Growth on a finite planet: resources, technology and population in the long run

We study the interactions between technological change, resource scarcity and population dynamics in a Schumpeterian model with endogenous fertility. We find a steady state in which population is constant and determined by resource scarcity while income grows exponentially. If labor and resources are substitutes in production, income and fertility dynamics are stable and the steady state is the global attractor of the system. If labor and resources are complements, income and fertility dynamics are unstable and drive the economy towards either demographic explosion or collapse. We calibrate the model numerically to match past US data on fertility and land scarcity, obtaining future scenarios for the current century and quantifying the response of fertility and productivity to exogenous shocks.