Distinct Solutions to Koopmans' Equation for Thompson Aggregators Represent Distinct Preference Orders

Thompson aggregators generate recursive utility functions as solutions to Koopmans' functional equation. Multiple solutions may occur when the underlying commodity space is the positive cone of the space of bounded real-valued consumption sequences. Consider the case of extremal solutions: distinct least and greatest solutions exist. We show that these recursive utility functions represent distinct preference orders on the commodity space. We discuss the significance of this observation for uniqueness theory and optimal growth modeling with a Thompson aggregator based objective function