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Title:Measuring inequality without the Pigou-Dalton condition PDF Logo
Authors:Chateauneuf, Alain
Moyes, Patrick
Issue Date:2005
Series/Report no.:Research Paper, UNU-WIDER, United Nations University (UNU) 2005/02
Abstract:Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials, deprivation and satisfaction quasiorderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model – the so-called expected utility model in the theory of risk – does not permit one to make a distinction between the views embedded in the differentials, deprivation, satisfaction and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99–115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials, deprivation and satisfaction quasi-orderings, respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.
Subjects:income differentials
Lorenz dominance
progressive transfers
expected utility
generalized Gini social welfare functions
Document Type:Working Paper
Appears in Collections:WIDER Research Papers, United Nations University (UNU)

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