Dominique Thon

Redistributive properties of progressive taxation

Abstract This note generalizes an equivalence between progressive taxation and the Lorenz-dominance ordering. The results are quite general, allowing for both non-differentiable tax functions and negative taxes.

Second-Degree Stochastic Dominance Decisions and Random Initial Wealth with Applications to the Economics of Insurance

It is known that if random prospect Y stochastically dominates prospect X by the second degree, then all risk-averse agents prefer to hold Y and some random initial wealth Z rather than X and the same initial wealth Z, if Z is statistically independent of both X and Y. We give more general conditions for the invariance of the stochastic dominance ordering to initial wealth to hold: that X be more positively dependent on Z than Y is, and that either X and Z or Y and Z be positively dependent. Applications to the choice of an insurance deductible and of insurance coverage are given.

Dalton transfers, inequality and altruism

Abstract.This paper characterizes the set of income allocations attainable through a sequence of equalizing decentralized pair-wise transfers that each preserve the original ranking of the donor and the recipient. This kind of transfer has been considered in the literature on income distribution following Dalton’s famous 1920 article, and the concept is often attributed to him. We provide a description of the set of allocations attainable through a sequence of such transfers. This paper argues that, although those transfers are often mentioned in the literature on income inequality, they do not really play any role there. It also argues that such a transfer concept is, on the other hand, of great interest in modeling altruism and its consequences.

The value of perfect information in a simple investment problem

Abstract The paper studies the value of obtaining perfect information in the problem of investing a given income in basic contingent claims. The class of agents for whom the value of information is monotone in the worth of the contingent claims and their riskiness are identified. Conditions which make the value of information and the willingness to pay for perfect information maximal are also given.

Stochastic dominance and Friedman-Savage utility functions

Abstract Two-way stochastic dominance is defined as the ordering corresponding to the unanimous ranking given by all risk-averse and risk-loving agents. This new ordering of random incomes is shown to have an intuitive economic interpretation and to be a potential substitute for first degree dominance. Two-way dominance is shown to be closely related to a class of utility functions which has been studied by Friedman and Savage. The analysis draws on the geometry of cone orderings, a technique which yields rather directly the price characterization of random variables efficient with respect to two-way dominance.

Alternative petroleum taxation systems. Comparisons under uncertainty

Abstract Consider a profit tax, a royalty and a fixed fee. Conventional wisdom holds that at constant expected post-tax payoff, a risk-averse agent will prefer to be subjected to a profit tax rather than to a royalty and to the latter rather than to a fixed fee. The paper reconsiders this ranking by rigorously approaching the problem in an expected utility framework and derives sufficient conditions for unambiguous ranking of the alternative tax systems.

Second degree Pareto dominance

We present and discuss a binary relation aimed at the study of the re-distribution of income. We characterize, in a number of ways, the set of income allocations that can be reached from an initial allocation through a sequence of pair-wise equalizing transfers, where the sequence contains no flow of income from any donor to anyone else who ends up strictly richer than this donor himself ends up at the outcome of the entire sequence.

Equity in dyads:the notion of more equitable

The idea that equity has to do with allocating, say, income, between different actors proportionately to their inputs, deserts, or needs goes back at least to Aristotle, and has been the object of a number of modern examinations, reformulations, and refinements. We base our analysis on a partial order and are concerned with the de.nition and properties of ‘a step in the direction of more equity’ when the total to be allocated is constant. While this approach to equity seems to be novel, we obtain results that are remarkably consistent with those of earlier work.

Transfer principles and relative inequality aversion a majorization approach

Abstract This paper characterizes two preorders over vectors, representing here income distributions, which, for the case of an order-preserving additive welfare function W =∑ 1 n u ( x i ), correspond to the increasing concave functions u which are more concave than u ( x )=ln x and than u ( x )=−1/ x , respectively. We provide a characterization of those W functions that is quite distinct from the one recently provided by Fleurbaey and Michel, Mathematical Social Sciences , 2001. The two sets of results are shown to be complementary.

Reallocations of Income Between Heterogeneous Units

This paper extends the standard redistribution axioms to the case where the income units differ for example by size, deserve or need. It is essentially based on a generalization of Muirheads Lemma. The standard case where all units are alike falls off as a particular case.