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Abstract
In determining the optimal redistribution of a given population’s income, we ask which
factor is more important: the social planner’s aversion to inequality, embedded in an
isoelastic social welfare function indexed by a parameter alpha, or the individuals’ concern
at having a low relative income, indexed by a parameter beta in a utility function that is a
convex combination of (absolute) income and low relative income. Assuming that the
redistribution comes at a cost (because only a fraction of a taxed income can be transferred),
we find that there exists a critical level of beta below which different isoelastic social
planners choose different optimal allocations of incomes. However, if beta is above that
critical level, all isoelastic social planners choose the same allocation of incomes because
they then find that an equal distribution of incomes maximizes social welfare regardless of
the magnitude of alpha.