Conrad and Kotani have a forthcoming paper in Resource and Energy Economics, "When to drill? Trigger prices for the Artic National Wildlife Refuge." The basic idea is to find the minimum price at which a barrel of oil must be before it is efficient (i.e., the benefits exceed the costs) to drill in then ANWR.
For geometric Brownian motion, it was possible to derive an analytic solution for the trigger price. For [γ = η = 0], and for variations in A ranging from $ 200 million to $ 300 million per year, the trigger price ranged from $ 19.84/barrel to $ 21.26/barrel. With no amenity loss (A = 0) the trigger price was $ 17.01/barrel. If amenity value is exponentially growing and/or oil production is exponentially declining (but with cumulative production constant over the life of the field), it is still possible to obtain an analytic expression for P*, if oil prices follow a process of GBM. If amenity values were instantaneously growing at a rate γ = 0.005 from A0 = $ 200 million, while oil production was constant at Q = 100 million barrels, P* = $ 19.99, only slightly greater than P* = $ 19.84 when γ = 0. For GBM, increases in amenity value did not significantly increase the trigger price.
(Got that?) A is the amenity value of ANWR; i.e., the total willingness to pay (WTP) to avoid drilling for oil. They assume that WTP is between $2-$3 per household/year and with 100 million households the aggregate WTP is $200 million to $300 million. They conclude that when the price of oil is greater than, about, $20/barrel then the benefits of drilling exceed the opportunity costs (the WTP). Further:
If crude oil prices follow a mean-reverting process, it is not possible to derive a closed-form solution for P*, but it is possible to numerically solve for the trigger price after approximating the value function. When A ranges from $ 200 million to $ 300 million per year, the price which would trigger exploration ranges from $ 25.41/barrel to $ 31.42/barrel, respectively.
Under this assumption the trigger price is 25% to 33% higher but still well below current prices (about $50 barrel).
So, go ahead and drill for oil ... right? Not so fast. The analysis depends crucially on the $200 million to $300 million opportunity cost. This number was assumed and justified in a footnote because it is less than the $10 annual WTP for a water-based amenity. A bit bogus? Yes, the analysis should be based on a more reliable number for the opportunity cost. Unfortunately, there may be nothing better available in the literature.
In contrast, take a look at my back of the envelope "benefit cost analysis of drilling for oil in ANWR." I use an annual WTP of $35, an order of magnitude higher than the estimate in Conrad and Kotani. The trigger price I find is $42/barrel and $32/barrel when the future is discounted at r = 2% and r = 7%. These prices are higher than in Conrad and Kotani but still well below current prices.
Note: According to the WSJ's commodities column (5/25):
Benchmark light, sweet crude futures for July ended up $1.31 at $50.98 a barrel on the New York Mercantile Exchange. The back months mostly settled above $52 a barrel, reflecting concerns about oil supplies.
Here is the WSJ page for oil price futures.