In the history of economic thoughts the problem of a just tax rate structure has played an important role. The paper reconsiders the discussions of the last two centuries and sheds additional light on the concrete tax schedules using the more recent methods of tax theory. Even if the substitution effects which play an important role in the theory of optimal taxation are neglected, the slope in the diminishing marginal utility of income causes tax rate structures reaching from accelerated progression to delayed regression. Interestingly the principle of equal relative sacrifice combined with a Bernoulli utility function yields a delayed progression, which is connected with a negative income tax.
income tax sacrifice principle tax rate schedule cardinal utility function