The Big Problem of Small Change

The Big Problem of Small Change

Thomas J. Sargent
François R. Velde
Copyright Date: 2001
Pages: 434
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  • Book Info
    The Big Problem of Small Change
    Book Description:

    The Big Problem of Small Changeoffers the first credible and analytically sound explanation of how a problem that dogged monetary authorities for hundreds of years was finally solved. Two leading economists, Thomas Sargent and François Velde, examine the evolution of Western European economies through the lens of one of the classic problems of monetary history--the recurring scarcity and depreciation of small change. Through penetrating and clearly worded analysis, they tell the story of how monetary technologies, doctrines, and practices evolved from 1300 to 1850; of how the "standard formula" was devised to address an age-old dilemma without causing inflation.

    One big problem had long plagued commodity money (that is, money literally worth its weight in gold): governments were hard-pressed to provide a steady supply of small change because of its high costs of production. The ensuing shortages hampered trade and, paradoxically, resulted in inflation and depreciation of small change. After centuries of technological progress that limited counterfeiting, in the nineteenth century governments replaced the small change in use until then with fiat money (money not literally equal to the value claimed for it)--ensuring a secure flow of small change. But this was not all. By solving this problem, suggest Sargent and Velde, modern European states laid the intellectual and practical basis for the diverse forms of money that make the world go round today.

    This keenly argued, richly imaginative, and attractively illustrated study presents a comprehensive history and theory of small change. The authors skillfully convey the intuition that underlies their rigorous analysis. All those intrigued by monetary history will recognize this book for the standard that it is.

    eISBN: 978-1-4008-5162-1
    Subjects: Economics

Table of Contents

  1. Front Matter
    (pp. I-VI)
  2. Table of Contents
    (pp. VII-XII)
  3. List of Illustrations
    (pp. XIII-XIV)
  4. List of Tables
    (pp. XV-XVI)
  5. Preface
    (pp. XVII-XX)
  6. Acknowledgments
    (pp. XXI-XXII)
    Thomas Sargent and François Velde
  7. Part I: A Problem and Its Cure
    • Chapter 1 Introduction
      (pp. 3-14)

      A century ago few would have foretold the kind of money we use today. In 1873, the U.S. Congress had passed a law, section 14 of which states: “the gold coins of the U.S. shall be a one-dollar piece, which, at the standard weight of 25.8 grains, shall be the unit of value” (Statutes at Large of USA17: 427). Section 14 thus defined the American unit of account,¹ the dollar, as a specified quantity of a particular metal. In doing so, it embodied a shared wisdom accumulated from centuries of experience. And, while some countries did not adhere to...

    • Chapter 2 A Theory
      (pp. 15-36)

      This chapter presents the main elements and outcomes of our model. The exposition here contains enough to reveal the features that we watched in history. A complete account of the model appears in part V.

      Our theory allows us to interpret a pervasive and persistent depreciation of small denomination coins, exhibited for example in the data shown in figure 2.1. The six panels record estimates of the (inverse of the) silver content of small denomination coins from 1200 to 1800 for six countries. Increases in exchange rates of large for small coins and recurrent shortages of small coins accompanied these...

    • Chapter 3 Our Philosophy of History
      (pp. 37-42)

      Subsequent chapters contain selective histories of thoughts and events that pertain to managing the coinage. We present only a sample from a vast record of thoughts and events. Our model helped us select it, so our sample is biased. Because we are prejudiced observers, we tell the reader what we watched for in the historical record and how our model directed our search.

      Our model assumes that coins of a given denomination circulate by tale. The intervals between the minting points and melting points permit gaps between valuations by tale and by weight. That feature of our model implies a...

  8. Part II: Ideas and Technologies
    • Chapter 4 Technology
      (pp. 45-68)

      Our model identifies economically significant features of the technology of coin production, including ones that govern the costs of entering the business of producing counterfeits. This chapter is about technologies for producing coins. We describe the constituent metals of coins and the methods and machines available for making them. Three major technologies produced coins: (1) the hammer and pile, which prevailed from the beginning until at least 1550; (2) the screw press and the cylinder press, which were available after 1550; and (3) Boulton’s steam press, which became available after 1787. Later chapters describe how technological innovations joined with advances...

    • Chapter 5 Medieval Ideas about Coins and Money
      (pp. 69-99)

      Implementing the standard formula required both a theory of convertible tokens and a technology for producing counterfeit-proof small denomination coins. Having described the history of the relevant technology, we now recount theoretical developments that culminated in the discovery of the standard formula. This chapter summarizes the contributions of medieval jurists and how they constructed and then gradually qualified a money-as-commodity view. The next chapter then tells about the fresh approach and new findings about monetary theory brought by the Renaissance. In both chapters, we can’t help seeing theorists discovering features of our model and arguing about its parameters.

      Our story...

    • Chapter 6 Monetary Theory in the Renaissance
      (pp. 100-120)

      Renaissance writers dismantled the medieval “communis opinio” that ideally coins should be valued according to their intrinsic metallic content. They discovered three important and enduring ideas in monetary theory that undermined the “communis opinio.” The first is that the value of a coin could exceed that of its constituent metal. A related second idea is that intrinsically worthless objects can function as money and displace full-bodied specie. A third idea is that using an intrinsically worthless object as money might generate inflation, but that whether it does depends on various circumstances, including the amount issued. Episodes with token coins that...

