Beyond the Horizon: Attainability of Pareto Optimality when the Indefinite Future Matters

In this paper we study the attainability of Pareto optimal allocations in infinitedimensional exchange economies where agents have utility functions that value consumption at infinity. Such a model can be used to model economic settings where the indefinite future matters. The commodity space that we use is the space of all convergent sequences. We derive a necessary and sufficient condition for the attainability of the Pareto optimal allocations, which states that, for each pair of consumers, the ratio of the weights they place on utility in finite time periods should converge to the ratio of their utility weights at infinity. This, in turn, implies that efficiency can only be attained if consumers’ valuations of time are very similar. We extend the model to include consumers with Rawlsian preferences and find that this does not change the attainability of Pareto optimal allocations.