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

  • Louis Kaplow

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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Publication status: published as Louis Kaplow, 2010. "Concavity of utility, concavity of welfare, and redistribution of income," International Tax and Public Finance, Springer, vol. 17(1), pages 25-42, February.
Handle: RePEc:nbr:nberwo:10005
Note: LE
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  1. 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.
  2. repec:cup:cbooks:9780521497695 is not listed on IDEAS
  3. 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.
  4. Narayana R. Kocherlakota, 1995. "The equity premium: it's still a puzzle," Discussion Paper / Institute for Empirical Macroeconomics 102, Federal Reserve Bank of Minneapolis.
  5. 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.
  6. Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
  7. Joel Slemrod & Shlomo Yitzhaki & Joram Mayshar, 1991. "The Optimal Two-Bracket Linear Income Tax," NBER Working Papers 3847, National Bureau of Economic Research, Inc.
  8. Robert B. Barsky & Miles S. Kimball & F. Thomas Juster & Matthew D. Shapiro, 1995. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Survey," NBER Working Papers 5213, National Bureau of Economic Research, Inc.
  9. 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.
  10. 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.
  11. 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.
  12. Mirrlees, James A, 1971. "An Exploration in the Theory of Optimum Income Taxation," Review of Economic Studies, Wiley Blackwell, vol. 38(114), pages 175-208, April.
  13. 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.
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