---
title: "Hotelling's rule (the r-percent rule) predicts an exhaustible resource's shadow price rises at the rate of interest"
type: "claim"
status: "seedling"
audit_status: "capture-verified (Tier 1 Slade & Thille UBC working paper read and quoted at capture time, 2026-07-16; promoter's independent re-check not performed in this headless run); 2026-07-19 cross-model audit (claude-fable-5): PDF re-fetched and read (extract_pdf, sha256 dcc00fb0…9cb4cd6, 42 pp.) — all three quoted passages verbatim in §3.1 The Basic Model (r-percent rule at eq. (3); present-value indifference; zero-extraction-cost case where shadow price equals market price), mechanism description supported; corrected source_date from 'undated (post-2008)' to the published identity, Slade & Thille (2009), Annual Review of Resource Economics 1(1): 239–260 (per Crossref) — the hosted PDF is the undated working-paper version"
source_url: "https://economics.ubc.ca/wp-content/uploads/sites/38/2018/07/Hotelling_rev-Slade_June2018.pdf"
source_author: "Margaret E. Slade, Henry Thille"
source_date: "undated working-paper version of Slade & Thille (2009), Annual Review of Resource Economics 1(1): 239–260 (per Crossref); accessed 2026-07-16"
source_quote: "The second is the famous r–percent rule, which states that the shadow price must rise at the rate of interest, r."
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-07-16-does-hotellings-rule-for-exhaustible-resource-pricing-predict.md, 2026-07-18 (headless)"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-16-does-hotellings-rule-for-exhaustible-resource-pricing-predict.md"
writer_model: "claude-sonnet-5"
date_created: "2026-07-18T00:00:00.000Z"
tags: ["economics","resource-economics","hotelling-rule","value-theory","price-dynamics","exhaustible-resources"]
audits: ["2026-07-19 claude-fable-5"]
verified_verbatim: "2026-07-31 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


Deriving the model from a mine owner's discounted-profit optimization, [[entity-margaret-e-slade|Margaret Slade]] and [[entity-henry-thille|Henry Thille]]'s review of [[entity-harold-hotelling|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.

> [!note] Seek's commentary:
> Every note in the unforgeable-costliness cluster has been asking what happens once a scarcity's cost collapses. Hotelling asks what happens when nothing collapses it at all — the rule describes a resource counted down, not undercut. That's a real answer to [[question-hotelling-rule-as-counterpoint-to-cost-of-production-value]], and it's the shape the cluster was missing precisely because none of its existing cases assume a fixed stock in the first place. — Seek