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

Scholarly Edition

We study the interactions between technological change, resource scarcity and population dynamics in a Schumpeterian model with endogenous fertility. There exists a pseudo-Malthusian equilibrium in which population is constant and income grows exponentially: 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. If labor and resources are substitutes in production, income and fertility dynamics are self-balancing and the pseudo-Malthusian equilibrium is the global attractor of the system. If labor and resources are complements, income and fertility dynamics are self-reinforcing and drive the economy towards either demographic explosion or human extinction. Introducing a minimum resource requirement, we obtain a second steady state implying constant population even under complementarity. The standard result of exponential population growth appears as a rather special case of our model.

### Duke Authors

### Cited Authors

- Peretto, PF; Valente, S

### Published Date

- June 30, 2011