Academic journal article Journal of Money, Credit & Banking

The Big Problem of Small Change

Academic journal article Journal of Money, Credit & Banking

The Big Problem of Small Change

Article excerpt

Our title paraphrases one by Carlo Cipolla.(1) Like Cipolla, our subject is the process through which Western monetary authorities learned how to supply small change. Along with many other writers, Cipolla described how Western Europeans long struggled to sustain a proper mix of large and small denomination coins, and to break away from the idea that a commodity coinage requires coins of all denominations to be full-bodied.(2)

The Carolingian monetary system, born about A.D. 800, had only one coin, the penny. At the end of the twelfth century, various states began also to create larger denomination coins. From the thirteenth to the nineteenth century, there were recurrent "shortages" of the smaller coins. Cipolla (1956, p. 31) states that: "Mediterranean Europe failed to discover a good and automatic device to control the quantity of petty coins to be left in circulation," a failure that extended across Europe.(3)

By the middle of the nineteenth century, the mechanics of a sound system were well understood, thoroughly accepted, and widely implemented. According to Cipolla (1956, p. 27):

   Every elementary textbook of economics gives the standard formula for
   maintaining a sound system of fractional money: to issue on government
   account small coins having a commodity value lower than their monetary
   value; to limit the quantity of these small coins in circulation; to
   provide convertibility with unit money.... Simple as this formula may seem,
   it took centuries to work it out. In England it was not applied until 1816,
   and in the United States it was not accepted before 1853.

Before the triumph of the "standard formula," fractional coins were more nearly full-bodied and contained valuable metal roughly in proportion to their nominal values, contradicting one element of the standard formula. Supplies were determined by private citizens who decided if and when to use metal to purchase new coins from the mint at prices set by the government, contradicting another element of the standard formula. That system produced chronic shortages of small coins, but also occasional gluts. Gradually over the centuries, theorists proposed components of the standard formula; occasionally policy makers even implemented some of them. Full implementation waited until 1816, in Britain; and over the following sixty years, in France, Germany, the United States, and other countries, culminating in the establishment of the Classical Gold Standard with silver and bronze or copper coinage as subsidiary money.

Our goal is to understand the defects in the medieval monetary system and why it took so long to implement the standard formula. We present a model of supply and demand for large and small metal coins designed to simulate the medieval and early modern monetary system, and to show how its supply mechanism was vulnerable to alternating shortages and surpluses of small coins. We extend Sargent and Smith's (1997) model to incorporate demands and supplies of two coins differing in denomination and possibly in metal content. We specify cash-in-advance constraints to let small coins make purchases that large coins cannot. For each type of coin, the supply side of the model determines a range of price levels whose lower and upper boundaries trigger coin minting and melting, respectively. These ranges let coins circulate above their intrinsic values. The ranges must coincide if both coins are to circulate. The demand side of the model delivers a sharp characterization of "shortages" of small coins. Shortages of small coins have two symptoms: (1) the quantity theory of money splits in two, one for large coins, another for small; and (2) small coins must depreciate relative to large ones in order to render binding the "small-change-in-advance constraint" and thereby provide a motive for money holders to economize on small change. In conjunction with the supply mechanism, the second response is perverse and aggravates the shortage. …

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