A generalization of the Cairns–Krautkraemer model and the optimality of the mining rule

There exists a rule of thumb of mines, which decides how the cut-off grade (the lowest grade of extracted ore) should change in response to a change in the price of the metal. It requires that the cut-off grade should decrease (increase) when the present value price of metal increases (decreases). In this paper, the optimality of the rule will be examined by generalizing the Cairns–Krautkraemer model under the perfect foresight assumption.