Normative economics is generally opposed to positive economics. Positive studies aim at understanding the properties of economic systems, thus elucidating here the structure of the set of tax equilibria. Normative studies are concerned with the welfare effects of economic choices, here with the consequences, for the agents' welfare of different tax policies. Normative studies are not opposite but complementary and in fact logically consecutive to positive studies: the results of positive analysis are normally a prerequisite to a comprehensive welfare assessment. This logical order is the one adopted here. The study of the normative economics of taxation will utilize our understanding of the positive economics of taxation gained in the previous chapter.

The present chapter proceeds as follows:

Sections 3.1 and 3.2 are devoted to the welfare analysis of tax equilibria when at first only small changes are considered. The title ‘tax reform’ reflects both the normative emphasis of the analysis and the fact that small tatonnement changes - rather than the large once and for all changes suggested by optimal taxation - are a priori considered. These first two sections can indeed be viewed as extensions in the normative direction of the positive study of section 2.2, chapter 2; they provide a comprehensive welfare analysis of a neighbourhood of a given tax equilibrium whose structure has been ascertained in the just recalled ‘positive’ investigation. The third section, 3.3, gives up the purely local viewpoint by examining how the infinitesimal changes suggested in the previous subsections can be linked along a finite path of tax reform. This subsection is more technical and can be, at first, skipped by the reader.

Section 3.4 continues the discussion of tax reform in two directions. First, it transposes the analysis of tax reform of sections 3.1 and 3.2 to the case where the welfare of individual agents can be aggregated into a social welfare function. In subsection 3.4.1, a more specific algorithm of tax reform - of the gradient projection type - is suggested; a ‘Musgravian’-like interpretation of its instructions is proposed in subsection 3.4.2.