Sustainable per capita consumption under population growth

We establish two investment rules for maximal constant per capita consumption under exogenous population growth, one in terms of total capital stocks and the other in terms of per capita capital stocks. Both rules show the importance of the development of future population growth. The investment rules are illustrated in the one-sector model of capital accumulation, the DHSS model of capital accumulation and resource depletion, and the Stollery-d'Autume-Schubert model in which natural capital provides amenities. Application to recent empirical evidence indicates that actual genuine savings might be insufficient to sustain per capita consumption, when future population growth is combined with a large per capita consumption-wage gap.(c) 2023 Elsevier B.V. All rights reserved.