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.