The optimum growth rate for population under critical-level utilitarianism

We characterize optimal consumption, capital, and population growth of a production economy under critical-level utilitarianism. First, we show that neither classical utilitarianism nor average utilitarianism can avoid a corner solution for the population growth rate, in that under the former, population grows at the maximum speed (the so-called repugnant conclusion) while under the latter, it grows at the minimum. Second, we show that critical level utilitarianism yields an interior solution for the population growth rate provided the critical level belongs to a positive, open interval. Finally, we characterize the transition to the steady state and perform comparative dynamics analysis.