For a Neoclassical growth model, the literature highlights that exponential discounting
is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount
rate decreases asymptotically towards a positive value. Conversely, in this paper a zero longrun
value allows a solution without stagnation. We prove that a less than exponential but
unbounded growth can be attained, even without technological progress. The growth rate of
consumption decreases asymptotically towards zero, although so slowly that consumption
grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state
which saving rate matches the intertemporal elasticity of substitution and the speed of
convergence towards this equilibrium are analyzed.
