On the profitability of exhausting natural resources

Two models are treated. One deals with a mineral deposit, the other with a biological substance. It is assumed that in the deposit there exist all grades of ore, and that, the biological substance grows as long as a positive quantity is left. The course of investment, and production decisions is derived when capital is expressly built up for the purpose of exploitation of the specific resource. Within the simple linear control problem it is concluded that exhaustion is never profitable. The steady state in the biological case is discussed and compared to maximum sustainable yield.