The Evolution of Small Change: Beliefs, Experiments, and ...

Supply 15
arbitrage profits for coin i, the price level must satisfy 8
ei (1 − σi) γi ≤ p ≤ eiγi. (2.1)
The left side of this inequality gives the rate at which consumption goods
can be exchanged for silver and then taken to the mint to get dollars in
denomination of coin i. The right side gives the rate at which coins of
denomination i can be converted from dollars to consumption goods by
melting them down and then exchanging the silver for consumption goods.
Notice that the rates of transformation from consumption goods to dollars
(on the left, by minting) and from dollars to consumption goods (on the
right, by melting) are irreversible.
Coin by coin, (2.1) identifies counterparts of ‘gold points’ for melting
(the right endpoint) or coining (the left endpoint) a commodity money.
By making the range narrow, a commodity money system links the price
level to φ, the relative price of consumption goods in terms of the metal.
Standard treatments of a gold or silver standard typically mention (2.1)
for the leading coin only, the dollar or the pound, not the subsidiary ones.
But equation (2.1) imposes the ‘gold points’ throughout the denomination
structure. A mid nineteenth century Western European would have
thought that feature strange, but it embodied what a Medieval European
meant by a commodity money. The medieval monetary authority intended
that coins of all denominations should be full bodied. 9
We complete our model of supply with identities that track stocks of
coins:
mit = mit−1 + nit − µit, (2.2)
8 Our specification of supply is consistent with the reasoning of Adam Smith (1776,
Ch. ), who described how coins must be valued more than by weight if citizens are ever
voluntarily to use metal to buy coins from a mint that charges seigniorage fees over and
above costs of production. Smith pointed out that if there were a delay in delivering the
coins after the metal was surrendered, an interest factor would drive an additional wedge
beyond the seigniorage fee and production costs. Smith presumed valuation by tale, and
considered the range of departures that seigniorage fees, costs, and time delays open for
coins to bear values in exchange exceeding ones based on weight.
9 Cipolla’s standard formula suspended (2.1) for all but one basic coin, and made all
other coins tokens that the government promised to convert into the standard coin on
demand.