When incomes are exogenously given, a progressive tax structure reduces inequality in the sense that the Lorenz curve of after tax incomes is nowhere below that of before tax incomes whatever the circumstances as it was shown by U. Jakobsson (Journal of Public Economics 5 (1976), 161-168) The...

We provide a characterization of the generalised satisfaction - in our terminology nondeprivation - quasi-ordering introduced by S.R. Chakravarty (Keio Economic Studies 34 (1997), 17-32) for making welfare comparisons based on the absence of deprivation. We show that the non-deprivation...