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# Single Crossing Lorenz Curves and Inequality Comparisons

## Author

Listed:
• Thibault Gajdos

() (CREST - Centre de Recherche en Économie et Statistique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique, EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

## Abstract

Since the order generated by the Lorenz criterion is partial, it is a natural question to wonder how to extend this order. Most of the literature that is concerned with that question focuses on local changes in the income distribution. We follow a different approach, and define uniform $\alpha$-spreads, which are global changes in the income distribution. We give necessary and sufficient conditions for an Expected Utility or Rank-Dependent Expected Utility maximizer to respect the principle of transfers and to be favorable to uniform $\alpha$-spreads. Finally, we apply these results to inequality indices.

## Suggested Citation

• Thibault Gajdos, 2004. "Single Crossing Lorenz Curves and Inequality Comparisons," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086028, HAL.
• Handle: RePEc:hal:cesptp:halshs-00086028
DOI: 10.1016/S0165-4896(03)00078-7
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00086028
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File URL: https://halshs.archives-ouvertes.fr/halshs-00086028/document

## References listed on IDEAS

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Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
2. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke.
3. Paul Makdissi & Stéphane Mussard, 2008. "Decomposition of s-concentration curves," Canadian Journal of Economics, Canadian Economics Association, vol. 41(4), pages 1312-1328, November.
4. Uberti, Pierpaolo & Figini, Silvia, 2010. "How to measure single-name credit risk concentrations," European Journal of Operational Research, Elsevier, vol. 202(1), pages 232-238, April.
5. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.

### Keywords

Inequality measures; Intersecting Lorenz Curves; Spreads;

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