THE TIME PATH OF SCARCITY RENT IN THE THEORY OF EXHAUSTIBLE RESOURCES

There is now a consensus in the literature on resource economics that a depletable resource should command a price in excess of its marginal extraction cost, simply to reflect the opportunity cost of using a unit of it today rather that conserving it for the future. But how this excess is to change along an optimal (or, competitive equilibrium)' path of resource use is still an unresolved question. This might at first seem puzzling, since according to the fundamental theorem of economics of exhaustible resources, or Hotelling (I 93 I) rule, on an optimal path, price minus marginal extraction cost (also termed interchangeably as 'scarcity rent', 'user cost', or 'royalty') should steadily grow over time at the social rate of discount. However, the literature contains sharply contrasting views on the subject. For example, Kay and Mirrlees (1975) have argued that since along an optimal path the scarcity rent grows exponentially as a finite stock of a resourceXnears exhaustion, then situations in which the resource stock is still very large and yet the price greatly exceeds the marginal extraction cost should indicate that the price is significantly above its optimal level and that the resource is overconserved. In stark contrast to this view, Heal (I976) has argued that as the resource stock nears exhaustion the difference between price and marginal cost (or, what he termed, 'social cost of extraction') falls monotonically to zero. Hanson (i980) analyses the same model as Heal's, but unlike Heal who assumes the unit extraction cost to be convex, he postulates it to be concave, and yet, like Heal, concludes that the scarcity rent will be monotonically declining over time. Solow and Wan (I976) analyse a still different situation where resource deposits differ in quality and the unit extraction cost increases as higher-grade deposits are exhausted and extraction proceeds to lower grades. They show that along an optimal path the shadow price of a resource must rise at the real rate of interest despite differential extraction costs, but that the difference between price and the marginal extraction cost, or what they call ' degradation charge' declines monotonically over time to zero. These sharply differing conclusions suggest that, far from being resolved, the question of how scarcity rent changes over time is much in want of a close scrutiny. The need for such a scrutiny becomes even stronger once it is noted