We analyze an endogenous growth model considering agents with an
isoelastic utility. Preferences are characterized by a utility affected
by a negative externality, and a level of impatience which decays with
the time distance from the present. Agents who cannot commit the actions
of their future selves, play a game against them. The stationary
equilibrium of this game defines a balanced growth path with a slower
growth when played by subsequent central planners than when played by
decision makers in the market economy. First, we prove that the fast
growing market economy implies higher welfare if the negative
externality is small, while the centralized economy is welfare improving
above a given threshold for the externality (obtained for a specific
family of non-constant discount functions). Secondly, we observe that
this threshold increases with the elasticity of intertemporal
substitution in consumption. Therefore, the greater this elasticity the
more likely it is that the externality lies below this threshold, where
policy interventions would not be adequate. Finally, as one would
expect, the range of values of the externality for which the market
equilibrium provides higher welfare 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.
