Hotelling's rule (the r-percent rule) predicts an exhaustible resource's shadow price rises at the rate of interest

Deriving the model from a mine owner's discounted-profit optimization, Margaret Slade and Henry Thille's review of Harold Hotelling's 1931 theory states the core result directly: "The second is the famous r–percent rule, which states that the shadow price must rise at the rate of interest, r." The mechanism is an intertemporal arbitrage condition: because the resource owner discounts the future at rate r, "the shadow price is constant in present–value terms, which ensures that, at the margin, the producer is indifferent between extracting one unit today or at some time in the future." Under Hotelling's original zero-extraction-cost assumption, "the shadow price equals the market price and both rise at the rate of interest" — so the observable market price itself should trace the same smooth, continuous appreciation.

This is a structurally different mechanism from the vault's cost-of-production cluster, e.g. claim-szabo-bit-gold-grounds-value-in-unforgeable-cost-of-production: Hotelling's rule governs a fixed, depleting stock with no cheaper substitute assumed to ever arrive, driven purely by indifference between extracting now versus later — not by the cost of replicating or forging scarcity. See entity-hotellings-rule for the concept generally, and claim-hotellings-rule-predicts-shape-distinct-from-cost-of-production-cluster for how this prediction compares against the vault's two existing commodity-price shapes.