Discussion of the issue of the welfare effects of direct, as compared with indirect, taxes have been greatly clarified by the recent contributions of Mr. Little and Professor Friedman. Both of them show that the usual method of using indifference curves to prove the superiority of income tax over sales tax makes “no overt reference to marginal costs. Yet it is well known that nothing can be proved without some such reference.” They employ an alternative mode of analysis which is designed to take account of conditions of cost of production.

Before the appearance of their articles, Professor Boulding showed the comparative welfare effects of proportional, progressive, and regressive income taxes by the use of indifference curves. His conclusion is that, even if the same amount of revenue is exacted, an individual is better off under a proportional than under a progressive income tax and still better off under a regressive one. Friedman questions the validity of Boulding's result because he thinks Boulding is one of those who base their arguments on a fallacious proof, although Friedman does not set out his criticism in detail. Since Boulding's results, if valid, are of great significance and since the weak point of his analysis cannot be derived directly from Friedman's contributions, it is the purpose of this paper to show the limitations of Boulding's conclusion, which, if known, would deprive it of much of its generality and usefulness.