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Measuring opportunity inequality with monetary transfers

Abstract

In this paper I consider the problem of measuring opportunity inequality when monetary transfers are possible. First, I consider the case in which agents have common evaluations (or identical preferences), as in the previous literature. I then propose an extension to the heterogeneous case. In both cases I identify an appropriate egalitarian benchmark relative to which inequality can be measured, and I establish that this yields a theory of measurement analogous to that of income inequality. Consequently, the introduction of money (or an infinitely divisible commodity) avoids the difficulty reported in Ok (J Econ Theory 77:300–329, 1997). The results of the paper are immediately applicable to the measurement of multidimensional economic inequality including economies with indivisible goods.

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References

  1. 1.

    Aczél, J., Kannapan, P., Ng, C.T., Wagner, C.: Functional equations and inequalities in ‘rational group decision making.’ In: Beckenbach, E.F., Walter, W. (eds.) General Inequalities, vol 3, 3rd International Conference on General Inequalities. Birkhäuser Verlag, Basel (1983)

    Google Scholar 

  2. 2.

    Arlegi, R., Nieto, J.: Equality of opportunity: cardinality-based criteria. In: de Swart, H. (ed.) Logic, Game Theory and Social Choice. Tilburg University Press, Tilburg (1999)

    Google Scholar 

  3. 3.

    Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)

    Article  Google Scholar 

  4. 4.

    Barberà, S., Bossert, W., Pattanaik, P.K.: Ranking sets of objects. In: Barberà, S., Hammond, P.J., Seidl, C. (eds.) Handbook of Utility Theory, vol. II. Springer, New York (2004)

    Google Scholar 

  5. 5.

    Bosmans, K., Lauwers, L., Ooghe, E.: A Consistent Multidimensional Pigou–Dalton Transfer Principle. Mimeo (2006)

  6. 6.

    Bossert, W., Fleurbaey, M., Van de gaer, D.: Responsibility, talent, and compensation: a second-best analysis. Rev. Econ. Des. 4, 35–55 (1999)

    Google Scholar 

  7. 7.

    Chaudhuri, A.: Some implications of an intensity measure of envy. Soc. Choice Welf. 3, 255–270 (1986)

    Article  Google Scholar 

  8. 8.

    Diamantaras D., Thomson, W.: A refinement and extension of the no-envy concept. Econ. Lett. 33, 217–222 (1990)

    Article  Google Scholar 

  9. 9.

    Dalton, H.: The measurement of the inequality of incomes. Econ. J. 30, 348–361 (1920)

    Article  Google Scholar 

  10. 10.

    Dasgupta, P., Sen, A., Starrett, D.: Notes on the measurement of inequality. J. Econ. Theory 6, 180–187 (1973)

    Article  Google Scholar 

  11. 11.

    Farina, F., Savaglio, E. (eds.): Multidimensional Inequality. Part IV. In: Inequality and Economic Integration. Routledge, London (2006)

  12. 12.

    Fields, G., Fei, J.: On inequality comparisons. Econometrica 46, 303–316 (1978)

    Article  Google Scholar 

  13. 13.

    Fleurbaey, M.: On fair compensation. Theory Decis. 36, 277–307 (1994)

    Article  Google Scholar 

  14. 14.

    Fleurbaey, M.: Three solutions for the compensation problem. J. Econ. Theory 65, 505–521 (1995)

    Article  Google Scholar 

  15. 15.

    Fleurbaey, M., Maniquet, F.: Compensation and responsibility. Mimeo (2005)

  16. 16.

    Foster, J.E.: Inequality measurement. In: Young, H.P. (ed.) Fair Allocation. American Mathematical Society, Providence RI (1985)

    Google Scholar 

  17. 17.

    Genest, C., Zidek, J.V.: Combining probability distribution: a critigue and an annotated bibliography. Stat. Sci. 1, 114–135 (1986)

    Article  Google Scholar 

  18. 18.

    Herrero, C.: Equitable opportunities: an extension. Econ. Lett. 55, 91–95 (1997)

    Article  Google Scholar 

  19. 19.

    Herrero, C., Iturbe-Ormaetxe, I., Nieto, J.: Ranking opportunity profiles on the basis of the common opportunities. Math. Soc. Sci. 35, 273–289 (1998)

    Article  Google Scholar 

  20. 20.

