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Equal shadow wealth: A new concept of fairness in exchange economies

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  • Kranich, Laurence

Abstract

In this paper I introduce a new notion of fairness in exchange economies as well as a measure of unfairness. First, I consider the benchmark case in which agents have identical preferences, and I then extend the framework to allow for heterogeneous tastes. In both cases, I identify an appropriate egalitarian benchmark which requires that a numeraire commodity be distributed in such a way so as to offset differences in the holdings of other commodities. Inequality is then measured as the deviation between the actual distribution of the numeraire and such an ideal distribution. This renders a complete social ordering. Next, I contrast this notion of equal shadow wealth with the notion of no-envy (Foley, 1967) and with the envy-intensity measures proposed by Chaudhuri (1986) and Diamantaras and Thomson (1990). I also investigate conditions which ensure the existence of equitable and efficient allocations. The concepts developed here may be generalizable to a wide range of environments including economies with externalities and indivisible goods as well as relatively unstructured environments such as those involving abstract opportunity sets. In addition, this approach offers a simple method to measure multidimensional inequality.

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  • Kranich, Laurence, 2015. "Equal shadow wealth: A new concept of fairness in exchange economies," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 110-117.
    • Handle: RePEc:eee:matsoc:v:76:y:2015:i:c:p:110-117
    DOI: 10.1016/j.mathsocsci.2015.04.006
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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, September.
    2. Corchon, Luis C. & Iturbe-Ormaetxe, Inigo, 2001. "A Proposal to Unify Some Concepts in the Theory of Fairness," Journal of Economic Theory, Elsevier, vol. 101(2), pages 540-571, December.
    3. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    4. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    5. Iturbe-Ormaetxe, Inigo & Nieto, Jorge, 1996. "On Fair Allocations and Monetary Compensations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 125-138, January.
    6. Laurence Kranich, 2009. "Measuring opportunity inequality with monetary transfers," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(4), pages 371-385, December.
    7. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    8. Koichi Tadenuma, 1996. "Trade-off between equity and efficiency in a general economy with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 445-450.
    9. Eric S. Maskin, 1987. "On the Fair Allocation of Indivisible Goods," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 11, pages 341-349, Palgrave Macmillan.
    10. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    11. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    12. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(4), pages 671-687.
    13. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    14. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    15. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    16. Thomson, William, 1982. "An informationally efficient equity criterion," Journal of Public Economics, Elsevier, vol. 18(2), pages 243-263, July.
    17. Christopher Chambers, 2007. "An ordinal characterization of the linear opinion pool," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 457-474, December.
    18. Philippe VAN PARIJS, 1990. "Equal Endowments as Undominated Diversity," Discussion Papers (REL - Recherches Economiques de Louvain) 1990034, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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