Eugenio Peluso

Does less inequality among households mean less inequality among individuals

Consider an income distribution among households of the same size in which individuals, equally needy from the point of view of an ethical observer, are treated unfairly. Individuals are split into two types, the dominant and the dominated. We look for conditions under which welfare and inequality quasi-orders established at the household level still hold at the individual one. A necessary and sufficient condition for the Generalized Lorenz test is that the income of dominated individuals is a concave function of the household income: individuals of poor households have to stand more together than individuals of rich households. This property also proves to be crucial for the preservation of the Relative and Absolute Lorenz criteria, when the more egalitarian distribution is the poorest. Extensions to individuals heterogeneous in needs and more than two types are also provided.

A stochastic dominance approach to the measurement of discrimination

This note suggests a bridge between stochastic dominance (Rothschild and Stiglitz, 1970 [17], 1973 [18]), inequality measurement (Atkinson, 1970 [1]) and discrimination measurement (Gastwirth, 1975 [10]). Discrimination orderings are defined and illustrated through discrimination curves, in the same spirit as stochastic dominance analysis. The main result, which links the second order discrimination curve and the Gastwirth discrimination index, also generalizes the equivalence between Generalized Lorenz dominance and second order stochastic dominance.

On the (Sequential) Majority Choice of Public Good Size and Location

This article studies majority voting over the size and location of a public good when voters differ both in income and in their preferences for the public good location. Public good provision is financed either by a lump sum tax or by a proportional income tax. We analyze both the simultaneous and the sequential determinations of the public good’s size and location. We show that, while the choice of the type of public good follows the traditional median logic, the majoritarian determination of the taxation rate need not coincide with the preferences of a median income citizen. With lump sum financing, income heterogeneity plays no role and the sequential equilibrium consists of the median location together with the public good level most-preferred by the individual located at the median distance from the median. This policy bundle also constitutes an equilibrium with simultaneous voting in the special case of a uniform bivariate distribution of individuals’ income and location. With proportional taxation, there is no policy equilibrium with simultaneous voting. We offer a complete characterization of the equations describing the sequential equilibrium in the general case and we show why and how our results depart from those most-preferred by the median income individual located at the median distance from the median. We also compare these majority voting allocations with the socially optimal one.

Preserving dominance relations through disaggregation: the evil and the saint

This article investigates the circumstances in which stochastic dominance relations at any finite degree at the household level can be assumed to be preserved at the individual level. We find necessary and sufficient conditions on the common sharing function adopted by households to divide the cake among a “strong” and a “weak” individual. The sharing function which maps the household income into the outcome of the weak individual must belong to the class of utility functions which supports the stochastic order. In addition, the household must follow a compensating rule, meaning that the share of resources devoted to the weak individual increases with household income. Applications to fiscal federalism are also proposed.“All inequality is a source of evil - for by the inferior more is lost in the account of happiness than is gained by the superior”J. Bentham,First Principle preparatory to Constitutional Code, 1822.

The Cake-Eating Problem: Non-Linear Sharing Rules

Consider the most simple problem in microeconomics, a maximization problem with an additive separable utility function over bundles of two goods which provide equal sat- isfaction to an agent. Although simple, this framework allows for a very wide range of applications, from the Arrow-Debreu contingent claims case to the risk-sharing problem, including standard portfolio choice, intertemporal individual consumption, demand for in- surance and tax evasion. We show that any Engel curve can be generated through such a simple program and the necessary and suffi cient restrictions on the demand system to be the outcome of such a maximisation process. Moreover, we identify three classes of utility function that generate non-linear sharing rules. The gap between the two expen- diture shares increases in absolute, average or marginal terms with the total amount of wealth, depending on whether DARA, DRRA and convex risk tolerance are considered. The extension of the different results to the case of more than two goods is provided.