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study, we reconsider the effect of variable transformations on the
redistribution of income. We assume that the density function is continuous. If
the theorems should hold for all income distributions, the conditions earlier
given are both necessary and sufficient. Different conditions are compared. One
main result is that continuity is a necessary condition if one demands that the
income inequality should remain or be reduced. In our previous studies, of tax
policies the assumption was that the transformations were differentiable and
satisfy a derivative condition. In this study, we show that it is possible to
reduce this assumption to a continuity condition.
In earlier papers, classes of transfer policies have been studied and maximal and minimal Lorenz curves ？？obtained. In addition, there are policies belonging to the class with given Gini indices or passing through given points in the ？plane. In general, a transformation ？describing a realistic transfer policy has to be continuous. In this paper the results are generalized and the class of transfer policies？？is modified so that the members may be discontinuous. If there is an optimal policy which Lorenz dominates all policies in the class, it must be continuous. The necessary and sufficient conditions under which a given differentiable Lorenz curve ？can be generated by a member of a given class of transfer policies are obtained. These conditions are equivalent to the condition that the transformed variable ？stochastically dominates the initial variable X. The theory presented is obviously applicable in connection with other income redistributive studies such that the discontinuity can be assumed. If the problem is reductions in taxation, then the reduction for a taxpayer can be considered as a new benefit. The class of transfer policies can also be used for comparisons between different transfer-raising situations.