[extropy-chat] Collapse, by Jared Diamond

[Hal Finney]

Lee makes another point I thought was interesting, about Diamond's
book:
> Lastly, he finally---but only belatedly and weakly---gets around
> to mentioning the discount factor. (Goods today are worth more
> than tomorrow.) I can even imagine that taking this into
> consideration, many of those societies (e.g. Easter Island) may
> have pursued optimal strategies, at least in terms of the greatest
> number of people enjoying the greatest prosperity over the longest
> period of time.  And it might be argued that in some cases even
> today, humanity is simply better off grabbing the resources and
> thus destroying some otherwise completely useless land: after all,
> chance are that not too long from now it can be very cheaply
> repaired.

I have been reading books on the economics of resource exhaustion
in order to get a better understanding of the Peak Oil situation.
It turns out that there is quite a mature theory on this topic which
goes back to the seminal work in the 1930s by Hotelling.  He came up
with a formula predicting how society should optimally extract value
from a fixed and exhaustible resource.  (Of course, trees on Easter
Island are actually a potentially renewable resource, so Hotelling's
model would not strictly apply, unless we were sure that treating them
as exhaustiable were optimal.)

Hotelling's formula is simple and is based on very general principles, and
the core of it can be described in a sentence.  Resource owners should
extract the resource at a rate such that the price climbs steadily,
with the price increasing at the general interest rate.  Doing this
maximizes the profits of resource owners and also maximizes the total
value of the resource to society, taking into consideration as Lee notes
the discount rate (which is modeled by the interest rate).

The idea behind this formula can be put into words (although this is
my own invention and none of the books I read described it like this,
so I might be missing something).  Suppose producers think the price
curve is steeper than this, so the resource price will climb faster
than the interest rate.  The resource will be worth more in the future
than today, so they will hold off on today's production and produce more
in the future.  This will increase today's price and reduce the future
price, putting the price trend back on the curve.  Likewise if they think
the curve will be flatter than this, future oil won't be worth as much
(discounted to today) as today's oil, hence they will produce more today
while it is valuable, thereby lowering today's prices and once again
getting back to the curve.

Hotelling's model is quite robust and applies to a variety of situations.
It is rather strange, then, that historically prices of exhaustible
resources like minerals generally do not follow a Hotelling price curve.
In constant dollars, most resource prices were roughly flat over the
20th century, with some ups and downs but no general trend.  It is as
though resource owners thought of these resources as renewable, perhaps
due to improved technology making more resources available as fast as
they were being used up.

In the last 5 years or so, almost all mineral prices have begun a
relatively fast climb.  I'm not sure how it compares to the interest rate,
so I don't know if it can be said that the Hotelling model is beginning
to apply.  But if we do start to approach physical limits in some of our
natural resources, this model is what would be predicted for how prices
will rise in the future, assuming that producers want to maximize their
expected discounted profits.

Hal