Debasements and Small Coins: An Untold Story of Commodity Money
What this paper finds — and why it matters
This paper applies a multiple-denomination commodity money model — building on Lee, Wallace, and Zhu (2005) — to coinage episodes in late medieval England, and derives two main findings. Shortages of small coins are severely inconvenient because halfpennies and farthings serve not merely as small change but as consumption-smoothing instruments: parameterized to 15th-century England (per-capita silver approximately 35 grams, penny approximately 1 gram), the model shows that adding a halfpenny is highly welfare-improving for poor agents even at infrequent expenditure, and welfare-improving for all agents when monetary transactions occur at least twice weekly. Debasing the penny by 50 percent has approximately the same welfare effect as introducing a halfpenny and replicates the three stylized facts of the debasement puzzle — large minting volumes, cocirculation of old and new coins, and no additional mint inducement — as equilibrium outcomes rather than paradoxes. However, full-bodiedness creates a commitment device against over-issuance that cannot be replicated by sufficiently small coins, since precious metals have a practical lower bound on coin content, so debasement relieves but does not solve the structural small-coin problem, pointing to the historical necessity of a transition to fiat money.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. What is the debasement puzzle and how does the paper resolve it?
The debasement puzzle, documented by Rolnick, Velde, and Weber, consists of three facts: following a debasement, minting volumes rose sharply, old and new coins cocirculated sometimes by weight, and yet people still paid minting fees rather than receiving inducements — all of which are puzzling because the absence of an inducement suggests no straightforward arbitrage. The paper resolves the puzzle by modeling a debasement as equivalent to introducing a new denomination: it draws agents to the mint because it supplies the welfare-improving small denomination that agents wanted, not because of a price arbitrage. Cocirculation by weight emerges naturally along the equilibrium path because agents hold both old and new coins in optimal portfolios, and the counterfactual welfare calculation shows the welfare gain from eliminating the shortage is large, explaining why agents willingly pay minting fees to obtain the new coins.
Q2. How does the paper measure the inconvenience of a coin shortage?
The paper measures inconvenience as the welfare difference between the shortage equilibrium and a hypothetical scenario in which the mint suddenly eliminates the shortage — an unanticipated shock that adds the missing denomination to the coinage structure. This counterfactual is tractably computable in the model and directly mirrors the intuition of a historical agent who compares their constrained experience to the imagined experience of having access to the missing coins. Applied to the penny, the model shows that adding a halfpenny (debasing the penny by 50 percent) yields a welfare gain equivalent to the full shortage inconvenience; the result is large for poor agents even at once-monthly expenditure and extends to all agents when transactions are at least twice weekly.
Q3. Why can debasement not permanently solve the small-coin problem?
Full-bodied coinage — coins whose face value equals their precious-metal content — constrains the minimum viable coin size: very small coins are practically too easy to counterfeit and too difficult to handle, so debasement merely pushes the lower denomination boundary down without eliminating it. The model uses this practical indivisibility of precious metals as the structural constraint that prevents an infinite regress of smaller and smaller coins. This constraint points to why fiat money — which severs the link between value and metallic content — ultimately emerged as the only way to provide arbitrarily small denominations at negligible production cost. The paper frames this as the resolution to the historical “big problem of small change.”
Key concepts
debasement puzzle : the simultaneous occurrence of unusually large minting volumes and cocirculation of old and new coins following a debasement, without any additional mint inducement; resolved in this paper as the equilibrium response to supplying a welfare-improving small denomination.
full-bodiedness : the property of commodity coins whose face value equals their precious-metal content; acts as a commitment device against over-issuance in the model but creates a practical indivisibility constraint on the minimum coin size.
multiple-denomination model : the Lee-Wallace-Zhu framework extended in this paper; explains the social demand for multiple coin denominations via wide transaction-value heterogeneity and the burden of carrying many coins.