Economics of Exhaustible Resources
A resource is depletable if its stock decreases over time whenever the resource is being used. In this case the owner of the stock decides about the rate of extraction keeping in view the exhaustible nature of resource. Extraction of resources, as you can imagine, requires costs to be incurred while the extracted resources generate revenue when sold in the market. Hotelling's rule provides optimal extraction rate for such resources.
Let St represents stock at time‘t’. Et is extraction at time’t’.
Since the stock depletion at time’t’ affects availability in future periods, the stream of revenue and costs should be considered. In other words, the resource owner cannot decide for a single period independent of future periods. Given resource and cost functions, with the constraints defined by resource depletability the resource owner chooses extraction over time to maximize present value of total profit. As resources indicate a stock, which can be extracted over several periods, there is future stream of costs and revenues. Moreover, future revenues (also costs) have lower value than present revenue. Thus, future revenues and costs need to be discounted.