Hotelling’s Theory

Hotelling’s theory (or Hotelling’s rule) describes how owners of nonrenewable resources decide whether to extract and sell now or leave the resource in the ground and wait for a potentially higher price. It links the optimal extraction decision to prevailing real interest rates: resource owners will extract only if the expected return from selling now and investing the proceeds is at least as high as the return from leaving the resource unextracted.

Key points

• Owners compare the expected rate of price appreciation for the resource with the real interest rate available from financial investments.
• If expected resource price growth > real interest rate → wait (leave resource in the ground).
• If expected resource price growth < real interest rate → extract and sell now, then invest proceeds.
• The difference between price and marginal extraction cost is called the Hotelling rent.
• The rule implies that, in the absence of changing extraction costs and other frictions, the net price of a depletable resource should grow at the real interest rate.

How it works (simple example)

An owner of an iron ore deposit faces a choice:
* If iron ore is expected to appreciate by 10% over the next year but the prevailing real interest rate is 5%, the owner is better off postponing extraction and selling later (10% > 5%).
* If expected ore appreciation is 5% and the real interest rate is 10%, the owner should extract now, sell, and invest the proceeds at 10% (5% < 10%).
* If both rates are equal, the owner is indifferent.

This decision ignores extraction costs in the basic formulation; when extraction costs are included, the rule applies to the net price (price minus marginal extraction cost).

Formal implications

• Hotelling rent: the surplus earned by owning a unit of resource rather than producing it immediately (price minus marginal extraction cost).
• r-percent growth rule: the after-cost price of an exhaustible resource should rise at the owner’s discount rate (real interest rate) over time.
• If marginal extraction costs are zero, the price of the extracted stock and the unmined resource align and should grow at the real interest rate. If extraction costs rise over time, the net price growth may be slower than the discount rate.

Limitations and empirical evidence

Real-world outcomes often diverge from Hotelling’s predictions. Empirical studies find that commodity price increases frequently fall short of matching real interest rates. Reasons include:
* Variable extraction costs and technological change that lower costs.
* Discovery of new reserves or changes in resource estimates.
* Market power, regulation, taxes, and political risk.
* Substitutes, demand shifts, and storage costs.
* Uncertainty and expectations that deviate from the simple model.

A notable study by the Federal Reserve Bank of Minneapolis (2014) concluded that observed commodity price appreciation rates were substantially below the corresponding U.S. Treasury real rates, suggesting additional factors (especially extraction costs) are important.

Historical note

Hotelling’s rule is named for Harold Hotelling (1895–1973), an American statistician and economist. Besides this rule for nonrenewable resource pricing, he is known for contributions such as Hotelling’s T-squared distribution, Hotelling’s law, and Hotelling’s lemma.

Takeaway

Hotelling’s theory provides a clear, tractable framework linking resource extraction timing to financial incentives: resource owners will hold off on extraction if future price growth beats available financial returns. In practice, extraction costs, technological and market developments, and institutional factors often alter the simple prediction, so the rule serves best as a baseline theoretical benchmark rather than a precise empirical law.