Aggregation of heterogeneous time preferences

We examine an economy whose consumers have different discount factors for utility, possibly not exponential. We characterize the properties of efficient allocations of resources and of the shadow prices that would decentralize such allocations. We show in particular that the representative agent has a decreasing discount rate when, as is usually posited, all of a group's members have a constant discount rate and decreasing absolute risk aversion preferences. We also identify conditions that lead the representative agent to have a rate of impatience that decreases with gross domestic product per capita.