We analyze an endogenous growth model with non-constant discounting and a negative externality of growth on utility. With a decreasing rate of impatience, time-consistent agents anticipate the behavior of their future selves and play a game against them. The strategic interaction between subsequent central planners implies slower growth than the market solution, where the externality is not internalized. Indeed, growth can be excessively slow from a social welfare standpoint. Contrary to exponential discounting, under non-constant discounting we prove that the market equilibrium is Pareto-improving provided that the negative externality is sufficiently small. Thus, policy interventions would only be meaningful when the externality surpasses a given threshold. For a specific family of non-constant discount functions we observe that the range for the intensity of the externality compatible with a Pareto-improving market solution widens with the elasticity of intertemporal substitution in consumption. Similarly, this range also widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.
Published May 2019 , 27 pages