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Hotelling's Rule.

Move extraction between two periods and compare discounted scarcity rent.

Interactive experimentintuitiveField note ·
Preparing the experiment…
THE SHORT VERSION

Hotelling's Rule, explained.

Hotelling's rule concerns the growth of net scarcity rent along an interior optimal extraction path under restrictive resource-market assumptions.

01 / THE MECHANISM

Why it happens

A stock of ten units has zero extraction cost. Sell x now at 10 or the remaining 10−x next period at an adjustable net price, discounted by 1+r. At a future price 10(1+r), present value is independent of the allocation. Otherwise this price-taking two-period exercise favours one boundary.

Hotelling's rule concerns the growth of net scarcity rent along an interior optimal extraction path under restrictive resource-market assumptions.

Read the result

Compare today's net price with the discounted future net price. The neutral extraction allocation occurs only at the indifference price in this two-period exercise.

02 / FOLLOW IT THROUGH

A worked example

Ten units sold now or later

  1. Use a ten-percent discount rate and future net price eleven, giving a discounted future price of ten.

  2. Move extraction from zero to ten current units. Present value remains one hundred because each unit earns the same discounted amount.

  3. Raise the future price above eleven. Waiting becomes more valuable in this price-taking exercise, without supplying an equilibrium price forecast.

OPTIONAL DEEPER DETAILGo deeper: inside the model

Inside this model

A stock of ten units has zero extraction cost. Sell x now at 10 or the remaining 10−x next period at an adjustable net price, discounted by 1+r. At a future price 10(1+r), present value is independent of the allocation. Otherwise this price-taking two-period exercise favours one boundary.

03 / BEYOND THE EXPERIMENT

Where this idea is useful

A practical use

Leaving a resource unextracted has an opportunity cost that can be compared with earning a return on current proceeds.

CHECK YOUR INTUITION

A common misconception

THE TEMPTING CONCLUSION

“Hotelling's rule predicts that every observed resource price grows at the interest rate.”

THE MORE USEFUL DISTINCTION

The rule concerns net scarcity rent under restrictive optimality assumptions. Real prices also reflect costs, uncertainty, technology, constraints and institutions absent here.

What this explanation leaves out

  • Prices are supplied rather than solved from demand and resource stocks. No discoveries, extraction capacity, environmental damage or uncertainty are modelled. The board is not a commodity-price forecast or an investment recommendation.
ONE MORE QUESTION

Why do the best choices move to a boundary away from indifference?

With fixed prices, zero costs and no extraction capacity limits, each unit independently favours the period with the higher discounted net price.

TAKE THE IDEA WITH YOU

Are you comparing gross prices or the net opportunity value of leaving a resource unextracted?

Associated thinkers

Associated withHarold Hotelling ↗

Associations marked provisional are awaiting source review.

Further reading

Explore the original research or the teaching reference behind this experiment.