# Hail Giacomo Ponzetto!

Since the option is perpetual, a closed-form solution is easy to

obtain if one makes standard assumptions: production from a developed

reserve is represented by exponential decline, the price of oil is a

geometric Brownian motion, asset markets span, etc.Following the authors cited above, assume:

— a payout yield of 4% from a developed field;

— a risk-free real interest rate of 1.25%;

— a volatility of 0.2

Then the option value of waiting is such that we should only drill when

the present value of the developed reserve is at least 1.6195 times the

cost of developing it.Suppose that the price of oil follows a martingale, so the current

price of $105 per barrel is also the expected future price at any time.

Suppose the ANWR reserve comprises 7.06bn barrels and that once the

oilfield is developed it will pump out 5% of the reserve every year at

a constant marginal cost of $5 per barrelThen at the 1.25% discount rate the developed reserve is worth

$564.8bn (which is reasonably close to Tyler’s $600bn estimate).

However, if we start drilling now the reserve will be developed in 10

years (EIA 2004, 2008), so we must calculate the present value of this

sum. The correct discount rate here is the payout rate of 4% (Dixit and

Pindyck 1994, p. 403), so the NPV of drilling now is $378.6bn.

Therefore, the option value due to volatile oil prices implies that we

should drill now only if the cost of drilling, including its

environmental impact, is below $233.78bn.Since the cost estimate above ($5 for getting a barrel of oil to

market from an existing well in Alaska) only accounts for an NPV of

$18.93bn, Kotchen and Burger’s figures leave me with a $103.87bn cost

of developing the reserve. Then we should drill now if the

environmental cost is less then $130bn, or the willingness to accept

compensation to allow drilling less than $590 per voter.Admittedly all my figures are very rough estimates, but I believe

this is the correct order of magnitude. The reserve is indeed worth

about $600bn, but that is not very important, because the choice is not

between drilling now or foregoing drilling forever, but between

drilling now or waiting and seeing.Furthermore I have ignored the possibility of cost-reducing

technical progress. I don’t see why drilling should become costlier or

more environmentally damaging; but it probably could become more

efficient on either account. That would increase the option value of

waiting.Obviously, we should rush to drill now if we expected oil prices to

decline sharply in the future, because then the reserve would be

rapidly depreciating while it is left in the ground. But that does not

seem to be the argument of the bozos on either side of the aisle.

It’s also worth noting:

1. Critics of drilling usually want to shut down the option forever and the political window cannot be expected to remain open forever.

2. There is a general global warming case against developing the resource. Note that supply restrictions can be far more effective than a Pigou tax. A Pigou tax doesn’t guarantee the stuff won’t be pumped anyway, albeit at lower profit.

3. The Pigouvian case against developing ANWR makes sense only if we are taking other systematic actions to raise the price of fossil fuels and restrict fossil fuel use. Otherwise we may just be leaving a $600 billion dollar bill on the proverbial sidewalk. This may be a classic case of twin-peaked preferences.

4. Depending how the money is spent, and on the general equilibrium properties of the system, it still may make sense to have a) a Pigou tax on fossil fuels, and b) ANWR development. For one thing, it does matter who captures the profits from fossil fuel development. You could imagine an even stiffer tax on imported fossil fuels (relative to what would be optimal without ANWR), combined with ANWR development. You can spin out lots of tricky problems here.