Endogenous growth, population growth and the repugnant conclusion

This paper studies the impact of endogenous population change on economic growth, analyzing the simplest optimal endogenous growth model, an AK type model, driven by human capital accumulation. We show that in steady state both demographic change and economic growth are constant, but the rate of these growth can be positive, negative or null accordingly to parameter values. Population dynamics is determined by the difference between the stationary fertility rate and the exogenous mortality rate: if this is positive population size indefinitely increases, otherwise it reaches a stationary level, which can be positive (if the difference is null) or null (if it is negative). If fertility is strictly lower than mortality, population size will constantlydecrease in finite time and we end up with a complete collapse of the economy, characterizedby the total extinction of the population. We also analyze the problem of optimal populationsize and its relationship with growth. The seminal work of Parfit (1984) suggests that totalutilitarianism leads to increase population size indefinitely, even if it the average welfare tendsto zero. We show that in our model economy, under certain parametric conditions, the repugnant conclusion holds; in particular, this happens when consumption growth is negative and the stationary fertility rate is higher than the exogenous mortality rate.