An outline of a theory of progressive individual income-tax functions

Summary

In sections 2 and 3 we gave a general outline of the requirements for a progressive income-tax function to be consistent, progressive and efficient. On the basis of the theoretical framework set up in the first three sections we then were able to present (sec. 4) and criticise (sec. 5) the socalled „traditional income-tax formula”, i. e. the income-tax function with a discontinuous marginal tax-rate function, which has been widely adopted by modern income-tax legislation.

In the second part of our paper (sec. 6–9) we outlined and discussed a proposed frame for a theory of progressive income-tax functions, resting on a generalized abatement-system with differentiable abatements. We indicated the conditions for both the consistency and progressiveness of the composed income-tax function [P. 6 and (8)], and moreover for its efficiency [P. 6 and (10)]. Examples for eligible tax- and abatement-functions were given in sec. 7; sec. 7.3 analysed the effect of the abatement-function upon the income-tax function proper. Sec. 8 highlighted the importance of the adjustment-parameter,ξ, as an automatic stabilizer and as a means of economic policy for the elimination of distortions in the structure of incomes, and sec. 9 revealed the usefulness of a differentiable income-tax function for the estimation of the total revenue from income-tax.

We were able to show that a (composed) differentiable income-tax function is in many respects superior to the traditional income-tax formula and could serve as a platform for further income-tax legislation.