Renewable Resource And Capital Accumulation Under Uncertainty

An economy endowed with a renewable natural resource and physical capital is considered in order to examine the characteristics of possible transformation from natural to man†made capital, as a potential means of surviving over long periods of time if the natural resource may be depleted or fall short of certain sustainable levels. Natural resource together with physical capital is utilized to produce a commodity that is either to be sold in a market to earn sales revenue or invested to accumulate physical capital. The reserve size of resource and the production technology are both subject to uncertainties that are modeled by Wiener processes. The Wiener process is used to express the intrinsic nature of uncertainty for a long planning horizon such as on natural resources, in which distant futures are more difficult to foresee than the near future. It is shown that there exists a steady†state equilibrium in this economy under certainty and that, under some plausible conditions, the expected rate of change in resource harvest over time under uncertainty is less than the rate under certainty, while that of product sales is not affected by uncertainty.