Endogenous population growth and the exploitation of renewable resources

Abstract

We consider a demo-economic model where the economy consists of two sectors (“hunting and farming' and 'industry'), and both sectors depend directly or indirectly on the exploitation of a renewable resource. The primary sector harvests a renewable resource (fish, corn or wood) which is used as the input into industrial production, the secondary sector of our economy. Labour is divided up between these two sectors under the assumption of competitive labour markets. A system of two nonlinear differential equations for the resources and the population is studied by phase space analysis. Using the Hopf bifurcation theorem, we obtain two different routes to limit cycles and prove numerically the existence of a stable Malthusian limit cycle. © 1994, Taylor & Francis Group, LLC. All rights reserved.