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Inequality minimising subsidy and taxation

Author

Listed:
  • Satya R. Chakravarty

    (Indian Statistical Institute
    Indira Gandhi Institute of Development Research)

  • Palash Sarkar

    (Indian Statistical Institute)

Abstract

We address the problem of procuring a certain amount of tax from the individuals in a society together with allocating a specific quantity of subsidy to the same set of individuals in an inequality minimising manner, where the tax and subsidy sizes need not be the same. If the combined tax-subsidy schedule does not modify the aggregate income, then Fei’s (Econometrica 49:869–881, 1981) inequality minimising solution for a balanced budget plan becomes a particular case of our tax-subsidy program, considered in a more general and practical situation in which the subsidy and tax aggregates may not be equal.

Suggested Citation

  • Satya R. Chakravarty & Palash Sarkar, 2022. "Inequality minimising subsidy and taxation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 53-67, May.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:1:d:10.1007_s40505-022-00218-2
    DOI: 10.1007/s40505-022-00218-2
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    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 283-295, February.
    3. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    4. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
    5. Biung-Ghi Ju & Juan Moreno-Ternero, 2008. "On the equivalence between progressive taxation and inequality reduction," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 561-569, May.
    6. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    7. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    8. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    9. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    10. Fei, John C H, 1981. "Equity Oriented Fiscal Programs," Econometrica, Econometric Society, vol. 49(4), pages 869-881, June.
    11. Elena Bárcena-Martin & Jacques Silber, 2013. "On the generalization and decomposition of the Bonferroni index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 763-787, October.
    12. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 43-62, February.
    13. Mitra, Tapan & Ok, Efe A, 1996. "Personal Income Taxation and the Principle of Equal Sacrifice Revisited," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 925-948, November.
    14. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    15. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-266, March.
    16. Satya R. Chakravarty & Patrick Moyes, 2003. "Individual welfare, social deprivation and income taxation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 843-869, June.
    17. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, vol. 44(4), pages 823-824, July.
    18. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, vol. 45(3), pages 719-727, April.
    19. Le Breton, Michel & Moyes, Patrick & Trannoy, Alain, 1996. "Inequality Reducing Properties of Composite Taxation," Journal of Economic Theory, Elsevier, vol. 69(1), pages 71-103, April.
    20. Oriol Carbonell-Nicolau & Humberto Llavador, 2021. "Inequality, Bipolarization, and Tax Progressivity," American Economic Journal: Microeconomics, American Economic Association, vol. 13(4), pages 492-513, November.
    21. Ok, Efe A., 1995. "On the principle of equal sacrifice in income taxation," Journal of Public Economics, Elsevier, vol. 58(3), pages 453-467, November.
    22. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    23. Marc Fleurbaey & François Maniquet, 2006. "Compensation and responsibility," Working Papers halshs-00121367, HAL.
    24. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    25. Moyes, Patrick, 2003. "Redistributive effects of minimal equal sacrifice taxation," Journal of Economic Theory, Elsevier, vol. 108(1), pages 111-140, January.
    26. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    27. Berliant, Marcus & Gouveia, Miguel, 1993. "Equal sacrifice and incentive compatible income taxation," Journal of Public Economics, Elsevier, vol. 51(2), pages 219-240, June.
    28. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    29. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    30. Mitra, Tapan & Ok, Efe A., 1997. "On the Equitability of Progressive Taxation," Journal of Economic Theory, Elsevier, vol. 73(2), pages 316-334, April.
    31. 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.
    32. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    33. Chakravarty,Satya R. & Mitra,Manipushpak & Sarkar,Palash, 2015. "A Course on Cooperative Game Theory," Cambridge Books, Cambridge University Press, number 9781107058798.
    34. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    35. Young, H. P., 1987. "Progressive taxation and the equal sacrifice principle," Journal of Public Economics, Elsevier, vol. 32(2), pages 203-214, March.
    36. Juan D. Moreno‐Ternero & Antonio Villar, 2006. "On the Relative Equitability of a Family of Taxation Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(2), pages 283-291, May.
    37. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    38. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    39. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    40. Eichhorn, Wolfgang & Funke, Helmut & Richter, Wolfram F., 1984. "Tax progression and inequality of income distribution," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 127-131, October.
    41. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    42. Hougaard, Jens Leth & Osterdal, Lars Peter, 2005. "Inequality preserving rationing," Economics Letters, Elsevier, vol. 87(3), pages 355-360, June.
    43. Jakobsson, Ulf, 1976. "On the measurement of the degree of progression," Journal of Public Economics, Elsevier, vol. 5(1-2), pages 161-168.
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    Cited by:

    1. Satya R. Chakravarty & Rama Pal & Rupayan Pal & Palash Sarkar, 2022. "Minimum inequality taxation, average and minimally progressive taxations and depolarization," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2022-010, Indira Gandhi Institute of Development Research, Mumbai, India.
    2. Chakravarty, Satya R. & Sarkar, Palash, 2022. "A synthesis of local and effective tax progressivity measurement," MPRA Paper 115180, University Library of Munich, Germany.

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    More about this item

    Keywords

    Subsidy; Tax; Minimum inequality; Constrained equal award; Lorenz domination;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies

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