The Relationship between Price and Extraction Cost for a Resource with a Backstop Technology

This paper analyzes the optimal depletion policy for a country with a resource which is inexhaustible but available in various grades and at various costs. Cost is assumed to increase with cumulative extraction up to a point, but then to remain constant as a "backstop" supply is reached. This models accurately the supply conditions of minerals which may eventually be extracted from marine sources or crystal rocks. Emphasis is placed on the behavior of prices along an optimal (competitive) path, and it is shown that the price-cost relationship is very different from the standard one of an exponentially growing royalty.