Hotelling's Rule
What is Hotelling's Rule?
Hotelling's rule states that, for efficient extraction of a nonrenewable resource, its net price (price minus marginal extraction cost) should rise over time at the rate of interest.
An owner of a finite resource like oil chooses between extracting now and selling, or leaving it in the ground as an asset. In equilibrium the in-ground 'scarcity rent' must grow at the interest rate; otherwise owners would shift extraction to earn a higher return elsewhere. This predicts that scarcity rents (and resource prices, absent cost or technology changes) rise over time, and it provides a benchmark for sustainable depletion of exhaustible resources.
Hotelling's Rule: a worked example
A quarry owner sits on a seam of ore that sells for $80 a tonne and costs $50 a tonne to extract, so the scarcity rent is $30. With interest at 10%, the rent must reach $30 x 1.10 = $33 next year, which means a price of $33 + $50 = $83 if extraction costs hold steady. The year after, the rent is $33 x 1.10 = $36.30 and the price $86.30. Test it: if next year's price came in at only $81, the rent of $31 would earn 31/30 minus 1, about 3.3%, well under 10%, so the owner extracts today and banks the $30 at 10% instead.
The mistake students make with hotelling's rule
The frequent error is reading the rule as a prediction that resource prices rise at the interest rate. It applies to the net price, price minus marginal extraction cost, not to the price on the pump or the exchange. Better extraction technology can cut costs faster than the rent grows, so the observed price falls while the rule holds perfectly. New discoveries do the same by enlarging the stock. A long stretch of cheap oil therefore does not refute Hotelling on its own.
Hotelling's Rule questions
Does Hotelling's rule mean oil prices always rise?
Hotelling's rule predicts a rising scarcity rent, not a rising market price. The rent is the gap between price and marginal extraction cost, so if better drilling technology cuts extraction cost faster than the rent grows, the price a buyer pays can fall while the rule still holds. New discoveries have the same effect, because they enlarge the stock against which the rent is priced.
What is scarcity rent in Hotelling's rule?
Scarcity rent is the part of a resource's price left over once the cost of getting it out of the ground is covered. If ore sells for $80 a tonne and costs $50 a tonne to extract, the rent is $30, and that $30 is what an owner gives up by selling today rather than keeping the ore as an asset. Hotelling's rule governs how fast that $30 must grow.
Why does resource rent grow at the interest rate?
Resource rent grows at the interest rate because ore left in the ground competes with every other asset the owner could hold. If the rent grew more slowly than interest, owners would extract and sell now and buy bonds, and the extra supply would push today's price down. If it grew faster, owners would hold back, cutting supply and lifting today's price. Only growth at rate r stops both moves.
Formula / Example
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