Discounting and altruism to future decision-makers

Is discounting of future decision-makers' consumption utilities consistent with “pure” altruism toward those decision-makers, that is, a concern that they are better off according to their own, likewise forward-looking, preferences? It turns out that the answer is positive for many but not all discount functions used in the economics literature. In particular, “hyperbolic” discounting of the form used by Phelps and Pollak (Rev. Econ. Studies 35 (1968) 201) and Laibson (Quart. J. Econ. 112 (1997) 443) is consistent with exponential altruism towards future generations. More generally, we establish a one-to-one relationship between discount functions and altruism weight systems, and provide sufficient, as well as necessary, conditions for discount functions to be consistent with pure altruism.