Non-Renewable Resource Supply: Substitution Effect, Compensation Effect, and All That

The interaction of supply and demand is at the root of market and other equilibria. Yet no systematic synthetic treatment of non-renewable resource supply exists; equilibrium analyses or welfare statements usually are formulated without any systematic decomposition into supply and demand. In this note, we examine the supply decision of individual non-renewable resource suppliers facing given prices. We establish instantaneous restricted (fixed reserves, treated as capital) and unrestricted supply functions. We decompose the effect of a price change into an intertemporal substitution effect and a stock compensation effect. The later arises when the stock of reserves to be extracted is endogenous. We show that the substitution effect always dominates so that a price increase at some date always causes supply to decrease at all other dates. Thus, despite the formal resemblance of resource supply over the time space with demand over the spectrum of goods, there is no such thing as a possible complementarity between resources extracted at different dates. Yet, as this theory of non-renewable resource supply makes clear, this is what researchers seeking exceptions to the green paradox are trying to identify. Nor is there any peculiarity similar to the Giffen paradox or to the inferior good paradox in resource supply. Besides unifying the treatment of conventional good supply and non-renewable resource supply, this theoretical exercise also shows how to avoid supply aggregation problems that make several existing results or modeling approaches questionable. The properties, first established within a parsimonious model, are shown to hold in a very general setup.