[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

operation causes. Thus, the price he charges will reflect both social and private
costs. The question of resource depletion now boils down to the question of whether
his bauxite is worth more to him in the market today or left in the ground for future
extraction. The answer depends on how much the owner of the bauxite thinks it will
be worth in the future, say thirty years from now. If the owner expects it to be sufficiently
more valuable thirty years from now to compensate him both for waiting and
for all the uncertainties associated with trying to predict what the bauxite will be
worth that far in the future, he will keep the bauxite in the ground.
In Chapter 9, we learned how to calculate the future value of something in terms of
its present discounted value. For example, if the price of the bauxite next year is expected
to be $25 per ton and the interest rate is 10 percent, the present discounted value of that
$25 is found by dividing $25 by 1 plus the interest rate, or 1.1. At an interest rate of 10 percent,
next year’s expected price of bauxite is equivalent to a price today of $25/1.1 =
$22.73. If the interest rate is 10 percent, then a dollar a year from now is worth 10 percent
less than a dollar today (a dollar today could be invested and would yield $1.10 in
one year). If the current price of bauxite is above $22.73, it will pay to mine the bauxite
today and sell it. If the current price is less than $22.75, the owner of the bauxite mine
will find it more profitable to leave the bauxite in the ground and mine it next year.
Now looking ahead to what the bauxite might be worth thirty years from now.
Suppose the owner’s best guess is that in thirty years bauxite will be selling for $75
per ton and that the interest rate will remain 10 percent for the next thirty years; then
the present discounted value of bauxite today will be $75/(1.1) 30 = $4.30. If the current
price is greater than $4.30, it will pay to mine the bauxite now—the price
expected in the future is not high enough to compensate the owner for waiting. If
the interest rate falls to 5 percent, however, the present discounted value rises to
$75/1.05 30 = $17.35. Now, if the current price is less than $17.35, it will pay to leave
the bauxite in the ground. At a lower interest rate, the owner of the bauxite has a
greater incentive to leave the bauxite in the ground until some future time. Higher
interest rates increase the incentive for firms to extract the bauxite earlier.
If this miner and all other bauxite producers choose to bring the bauxite to
market today, depleting the world’s supply of bauxite, there are two possible reasons
for their decision. Perhaps this is the socially efficient outcome—society values
bauxite more highly today than it will tomorrow. Or perhaps the miners have miscalculated
the value of bauxite thirty years from now and underestimated future
prices, though they have every incentive to forecast as accurately as they can.
If they have indeed miscalculated, we might view the result as a market failure;
but there would be no reason to expect a government bureaucracy to do any better
than the firms at guessing future prices.
However, there are two plausible reasons why private owners may habitually tend
to undervalue future benefits of a natural resource. First, in countries where property
rights are not secure, owners of a resource may feel that if they do not sell it soon, there
is a reasonable chance that it will be taken away from them. There may be a revolution,
for example, in which the government will take over the resource with no or only
partial compensation to the owners. Even in countries like the United States, where
owners are not worried about government confiscating their property, they might fear
that more stringent regulations will make it more expensive to extract the resource in
the future, or that higher taxes will make it less attractive to sell the resource in the
NATURAL RESOURCES ∂ 417