Can future generations achieve living standards at least equal to those of the present? We analyse this question in overlapping-generations (OLG) models, both a small analytical and a calibrated version, where natural capital is introduced following Dasgupta (2021). In standard OLG models, dynamic efficiency requires that the market rate of return exceeds population growth, r > n. With natural capital, the condition becomes r > n+e, where e reflects externalities from the natural capital stock. Economies may therefore satisfy r > n yet remain dynamically inefficient. Along the competitive equilibrium path, degrading natural capital can trigger tipping points in production and welfare, undermining intergenerational sustainability