Resources for the Future
Krautkraemer and Toman
One feature of the full opportunity cost of exploration activity is that it reduces the stock of exploration opportunities, so that future additions to reserves tend to become more costly. In other words, there is a user cost similar to that in (4) associated with depleting the stock of exploration opportunities, in addition to direct exploration costs. If we then combine the conditions for efficient exploration, development, and extraction, we get:
price = (marginal extraction cost) + (extraction user cost)
= (marginal extraction cost) + (marginal direct cost of finding new reserves)
+(user cost of reduced long-term development prospects)
The heuristic equality in (6) can be related to intuition about opportunity cost in economics more generally. The extraction user cost is the cost of depleting an existing inventory, which can be replenished but only (in the model) at an ever-rising cost. The sum of marginal extraction cost and marginal direct cost of finding new reserves gives a measure of the cost of using and replacing the inventory, but it ignores the ultimate cost of natural capital depreciation reflected in the user cost of reduced long-term development prospects.
Once we allow for reserves to vary endogenously with economic (and technological) conditions, the inexorable upward movement of prices implied by (3) or even (5) no longer need hold. Depending on the degree to which current extraction costs are rising as a consequence of depletion and the cost of new reserve additions, including their user cost, it is possible in the model for new discoveries to outstrip depletion, at least for a while, causing a U-shaped energy price path. This is a reassuring finding since such behavior has been observed in energy and other resource markets (Slade 1982), and a model incapable of replicating such behavior would have little use. The ability to de facto enlarge reserves through technological breakthroughs that increase recoverability and lower the costs of extraction from existing deposits, or make new deposits easier to find and access (lowering reserve replacement costs), likewise could exert downward pressure on prices, possibly for a long period of time.
The simple model of endogenous exploration and reserves makes the simplifying assumptions that reserves are found on average in order of increasing cost and can be found in infinitely divisible amounts. Given the uncertainties surrounding the exploration process, the former assumption obviously is an oversimplification. When the discovery of deposits is more