Nonrenewable Resource Allocation under Intertemporally Dependent Demand

This paper investigates the implications of an intertemporally dependent demand structure in the market for an exhaustible resource. The demand structure is derived endogenously in a partial equilibrium model where price-taking users combine the resource with capital to produce final output. It is shown that, when demand for the resource is modelled explicitly as a derived demand, the common assumption of an intertemporally independent sequence of instantaneous demand relationships is justified if there is a perfect rental market for capital equipment and there are no internal adjustment costs associated with either adding to the stock of equipment or subtracting from it. In the more realistic case where changes in capital stocks incur adjustment costs, the time-profile of demand is determined by the underlying programme of (dis)investment. In this case, changes in the resource price over time induce a lagged demand response. The paper goes on to study the properties of an intertemporal competitive equilibrium, with emphasis on the demand structure with underlying adjustment costs. Agents are assumed to transact on perfectly functioning forward markets, so expectations about the resource price are always fulfilled a post, The principal results to emerge from the analysis are that the resource utilization rate declines to zero in the long term as processes that use the resource in question are replaced by others; however, the precise time-path of substitution depends sensitively on the nature of adjustment costs. For example, if adjustment costs exhibit non-convexities, substitution away from processes that use the resource occurs in pulses, in contrast to the smooth substitution programme under convex adjustment costs.