In Part 1 of our Hotelling's Rule explanation, we laid out the basic economic observation that for a non-renewable, exhaustible resource with completely known stock, no discoveries possible, no alternatives, no recycling, private ownership and constant costs of extraction, the price of the resource will increase at the interest rate over time. Whew, that was a mouthful.
At the end of that post, we observed that real word graphs of prices for some (and this really holds for most) depletable resources seem to look nothing like the ever-increasing Hotelling price path--even over very long periods of time.
Was Hotelling wrong?
Is our explanation of Hotelling's Rule wrong?
Recall that in order to get to that explanation we had to assume that:
- A private owner owns the complete stock of a natural resource.
- The complete stock of the resource is fully known and there is no more.
- Once some of the stock is withdrawn, the resource withdrawn is used completely with no waste and nothing left over for reuse.
- The stock can never regenerate itself.
- The cost of withdrawing a unit of the resource is always the same (to make things really simple, we will assume the cost of extraction is $0).
- There are no alternatives to the resource.
As with any good economic model, making restrictive assumptions allows us to start to gain intuition about complicated economic interactions. But often, the assumptions become so restrictive that we move away from reality and end up with model predictions that, while intuitive, in no way resemble real world outcomes. In such cases it is useful to work backwards and relax some of the assumptions to see what happens to our basic model predictions.
So here goes (in no particular order).
What happens to the predicted Hotelling price path if:
- The complete stock of the resource is unknown and there might be more? If there is a non-zero chance that there is more of the resource out there somewhere, the upward pressure on the price caused by the Hotelling scarcity costs will result in increased incentive to explore and try to find new deposits. Assuming some of this exploration is successful, the increased supply will drive prices down and extend the Hotelling price path. Knowing that additional deposits are valuable can lead to significant investments in exploration and the required technologies to find more of the resource. For example:
"BP is leading an industry-wide push to develop technology that can retrieve oil from formations that are so deep under the sea floor, and under such high pressure and temperature, that conventional equipment would melt or be crushed by the conditions.
One BP field in the Gulf of Mexico, called Tiber, makes the Macondo field that the Deepwater Horizon rig was probing look like simple puddle of oil. It is thought to hold twenty times the amount of oil as Macondo. At 35,000 feet below the sea floor — 6.6 miles into the earth's crust — it is about twice as deep."
The cost of withdrawing a unit of the resource increases as more of the resource is extracted? In Part 1, we assumed that cost of extracting the first unit of the resource is the same as the cost of extracting the last unit ($0). This doesn't make a whole lot of sense. It's really easy to get peanut butter out of a jar when the jar is full, but when the jar gets close to empty, it's a pain in the butt to have to scrape the sides of the jar to get enough peanut butter for my late-night crackers and chocolate milk.
It's similar with extractable resources. Early on in Texas, people could just about walk around with a long stick, poke a hole in the ground and oil would start spewing out. Now, we are trying to figure out how to develop technologies to drill 35,000 feet under the sea (wasn't that a book or something?).
The cost of getting more of the resource out of the ground increases as more is extracted.
What does that do to the Hotelling price path? Increased marginal costs of extraction will cause the price to have to rise faster--to cover the increasing extraction costs plus the scarcity costs. So increasing marginal costs will cause prices to rise faster than otherwise and will increase incentives for additional exploration and the search for alternative resources.
- What happens if substitute resources exist? In part 1 we assumed that the resource has no substitutes. But that's not very realistic. Coal and natural gas are substitutes for oil (albeit imperfect), different metals can substitute for each other. Man-made capital can sometimes substitute for natural resources. Renewable energies are substitutes for fossil fuels.
While substitutes exist for most depletable resources, they are often more expensive per unit. Right now, solar energy is significantly more expensive per kilowatt hour than is natural gas. But as the price of natural gas increases due to scarcity (although given new technologies, natural gas is pretty plentiful right now), solar energy becomes relatively more affordable, even if the price of solar does not fall.
So the existence of an alternative resource (sometimes called a backstop resource) will lead to the potential for switching between resources. If the price of the backstop resource decreases, the switch would happen sooner. This is one reason policy makers will often subsidize the development of alternative resources in an attempt to move the Hotelling switch between resources forward in time.
An interesting side note on this discussion is the predicted smoothness of the switch between resources. As the price of the depletable resource rises and/or the price of the alternative resource decreases, incentives are created to switch between the resources. Once the price of the depletable resources rises far enough, the incentive to continue with extraction diminishes and investments in alternative resources increase. This critical understanding of the rationing role of prices is often missing from doomsday prediciions regarding world collapse due to running out of depletable resources. This is also, to me at least, the primary argument against price interventions in resource markets.
In this discussion I've only relaxed a few of the assumptions from Part 1. There a multitude of others we could discuss. For example, recycling can extend the life of a depletable resource and lower the Hotelling price path; Open access or common pool ownership of resources will lead to a tragedy of the commons scenario and lead to a literal 'race to the bottom' of the resource. I have also ignored uncertainty and commodity investment markets (futures/options) all of which have the potential to mess with the simple Hotelling price path.
Relaxing some assumptions will lead to predicted increases in prices over time while relaxing other assumptions leads to predicted decreases over time. As these market forces play out, the observed price path may look nothing like the simple Hotelling price path predicted in Part 1. Nevertheless, the simple Hotelling intuition is invaluable: The Hotelling Rule is really about the rationing role of prices in markets. Prices signal scarcity. If prices are artifically adjusted for political or 'fairness' purposes, the rationing signals get screwed up.
Prices have to reflect the true scarcity value of the resource.
And that's the real lesson from Hotelling's Rule.