Parfit’s Repugnant Conclusion stipulates that under total utilitarianism, it might be optimal to choose increasing population size while consumption per capita goes to zero. We evaluate this claim within a canonical AK model with endogenous population size and a reduced form relationship between demographic and economic growth. First we characterize the optimal solution paths for any capital dilution function. Second, we prove that while the Repugnant Conclusion can never occur for realistic values of intertemporal substitution in the traditional linear dilution model, it does occur when population growth is linked to economic growth via an inverted U-shaped relationship. Copyright Springer-Verlag 2013

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value function of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. Despite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.

This paper studies the different mechanisms and the dynamics through which demography is channeled to the economy. We analyze the role of demographic changes in the economic development process by studying the transitional and the long-run impact of both the rate of population growth and the initial population size on the levels of per capita human capital and income. We do that in an enlarged Lucas–Uzawa model with intergenerational altruism. In contrast to the existing theoretical literature, the long-run level effects of demographic changes, i.e. their impact on the levels of the variables along the balanced growth path, are deeply characterized in addition to the more standard long-run growth effects. We prove that the level effect of the population rate of growth is non-negative (positive in the empirically most relevant case) for the average level of human capital, but a priori ambiguous for the level of per capita income due to the interaction of three transmission mechanisms of demographic shocks, a standard one (dilution) and two non-standard (altruism and human capital accumulation). Overall, the sign of the level effects of population growth depends on preference and technology parameters, but numerically we show that the joint negative effect of dilution and altruism is always stronger than the induced positive human capital effect. The growth effect of population growth depends basically on the attitude to intergenerational altruism and intertemporal substitution. Moreover, we also prove that the long-run level effects of population size on per capita human capital and income may be negative, nil, or positive, depending on the relationship between preferences and technology, while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long term.

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