The big problem of small change

The medieval money supply mechanism implemented a commodity standard throughout the denomination structure by imposing mint and melt points for each coin. Mints stood ready to sell (but not to buy) coins for metal. Seigniorage and brassage fees determined the spreads between mint points and melt points for each coin. Because it was cheaper to make a large coin than a smaller one, there were difficulties in aligning the mint-melt points for various coins, and these exposed the system to recurrent shortages, especially of small coins. We build a model of the medieval money supply system and modify a cash-in-advance model of demand to capture a preference for small change. We use the model to study the behavior of exchange rates between large and small denomination coins across periods of shortages. We also use the model to study how a standard formula of the nineteenth century could be used to supply small change without shortages. The standard formula displaced the medieval supply mechanism with a token currency for all coins but one.