Discounting under Disagreement

A group of agents disagree about the appropriate inter temporal preferences to use when exploiting a common productive resource. They thus delegate decision making to a social planner who allocates consumption efficiently across heterogeneous individuals and over time. We define `policy equivalent' representative agents as those agents whose optimal consumption plan reproduces the optimal aggregate consumption plan of the group, and find conditions that must be satisfied by all such representative preferences. We then show that any policy equivalent representative agent must have a rate of time preference that approaches the lowest rate in the population asymptotically. We characterize the term-structure of separable policy-equivalent preferences in the the case of common felicity functions, and show that if the felicity function is iso-elastic, and time preferences are gamma distributed, representative agents must have hyperbolic time preferences. This gives a normative significance to such preferences, which have hitherto been seen as an entirely behavioral phenomenon. Finally, we examine the temporal stability of representative preferences if the planner cannot commit to inter temporal allocations. We show that while consumption plans are not time consistent, they are renegotiation proof, and thus stable under proposals for change. We argue that this feature has normative appeal for public decision-making.