7. Bivariate Income Distributions: Horizontal Equity and Taxation.

I propose an excursion through few mathematical notions arising in inequality measure-ment and related matters like for instance welfare or poverty measurement, horizontal equity and progressivity in taxation. Inequality measurement is an important branch of applied welfare economics. This area of public/welfare economics is devoted to the development of analytical tools to evaluate the level of inequality attached to the distribution of one or several resources (like for instance, income, wealth, health,...) and the application of these notions to real data. In this lecture notes, I will mostly devote my attention to the simplest setting. The ingre-dients of this setting will consist of a nite population N of n units (individuals, households, groups,...) and the distribution of a single divisible and transferable resource say income. An income distribution will be then a vector x = (x1; x2;::::; xn) 2 <n+. In this simple framework, each unit is identied by a number (say its social security number). In a more complicated setting, where the population would display some heterogeneity, relevant for the problem under consideration, we would have to describe explicitely the characteristics of the units. Any comparison of two income distributions rests on interpersonal comparisons of utilit