The Pareto Comparisons of a Group of Exponential Discounters

Agents with different discount factors disagree about some intertemporal trade-offs, but they will also agree sometimes. We seek to understand precisely the nature of their agreements and disagreements. A group of agents is identified with a set of discount factors. We characterize the comparisons that a given interval of discount factors will agree on, including what all discount factors in the interval [0, 1] will agree on. Our result is analogous to how all risk-averse and monotone agents agree on mean-preserving spreads. Motivated by a maxmin representation, we also characterize the comparisons that are consistent with some set of discount factors, when the set is not known or exogenously given. In other words, we describe the Pareto comparisons that are consistent with a society, or group, of exponentially discounting agents.