Recursive Utility and Thompson Aggregators, Ii: Uniqueness of the Recursive Utility Representation

We reconsider the theory of Thompson aggregators proposed by Mari-nacci and Montrucchio [30]. We demonstrate the Koopmans equation has a unique utility function solution given a Thompson aggregator. Uniqueness holds only on the interior of the commodity spaces positive cone. Our proof veries the Koopmans operator is a u0 concave operator. We verify this using general sufficient conditions due to Liang, et al [28]. Previous published results apply variants of the contraction mapping theorem to the space of possibly utility functions endowed with the Thompson metric. Concave operator methods work on the possible utility function space with its norm topology. Our approach combines order and metric structures to demonstrate uniqueness differently than in the existing literature.