Rigidity of Scattering Lengths and Traveling Times for Disjoint Unions of Convex Bodies

Obstacles $K$ and $L$ in $R^d$ ($d\geq 2$) are considered that are finite disjoint unions of strictly convex domains with $C^3$ boundaries. We show that if $K$ and $L$ have (almost) the same scattering length spectrum, or (almost) the same traveling times, then $K = L$

Relative advantage, queue jumping, and welfare maximizing wealth distribution

Suppose individuals get utilities from the total amount of wealth they hold and from their wealth relative to those immediately below them. This paper studies the distribution of wealth that maximizes an additive welfare function made up of these utilities. It interprets wealth distribution in a control theory framework to show that the welfare maximizing distribution may have unexpected properties. In some circumstances it requires that inequality be maximized at the poorest and richest ends of the distribution. In other circumstances it requires that all wealth be given to a single individual. JEL Categories: C61, D60wealth distribution, positional goods, status, inequality, relative advantage.

Geometry and marginals

AbstractIt is known that observations of a real-valued random variable defined over a smooth manifold M can be used to make inferences about M, at least when M is a curve or surface. We refine and extend the underlying asymptotic results and remove the condition dimM⩽2. New examples of nonsmoothness in marginals are described in detail for dimM=3,4, and methods are given for calculations in general