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Concavity of Utility, Concavity of Welfare, and Redistribution of Income

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Louis Kaplow

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Abstract

The marginal social value of income redistribution is understood to depend on both the concavity of individuals' utility functions and the concavity of the social welfare function. In the pertinent literatures, notably on optimal income taxation and on normative inequality measurement, it seems to be accepted that the role of these two sources of concavity is symmetric with regard to the social concern about inequality in the distribution of income. Direct examination of the question, however, reveals that this is not the case. Concavity of utility has a simple, direct effect on the marginal social value of redistribution, as might be expected, whereas concavity of the social welfare function has a more subtle influence, one that in some cases may not be very significant. The implications of this difference are examined for some standard forms of utility and welfare functions, including particular versions that appear in the optimal income taxation literature.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 10005.

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Date of creation: Sep 2003
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Handle: RePEc:nbr:nberwo:10005

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D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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  1. Slemrod, Joel & Yitzhaki, Shlomo & Mayshar, Joram & Lundholm, Michael, 1994. "The optimal two-bracket linear income tax," Journal of Public Economics, Elsevier, vol. 53(2), pages 269-290, February. [Downloadable!] (restricted)
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  2. Louis Kaplow & Steven Shavell, 2001. "Any Non-welfarist Method of Policy Assessment Violates the Pareto Principle," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 281-286, April. [Downloadable!] (restricted)
  3. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61, pages 434. [Downloadable!] (restricted)
  4. Robert B. Barsky & Miles S. Kimball & F. Thomas Juster & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Survey," NBER Working Papers 5213, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Boskin, Michael J & Sheshinski, Eytan, 1978. "Optimal Redistributive Taxation when Individual Welfare Depends upon Relative Income," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 589-601, November. [Downloadable!] (restricted)
  6. Blackorby, C. & Bossert, W. & Donaldson, D., 1995. "Income Inequality Measurement: The Normative Approach," UBC Departmental Archives 95-23, UBC Department of Economics.
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  7. Barsky, Robert B, et al, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 537-79, May.
  8. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Blackwell Publishing, vol. 38(114), pages 175-208, April. [Downloadable!] (restricted)
  9. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309. [Downloadable!] (restricted)
  10. Hochman, Harold M & Rodgers, James D, 1969. "Pareto Optimal Redistribution," American Economic Review, American Economic Association, vol. 59(4), pages 542-57, Part I Se. [Downloadable!] (restricted)
  11. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April. [Downloadable!] (restricted)
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  12. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March. [Downloadable!] (restricted)
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  13. Louis Kaplow, 2003. "The Value of a Statistical Life and the Coefficient of Relative Risk Aversion," NBER Working Papers 9852, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  1. Juan Carlos Cordoba & Genevieve Verdier, 2007. "Lucas vs. Lucas: On Inequality and Growth," IMF Working Papers 07/17, International Monetary Fund. [Downloadable!]
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  2. Louis Kaplow, 2005. "Why measure inequality?," Journal of Economic Inequality, Springer, vol. 3(1), pages 65-79, April. [Downloadable!] (restricted)
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