Growth on a Finite Planet: Resources, Technology and Population in the Long Run

We characterize the interactions between technological change, natural resource scarcity and population dynamics in a Schumpeterian model with endogenous fertility choices. We show that there exists a pseudo-Malthusian equilibrium in which population is constant and income grows at a constant rate: the equilibrium population level is determined by resource scarcity but is independent of technology. The stability properties are driven by (i) the income reaction to increased resource scarcity and (ii) the fertility response to income dynamics, and ultimately depend on whether labor and resources are complements or substitutes in production. Under substitutability, the pseudo-Malthusian equilibrium is a global attractor. Under complementarity, population follows diverging paths of explosion or implosion.