    Iturbe-Ormaetxe, I., Nieto, J.: On fair allocations and monetary compensations. Econ. Theory 7, 125–138 (1995)

    Article  Google Scholar 

  21. 21.

    Kolm, S.-C.: Justice et Equité. Editions du Centre National de la Recherche Scientifique, Paris (1972)

  22. 22.

    Kranich, L.: Equitable opportunities: an axiomatic approach. J. Econ. Theory 71, 131–147 (1996)

    Article  Google Scholar 

  23. 23.

    Kranich, L.: Equitable opportunities in economic environments. Soc. Choice Welf. 14, 57–64 (1997)

    Article  Google Scholar 

  24. 24.

    Lambert, P.: The Distribution and Redistribution of Income: A Mathematical Analysis, 2nd edn. Basil-Blackwell, Oxford (1993)

    Google Scholar 

  25. 25.

    Laslier, J.-F., Fleurbaey, M., Gravel, N., Trannoy, A. (eds.): Freedom in Economics: New Perspectives in Normative Analysis. Routledge, London (1998)

    Google Scholar 

  26. 26.

    Ok, E.A.: On opportunity inequality measurement. J. Econ. Theory 77, 300–329 (1997)

    Article  Google Scholar 

  27. 27.

    Ok, E.A., Kranich, L.: The measurement of opportunity inequality: a cardinality-based approach. Soc. Choice Welf. 15, 263–288 (1998)

    Article  Google Scholar 

  28. 28.

    Peragine, V.: The distribution and redistribution of opportunity. J. Econ. Surv. 13, 37–70 (1999)

    Article  Google Scholar 

  29. 29.

    Peragine, V.: Measuring and implementing equality of opportunity for income. Soc. Choice Welf. 22, 187–210 (2004)

    Article  Google Scholar 

  30. 30.

    Pigou, A.: Wealth and Welfare. MacMillan, London (1912)

    Google Scholar 

  31. 31.

    Roemer, J.E.: A pragmatic theory of responsibility for the egalitarian planner. Philos. Public Aff. 22, 146–166 (1993)

    Google Scholar 

  32. 32.

    Roemer, J.E.: Equality of Opportunity. Harvard Univ Press, Cambridge MA (1998)

    Google Scholar 

  33. 33.

    Savaglio, E., Vannucci, S.: Filtral preorders and opportunity inequality. J. Econ. Theory 132, 474–492 (2007)

    Article  Google Scholar 

  34. 34.

    Savaglio, E., Vannucci, S.: On Lorenz preorders and opportunity inequality in finite environments. Mimeo (2006)

  35. 35.

    Sen, A.: The Standard of Living. Cambridge Univ. Press, Cambridge (1987)

    Google Scholar 

  36. 36.

    Stone, M.: The opinion pool. Ann. Math. Stat. 32, 1339–1342 (1961)

    Article  Google Scholar 

  37. 37.

    Tadenuma, K., Thomson, W.: Refinements of the no-envy solution in economies with indivisible goods. Theory Decis. 39, 189–206 (1995)

    Google Scholar 

  38. 38.

    Thomson, W.: An informationally efficient equity criterion. J. Public Econ. 18, 243–263 (1982)

    Article  Google Scholar 

  39. 39.

    Thomson, W.: Fair Allocation Rules. Mimeo (2007)

  40. 40.

    Thomson, W., Varian, H.: Theories of justice based on symmetry. In: Hurwicz, L., Schmeidler, D., Sonnenschein, H. (eds.) Social Goals and Social Organization. Cambridge Univ. Press, Cambridge (1985)

    Google Scholar 

  41. 41.

    Van Parijs, P.: Equal endowments as undominated diversity. Rech. Econ. de Louvain 56, 327–355 (1990)

    Google Scholar 

  42. 42.

    Weymark, J.A.: Generalized Gini indices of equality of opportunity. J. Econ. Inequal. 1, 5–24 (2003)

    Article  Google Scholar 

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Correspondence to Laurence Kranich.

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Kranich, L. Measuring opportunity inequality with monetary transfers. J Econ Inequal 7, 371 (2009). https://doi.org/10.1007/s10888-008-9087-y

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Keywords

  • Equality of opportunity
  • Inequality measurement
  • Opportunity sets

JEL Classification

  • D63
  • D71