On Progressivity, Regressivity, and Proportionality: A Graphical Approach to the Teaching of the Income Tax Structure

Abstract

Adopting the geometric concepts of a tangent line and a secant ray allows for determining the curvature (convex, concave, or linear) and the behavior of the marginal and average tax rates of an income increasing tax function. Such information helps to determine whether the tax function is progressive, regressive, or proportional, as well as the possibility that it pro-pends to equity in the distribution of the social tax burden. Thus, several issues of public policy can be rigorously analyzed specifying different income tax functions that satisfy determinate graphical shapes, circumventing the need to use the traditional approach of differential calculus.