Far less platinum is produced each year than gold, and platinum has for long stretches traded below it. Rarity and price are related less directly than the comparison suggests.
Scarcity describes supply, not demand
Price is set by the meeting of supply and demand, and a small supply produces a high price only if there is demand competing for it.
Several metals are scarcer than platinum and trade for very little, because almost nobody needs them in quantity.
The relevant comparison is therefore not how much of a metal exists but how much of it people want relative to what is available.
Gold has a demand source platinum lacks
Gold is held as a store of value by individuals, institutions and central banks, and that demand is for the metal simply as an asset.
It is largely indifferent to industrial conditions and can expand enormously when confidence in financial assets weakens.
Platinum has never accumulated the same monetary role, so it has no comparable pool of buyers who want it regardless of what it is used for.
Stock versus flow changes the arithmetic
The gold available to the market is not just the annual mine output but the entire stock ever produced, most of which still exists and can be sold.
Platinum's above ground stock is small, so its price depends much more heavily on the balance of current production against current consumption.
That makes platinum more volatile and more responsive to industrial news, while gold's vast stock damps the effect of any single year's output.
Substitution caps industrial pricing
Where platinum is used as a catalyst, palladium can often perform a similar function, and manufacturers reformulate when the price gap justifies the engineering work.
That ceiling limits how far platinum can rise on industrial demand alone before buyers begin designing it out.
Gold's monetary demand faces no such substitute, because nothing else carries the same history of being accepted as a store of value.
The relationship has inverted repeatedly
Platinum has traded well above gold during periods of strong industrial demand and constrained supply, and well below during others.
Each reversal reflected a change in the balance between industrial and monetary drivers rather than any change in how rare either metal is.
Treating the ratio between them as a measure of relative demand conditions is more informative than treating it as a measure of value.