# Hotelling's Theory: Definition, How It Works, and History

## What Is Hotelling's Theory?

Hotelling's theory, or Hotelling's rule, posits that owners of nonrenewable resources will only produce basic commodities if doing so can yield more than could be earned from available financial instruments, such as U.S. Treasury or other similar interest-bearing [securities](https://www.investopedia.com/terms/s/security.asp). The theory assumes that markets are efficient and that the owners of the nonrenewable resources are motivated only by profit.

Hotelling's theory is used by economists to attempt to predict the price of oil and other [nonrenewable resources](https://www.investopedia.com/terms/n/nonrenewableresource.asp), based on prevailing interest rates. Hotelling's rule was named after American statistician Harold Hotelling.

### Key Takeaways

*   Hotelling's Theory defines the price or yield at which the owner of a nonrenewable resource will extract it and sell it, rather than leave it and wait.
*   It bases the relative price on U.S. Treasury bonds or some similar interest-bearing security.
*   The rule was devised by American statistician Harold Hotelling.

## Understanding Hotelling's Theory

Hotelling's theory addresses a fundamental decision for an owner of a nonrenewable resource: Keep the resource in the ground and hope for a better price the next year, or extract and sell it and invest the proceeds in an interest-bearing security.

Consider an owner of iron ore deposits. If this miner expects a 10% appreciation of iron ore over the next 12 months, and the prevailing real interest rate (nominal rate less inflation) at which he can invest is only 5% per year, he will choose not to extract the iron ore. Extraction costs are ignored in his theory. If the numbers were switched, with a price appreciation expectation of 5% and an interest rate of 10%, the owner would mine the iron ore, sell it, and invest the sales proceeds at a 10% yield. The miner will be indifferent at 5% and 5%.

## Theory and Practice

The difference between the marginal extraction costs of natural resources and their price is called the Hotelling rent. It follows that the rate of change in the price of a depletable resource must equal the interest rate that a miner or extractor uses to discount the future; this is known as the Hotelling _r_\-percent growth rule. Whenever marginal extraction costs are zero, the price of the resource in stock and that of the unmined resource are equivalent and the Hotelling rule applies equally to both. If, however, extraction costs increase over time, the price of the resource should rise at a rate that is lower than the discount interest.

Thus, all else being equal, an increase in the discount rate implies a higher price for the unextracted resource and would incentivize a faster rate of extraction. In theory, then, the price increase rates of nonrenewable resources like oil, copper, coal, iron ore, zinc, nickel, etc. should track the pace of real interest rate increases.

In practice, the Federal Reserve Bank of Minneapolis concluded in a 2014 study that Hotelling's theory fails. The price appreciation rates of all the basic commodities examined by authors fell short—some far short—of the annual average rate of U.S. Treasury securities. The authors suspected that extraction costs explained the difference.

## Who Was Harold Hotelling?

Harold Hotelling (1895 - 1973) was an American statistician and economist affiliated with Stanford University and Columbia University in his early and mid-career years, and later with the University of North Carolina-Chapel Hill until his retirement. Aside from the eponymous theory on prices of nonrenewable resources, he is known for Hotelling's T-square distribution, Hotelling's law, and Hotelling's lemma.