Abstract
Often from policy perspective it becomes necessary to arrive at an income distribution whose inequality value coincides with a targeted (low) inequality level. In the present article we address this duality problem in inequality measurement by using the well-known Gini and Bonferroni metrics of inequality. The duality theorem also enables us to determine the financial cost of achieving the targeted inequality value.
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References
Aaberge, R.: Gini’s nuclear family. J. Econ. Inequal. 5, 305–322 (2007)
Aristotle ( \(\sim \)350): Aristotle: Politics, Vol. 4, Part XI (350). (Trans. Jowett B). The University of Adelaide, eBooks@Adelaide
Bárcena-Martin, E., Silber, J.: On the generalization and decomposition of the Bonferroni index. Soc. Choice Welf. 41, 763–787 (2013)
Birdsall, N.: The (indispensable) middle class in developing countries. In: R. Kanbur, R., Spence, M. (eds.) Equity and Growth in a Globalizing World, pp. 157–187. The International Bank for Reconstruction and Development/The World Bank, Washington D.C. (2010)
Bossert, W., Pfingsten, A.: Intermediate inequality: concepts, indices, and welfare implications. Math. Soc. Sci. 19, 117–134 (1990)
Chakravarty, S.R.: Inequality, Polarization and Conflict: An Analytical Study. Springer, New York (2015)
Chakravarty, S.R., Sarkar, P.: An inequality paradox: relative versus absolute indices? Metron 79, 241–254 (2021a)
Chakravarty, S.R., Sarkar, P.: New Perspectives on the Gini and Bonferroni Indices of Inequality, Social Choice and Welfare (2021b). https://doi.org/10.1007/s00355-021-01311-4,
Chakravarty, S.R., Dutta, B.: A note on measures of distance between income distributions. J. Econ. Theory 41, 185–188 (1987)
Chancel, L., Piketty, T.: Indian income inequality, 1922–2014: From British Raj to Billionaire Raj?, Center for Economic and Policy Research, Washington. Discussion Paper No. 12409,(2017)
Dong, Z., Tillé, Y., Giorgi G. M., Guandalini, A.: Linearization and variance estimation of the Bonferroni inequality index, J. R. Stat. Soc. Ser. A, https://doi.org/10.1111/rssa.12701, (2021)
Giorgi, G.M.: A methodological survey of recent studies for the measurement of inequality of economic welfare carried out by some Italian statisticians. Econ. Notes 13, 145–157 (1984)
Kolm, S.C.: Unequal inequalities I. J. Econ. Theory 12, 416–442 (1976)
Weymark, J.A.: Generalized Gini inequality indices. Math. Soc. Sci. 1, 409–430 (1981)
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For comments and suggestions, we thank an anonymous referee. We offer special thanks to the referee for a highly innovative suggestion, which we have included in the appendix to enrich the paper.
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Chakravarty, S.R., Sarkar, P. Designing income distributions with specified inequalities. Econ Theory Bull 9, 297–311 (2021). https://doi.org/10.1007/s40505-021-00212-0
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DOI: https://doi.org/10.1007/s40505-021-00212-0