Optimal Population and Sustainable Growth Under Environmental Constraints

This paper develops a dynamic optimal growth model that integrates population dynamics, economic activity, and environmental constraints to investigate sustainable long-run development. The model incorporates capital accumulation, consumption, pollution abatement, and a demographic equation where population growth responds negatively to pollution. A critical environmental threshold is imposed, beyond which population growth collapses. Calibrations with plausible parameter values indicate that the sustainable steady state supports a global population of approximately 3–5 billion people, a level consistent with high per capita consumption and stable environmental conditions. The optimal policy involves devoting about one-third of output to pollution abatement, which is sufficient to stabilize pollution below the safe threshold without excessive economic costs. At this equilibrium, the economy achieves high consumption per person, stable capital, and environmental balance, while avoiding overshooting and collapse 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. The findings suggest that sustainable development requires actively managing population dynamics and abatement policies to ensure both ecological integrity and long-term economic prosperity.