The Possibility of Ordering Infinite Utility Streams

This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Svensson to a characterization theorem and we provide characterizations of all strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. In addition, infinite horizon extensions of leximin and of utilitarianism are characterized by adding an equity preference axiom and finite translation-scale measurability, respectively, to strong Pareto and finite anonymity.

Infinite-Horizon Choice Functions

We analyze infinite-horizon choice functions within the setting of a simple linear technology. Time consistency and efficiency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes-Sen, Pigou-Dalton, and resource monotonicity. We show that Suppes-Sen and Pigou-Dalton imply that the consumption and inheritance functions are monotone with respect to time—thus justifying sustainability—while resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource. Examples illustrate the characterization results.