Intertemporal Depletion of Resource Sites by Spatially Distributed Users

Abstract

Mineral deposits and other exhaustible resources are scattered around the globe-as are their users. Yet the theory for analyzing depletion of such resources assumes that all resource sites and all users are located in the same place. When applying the theory, therefore, one is forced to disregard what often seems to be an important real-world consideration. Our purpose here is to generalize Harold Hotelling's (1931) theory of exhaustible resources to accommodate situations in which resource sites and their users are spatially distributed. Our analysis has many applications. It can be applied to a conventional exhaustible resource like oil. Alternatively, it can be applied to an unconventional exhaustible resource like scarce landfill space.' Shipments of solid waste to landfills in other states or countries have become a prominent public policy issue (Eduardo Ley et al., 2000). Finally, our analysis can be applied in situations where the space reflects not geographical location but characteristics of the resource (e.g., the sulfur content, hardness, and so forth, of coal) which users find distinctive.2 Only two theoretical papers in resource economics have introduced spatial considerations.3 Jean-Jacques Laffont and Michel Moreaux (1986) studied the extraction of resources from sites located along a line segment with all users at one end. Charles Kolstad (1994) was the first to consider spatially distributed users. In his formulation, consumers are distributed uniformly along a line segment with resource sites at each end. Kolstad's approach, although innovative, requires that the set of users be parti-