Revisiting Sustainability Under Ecological Limits: A Dynamic Model of Capital Substitutability and the Case for Strong Sustainability

This paper develops a dynamic macroeconomic model to examine the long-term viability of economic growth under ecological constraints. The model integrates produced and natural capital in a CES production function, incorporates a logistic regeneration process, and introduces a nonlinear sustainability condition that penalizes ecological depletion near critical thresholds. We simulate four scenarios: a baseline, reduced extraction, enhanced regeneration, and a circular economy with declining extraction intensity. Results show that, even under high substitutability, natural capital depletion leads to eventual economic decline if ecological regeneration is insufficient. The baseline scenario follows an overshoot-and-collapse pattern, while improved ecological settings delay collapse and sustain output longer. Notably, the circular economy scenario prevents collapse entirely within the simulated horizon, highlighting the effectiveness of time-dependent efficiency gains. These findings challenge aggregate capital indicators and highlight the importance of ecological thresholds, dynamic feedbacks, and adaptive policy design. The model offers a unified and tractable framework to assess sustainability under biophysical limits and provides insights for policies that promote resource efficiency, ecosystem restoration, circular strategies, and long-term resilience.