# 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 barrel

Then 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.

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