When supply can’t respond

We take the transparent risk score and multiply it by a supply-response factor derived from supply-shock economics. The scarcity impact of a disruption scales inversely with supply elasticity — an outage bites harder when output can’t respond — so vulnerability ∝ 1/(1+ε). We infer each metal’s long-run supply elasticity from its companionality (a primary metal can scale, ε ≈ ε₀; a pure by-product cannot, ε ≈ 0):  ε(c) = ε₀(1 − c/100),  factor = (1+ε₀)/(1+ε(c)), normalised so a primary metal is unchanged and a 100%-by-product carries the full 1+ε₀. We then re-rank and report the movement — the rank change is the message, not the absolute value.

What makes ε₀ = 0.5 defensible, not arbitrary. It now has a structural meaning: it is the long-run supply elasticity of a scalable primary metal. The literature supports the two endpoints the model rests on — every non-fuel mineral is price-inelastic in the short run (mines can’t be built quickly: USGS / Fernandez 2025, 74 commodities; Dahl MEDS), while long-run primary supply is substantially elastic (Stuermer 2017; Radetzki 2008; Krautkraemer 1998) — so ε₀ = 0.5 is conservative (higher published values would only deepen the by-product penalty). And companion supply really is host-locked: the most rigorous open model of a by-product — the copper–cobalt–nickel supply-curve system (Nature Communications 2025, ~99% of cobalt a by-product) — is built on exactly this mechanism. Honest ceiling: per-material long-run elasticities are not published for the critical by-products (they’re too hard to estimate — the thesis itself), and the gold-standard structural models need proprietary cost curves. We tried estimating own-price response from 8 years of BACI trade data; too noisy (re-exports, quality mix, shared Ga/Ge/Hf HS code) to trust. So ε(c) is a calibrated inference from companionality, not a measurement — a re-ordering lens grounded in the economics, not a cardinal elasticity. Inputs: risk.json × companionality.json → risk_adjusted.json.