Theory of natural exhaustible resources : the cartel-versus-fringe model reconsidered

In this paper the binding-contracte open-loop v~n Stackelberg equilibrium in the cartel-vereus-fringe model of the eupply side of a market for a raw material from an exhaustible natural resource is reconsidered. It is shown that the equilibrium for this model differs from what the previoua literature on this model (e.g. Ulph and Folie (1981), Newbery (1981) and Ulph (1982)) suggests. The equilibrium is solved for by using optimal control techniques and it turns out that the previous literature should be corrected in two respects. Firstl,y, the marginal production costs for the cartel are not treated correctly and secondly, the resulting equilibrium price path may not be continuous, as ia implicitly assumed by previous authors. For some values oí the parameters the equilibrium is still time-inconsistent and thia turns out to be so in almost the same cases as in the previous literature. The time-inconsistency is one reason to reject the open-loop von Stackelberg equilibrium concept for this model. Another reason is that for plausible parameter values the equilibrium price path turns out to be discontinuoue. Especially in markets for raw materials such as crude oil, this will Iead to speculation. In that case the assumption that the demand only depends on the current price level is not valid anymore.