Optimal pricing, use, and exploration of uncertain natural resource stocks

The classic Hotelling (Ref. 1) model of exploitation of exhaustible resources assumes in its simplest form that the stock of the resource is known from the beginning. If there are no extraction costs, then the shadow prices associated with an optimal extraction policy rise at the rate of the market rate of interest. The only variable that has to be determined is the initial price, which then determines all future prices; the initial price depends on the interaction of demand (or utility) considerations with the initial stock. In a competitive world, prices would clearly have to rise at the rate of interest to keep resource holders indifferent between extracting the resource now and later.