Tuesday, August 05, 2008
That story looked kind of familiar to me; it has the flavor of the Hotelling extraction story but told in a simple way. My recognition was of the story of the trees in Alchian and Allen's Exchange and Production. Let me type out a little bit of this for you. Imagine a tree that can yield only one service, producing lumber, which it can provide at only one date in the future. (Oil wells can provide service over many years, we'll get to that in a minute.) At the moment of planting the present value of the tree as lumber at some future date will be greater than the cost of planting the tree.
Imagine that you are sitting on a huge oil deposit, which has (let us suppose) one billion barrels that can be brought to the surface for $20 each, so long as you don't pump more than one million barrels per day. (If you want to pump at a higher rate, you have to spend more money per barrel, and you might reduce the total number of barrels you can extract from the deposit.) So the question is, how fast should you pump?
You might at first think that you should pump at the maximum extraction rate, without raising your marginal costs � i.e., that you should pump at one million bbls/day. But this clearly is wrong, if you expect oil prices to keep rising. Why sell 365 million barrels in 2008 at an average of $150 each, when you could postpone production for a year and then sell those same million barrels for, say, $200 each?
In light of this consideration, maybe you think you should just hold your barrels off the market forever. By letting them sit in the ground, the market value of your asset rises over time, as the market price of oil rises.
But that isn't necessarily the right thing to do, either. What if oil prices rise an average of only 10 percent per year over the next two decades? Do you really want to put all your eggs (oil) in one basket, by leaving them sitting underground? Especially if your deposit is located in the Middle East, you might feel more comfortable selling off some of the oil now, and then using the revenue to buy stocks and bonds, not to mention a few surface-to-air missile silos. (And of course, you could be wrong in your forecasts; maybe oil prices will tank in two years.)
As time passes and we apprach that future date, the present capital value rises towards that anticipated future value, and rises at the market rate of interest. Consequently, the date at which you might invest in that resource has no effect on your realized rate of return. If you invest in the first year, or any year, you will get the same annual percentage rate of growth, as long as beliefs about the future value of the lumber don't change. (p. 122)The return on the tree, or an oil field, is equalized at the market rate of interest whether you buy a new or old tree, a new oil lease or an established field.
What ensures that equilibrium? People don't give away opportunities to get more than the rate of interest -- that is, profitable opportunities. If a young tree were priced so low that people expected to get a higher return over its life than [the market rate] per year, everyone would want to buy it; if it were priced to high, the return would be smaller, so no one would want to buy it: The price would adjust. Every durable good whether new or old will be priced on the expectation of the same interest rate of return. (ibid.)The risk of holding that asset is that there would be additional supplies that reduce the rate at which the price of your asset increases. This intertemporal analysis would make an increase in future supply of trees -- reducing future prices -- encourage the cutting of trees now. Likewise, an increase in future production of oil would reduce the rate of return to the Saudis of their reserves, and encourage them to produce more oil now. Such a point is made explicitly by Coats* and Pecquet , but the same can be found in Lee [1978 J Pol Econ; JSTOR link here if you have access.] Coats and Pecquet demonstrate that the effect of a reduction in scarcity rents -- the marginal cost of using oil now rather than later -- has an identical effect to a reduction in extraction costs. This applies to a good that grows until harvest or a durable asset that generates revenue over time. And this applies both to the monopolist or cartel as it does to a competitive oil industry.
This difference between comparative static and dynamic analysis is at the base of the argument between the drill and don't drill debaters. The don't drill side has an argument that future oil production can only affect future oil prices; good economic analysis would tell you otherwise.
*updated to get Morris Coats' last name in that post. He blogs, by the way, and wrote a nice letter. The paper was presented at the Southern Economics Association. Professor Coats reports that he was inspired on this by Dwight Lee's work.