Non-linear dynamics of population and natural resources: The emergence of different patterns of development

This paper studies the long-term dynamic interaction between the exploitation of natural resources and population growth. Brander and Taylor [Brander, J.A. and Taylor, M.S. (1998) “The Simple, Economics of Easter Island: a Ricardo–Malthus Model of Renewable Resource Use”. American Economic Review, 88 (1) 119–138.] started a sequence of papers which sought to deduce from historical and archaeological studies some stylized links between ecological and economic systems. In this strand of literature all the services of the natural environment are aggregated in an ecological complex which is characterized by a simple logistic dynamics. Given such assumptions, these models show a unique long-term steady state. The aim of this paper is to obtain a more general framework that could account for the heterogeneity of environmental development paths followed by past societies. Two new assumptions are introduced: i) the disaggregation of the ecological complex into two different resources; ii) irreversibility — namely, an inexorable tendency to exhaustion when the renewable resource stock is below a certain threshold. Analysis of the dynamic properties of the system shows a multiplicity of steady states which makes it possible to consider the effects of technical progress, cultural and climate changes on the resilience of the existing development path.