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.
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.
A worked example
Ten units sold now or later
Use a ten-percent discount rate and future net price eleven, giving a discounted future price of ten.
Move extraction from zero to ten current units. Present value remains one hundred because each unit earns the same discounted amount.
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.
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.
A common misconception
“Hotelling's rule predicts that every observed resource price grows at the interest rate.”
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.
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.
Are you comparing gross prices or the net opportunity value of leaving a resource unextracted?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.