Abstract
A classical problem in public finance is: when does equal sacrifice imply progressive taxation? Suppose that a tax schedule imposes equal sacrifice on all taxpayers in loss of utility, and that this property is preserved under re-indexing of the schedule. Then the utility function must exhibit constant relative risk aversion, i.e. it must be logarithmic or a power function. If equal sacrifice relative to such a utility function holds for all taxable incomes, and if tax rates do not exceed 100 percent, then the degree of relative risk aversion must be at least unity, and the tax must be nonregressive.
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