Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths

Abstract

The proposition that limited natural resources provide a limit to growth and to the sustainable size of population is an old one. The natural resource that was the centre of the discussion in Malthus' day was land; more recently, some concern has been expressed over the limitations imposed by the supplies of oil, or more generally, energy sources, of phosphorus, and of other materials required for production. Those who predicted imminent doom in the nineteenth century were obviously wrong. Were they simply wrong about the immediacy of catastrophe, or did they leave out something fundamental from their calculations? There are at least three economic forces offsetting the limitations imposed by natural resources: technical change, the substitution of man-made factors of production (capital) for natural resources, and returns to scale. This study is an attempt to determine more precisely under what conditions a sustainable level of per capita consumption is feasible, to characterize steady state paths in economies with natural resources, and to describe the optimal growth path of the economy, in particular to derive the optimal rate of extraction and the optimal savings rate in the presence of exhaustible natural resouces. One of the interesting problems posed by the presence of exhaustible natural resources is that some of the basic concepts of growth theory, such as steady state and natural rate of growth , need to be re-examined. If, for instance, there are two unproduced factors, labour and natural resources, one of which is growing exponentially, the other of which is not growing at all, what is the natural rate of growth ? In conventional economic discussions, the long-run growth rate of the economy is determined simply by the natural rate of growth and is independent of the savings rate. We shall show that in economies with natural resources, efficient growth paths which differ with respect to savings rate also differ, even asymptotically, with respect to the rate of growth. The analysis of optimal growth paths presents certain technical difficulties, because there are two state variables (the stock of capital per man and the stock of natural resources per man) and two control variables (the rate of extraction of natural resources and the savings rate). Fortunately, by the appropriate choice of variables, the qualitative properties of the path can be completely described. Optimal growth paths for economies with only capital or with just natural resources have been examined elsewhere. Typically, a country begins with little capital and hence, in the former models, optimal growth is characterized by increasing consumption per capita. On the other hand, natural resources act much like a capital good; since the stock