How to Calculate Prices Under Hotelling's Rule
Hotelling's rule holds that the net price of a nonrenewable resource, its price minus marginal extraction cost, grows at the interest rate each year.
The Hotelling's Rule formula
Calculator
Enter today's price, extraction cost and the interest rate to watch the net price and the market price grow apart.
What one unit of the resource sells for right now.
The cost of getting one more unit out of the ground.
The return the owner could earn by selling now and investing instead.
How far into the future you want the price for.
The resource sells for $62.58 at that date if extraction cost has not moved.
- Net price today
- $20
- Net price next year
- $21
- Price next year
- $51
- Net price at your horizon
- $32.58
- Annual growth in the market price
- 2.27%
Taking extraction cost out of the price leaves $20 of scarcity rent, the part that has to grow at the interest rate.
One year of compounding lifts the rent to $21, which is what keeps an owner indifferent between selling and waiting.
Adding extraction cost back gives a market price of $51 a year from now.
Compounded over the whole horizon the rent reaches $32.58.
The observed price climbs 2.27% a year, slower than the interest rate, because the extraction-cost part of the price does not compound.
How to calculate Hotelling's Rule, step by step
- 1Strip extraction cost out of the price. Net price, also called scarcity rent or user cost, is the market price minus the marginal cost of getting one more unit out of the ground.
- 2Choose the interest rate. Use the return the owner could earn by selling a unit today and investing the proceeds. That return is the opportunity cost of leaving the unit in the ground.
- 3Compound the net price forward. Multiply the net price by (1 + r) once for each year, exactly the way a bank balance compounds.
- 4Add extraction cost back. The market price at that date is extraction cost plus the grown net price, on the assumption that lifting a unit still costs the same.
- 5Compare the two growth rates. The market price grows more slowly than the net price whenever extraction cost holds still, because only part of the price is compounding.
Worked example: Hotelling's Rule
A barrel sells for $50 and costs $30 to lift, so today's net price is $20. At a 5% interest rate the net price a year later is 20 × 1.05 = $21 and the barrel sells for 30 + 21 = $51. Over ten years the net price grows to 20 × 1.05^10 = $32.58, so the price reaches 30 + 32.58 = $62.58. Across that stretch the market price rises only 2.27% a year, well under 5%, because the extraction-cost half of the price never compounds.
Hotelling's Rule questions
What is scarcity rent?
Scarcity rent is the net price, the gap between the market price and the marginal cost of extraction. It is what an owner gives up permanently by selling a unit today, and it is the piece that has to compound at the interest rate.
Why do real resource prices often fail to rise the way the rule predicts?
The rule assumes extraction cost and known reserves hold still. Discoveries and better technology cut extraction costs and enlarge the usable stock, and that downward pressure can swamp the rising rent for decades.
What happens if owners expect the net price to grow more slowly than the interest rate?
Selling now and investing the money beats waiting, so owners extract more today. The extra supply pushes today's price down until the expected growth in the net price matches the interest rate again.
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