Transfer Policies with Discontinuous Lorenz Curves

In earlier papers, classes of transfer policies have been studied and maximal and minimal Lorenz curves L( p) obtained. In addition, there are policies belonging to the class with given Gini indices or passing through given points in the ( p, L) plane. In general, a transformation h( x) describing a realistic transfer policy has to be continuous. In this paper the results are generalized and the class of transfer policies {h( x)} 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 L( p) 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 Y = h(X ) 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.