Optimal Population and Sustainable Growth Under Environmental Constraints

This paper develops a dynamic optimal growth model integrating population, economic activity, and environmental constraints to investigate sustainable long-run development. The model incorporates capital accumulation, consumption, pollution abatement, and an endogenous demographic equation in which population growth responds negatively to pollution. A critical environmental threshold is imposed beyond which population growth collapses. Calibrating the model with plausible parameter values indicates that a sustainable steady state can support a global population of approximately 5 billion, a level consistent with high per capita consumption and stable environmental conditions. The optimal policy entails devoting roughly one-third of output to pollution abatement, which is sufficient to stabilize pollution below the safe threshold without imposing excessive economic cost. In this equilibrium, the economy achieves high consumption per person, a stable capital stock, and environmental balance, thereby avoiding overshoot and collapsing scenarios. The results highlight the trade-off between economies of scale and environmental limits. Larger populations can stimulate production and innovation but risk unsustainable pollution levels, whereas smaller populations allow higher per capita welfare within ecological boundaries. These findings suggest that achieving global sustainability requires balancing population size, consumption, and ecological limits through effective pollution abatement.