abdullah Selim, 2019. "A Characterization for Marginal Income Tax Schedules," MPRA Paper 103046, University Library of Munich, Germany, revised 02 Dec 2019.
    15. Amedeo Spadaro, 2002. "Redistribución e incentivos a la oferta de trabajo: Desarrollos recientes de la teoría de la imposición óptima sobre la renta," Hacienda Pública Española / Review of Public Economics, IEF, vol. 160(1), pages 147-173, march.
    16. Lockwood, Benjamin B. & Weinzierl, Matthew, 2015. "De Gustibus non est Taxandum: Heterogeneity in preferences and optimal redistribution," Journal of Public Economics, Elsevier, vol. 124(C), pages 74-80.
    17. Henrik Jordahl & Luca Micheletto, 2005. "Optimal Utilitarian Taxation and Horizontal Equity," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(4), pages 681-708, October.
    18. Sören Blomquist & Vidar Christiansen, 2008. "Taxation and Heterogeneous Preferences," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 64(2), pages 218-244, June.
    19. Thomas Piketty & Emmanuel Saez, 2012. "Optimal Labor Income Taxation," NBER Working Papers 18521, National Bureau of Economic Research, Inc.
    20. Robin Boadway, 1998. "The Mirrlees Approach to the Theory of Economic Policy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 5(1), pages 67-81, February.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:1178. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mark Babcock (email available below). General contact details of provider: https://edirc.repec.org/data/qedquca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.