  9. Part III: Endemic Shortages and “Natural Experiments”
    • Chapter 7 Clues
      (pp. 123-130)

      In parts III and IV, we read history in the light of our model. Part III describes events before and part IV events after the technological and theoretical innovations of the Renaissance.

      In part III, we document the recurrent shortages and debasements that were symptomatic of the medieval money supply system. We first provide a sample of problems from various parts of Europe, then focus in more detail on evidence from three places where documentation is relatively abundant: Florence, Venice, and sixteenth-century France. We close with some early experiments with convertible coinage that emerged under special circumstances. We find evidence...

    • Chapter 8 Medieval Coin Shortages
      (pp. 131-138)

      Complaints of coin shortages abound in the record since the Middle Ages.¹ The complaints were sometimes general and vague. When they were specific enough, they often mentioned a lack of coins of small denomination. Other concurrent phenomena were sometimes cited, such as exports of metal and invasions of foreign coins, always of lower quality than the domestic coins that they replaced. Our model tells us to expect such things to occur when the penny-in-advance constraint binds. To the witnesses, it often seemed that these symptoms were causes, and they sought palliatives to suppress them.

      This chapter reviews some of the...

    • Chapter 9 Medieval Florence
      (pp. 139-159)

      This chapter describes the circumstances surrounding the early coins of pre-Renaissance Florence and other Tuscan towns. After they issued multiple denominations, Tuscan towns encountered flaws in the theoretically self-regulating commodity money system, with its set melting points and minting points for coins of various denominations. Shortages and debasements of smaller denomination coins soon occurred. We discuss several episodes in Florence, including one that Carlo Cipolla called the “Quattrini affair.” By the time of that episode, the monetary authorities had struggled with limited success to repair the supply mechanism.

      Our story begins before Florence had become leader among Tuscan cities. A...

    • Chapter 10 Medieval Venice
      (pp. 160-185)

      Venice originally used one coin, the penny of Verona. Then starting around 1182, it minted its own penny ordenaro, a silver coin about 25% fine.¹ In 1201, so the story goes, Venice had exacted ten tons of silver from the leaders of the Fourth Crusade to ferry them to the Holy Land. Turning that mass of metal into pennies at the current standard would have produced 100million coins. So Venice decided to mint a new silver coin, both heavier and of higher fineness, called the(denaro) grossoor “ large penny.” The penny became known as thepiccoloor...

    • Chapter 11 The Price Revolution in France
      (pp. 186-215)

      The “Price Revolution” was a European-wide inflation during the sixteenth and early seventeenth centuries. A century of shortages and depreciations of small coins led the French authorities in 1577 to entertain issuing token small coins as a possible cure for shortages.

      In France, a famous dispute about the causes of this inflation arose between amonetary official named Jean Cherruyer de Malestroit and the jurist Jean Bodin. In 1566, Malestroit published the results of his research into this “strange dearness of all things.” He claimed that the price of silver relative to commodities displayed no long term trend, and attributed the...

    • Chapter 12 Token and Siege Monies
      (pp. 216-224)

      Medieval jurists’ preference for full-bodied coinage discouraged but did not entirely stop various forms of tokens or redeemable promises from circulating as currency. Occasionally, siege and other token coins were temporarily issued to relieve extraordinary shortages of small change and other coins. These early siege monies contained lessons about how the medieval monetary mechanism would eventually be reformed with the standard formula. Near the close of the Middle Ages, in Catalonia and Castile, these lessons were brought together to inspire early attempts to implement Cipolla’s standard formula, with governments promising to convert token coins. Those attempts were ultimately defeated by...

  10. Part IV: Cures and Side-effects
    • Chapter 13 The Age of Copper
      (pp. 227-229)

      Chapter 4 described a substantial technological change that occurred around 1550, making coins more immune to counterfeiting. As the innovation diffused across Europe, governments sought to dissociate the metallic currency from its intrinsic content, a possibility already contemplated in theory. Governments issued copper coinage, initially as a substitute for small change. For a time it circulated at much more than its intrinsic content. Variations of these experiments occurred across Europe. Some of these experiments sought to improve the efficiency of the money supply mechanism by implementing a version of Adam Smith’s thought experiment (see page 101). Theorists soon drew lessons...

    • Chapter 14 Inflation in Spain
      (pp. 230-253)

      The standard formula recommends that the government make over-valued tokens that it redeems for full-bodied coins. To create tokens, the government should terminate free minting of small denominations and thereby end the associated automatic mechanism governed by the minting and melting points, with the purpose of divorcing the value of small coins from that of the metals they contain. To determine the exchange value of the small coins, the standard formula instructs the government to offer to convert token coins into full-bodied coins. The possibility of pushing overvalued small coins into circulation was discovered before the importance of convertibility was...

    • Chapter 15 Copycat Inflations in Seventeenth-Century Europe
      (pp. 254-260)

      This chapter describes how several European countries were tempted to replicate the Castilian experiment with token coins. Some resisted but others accepted the temptation and took the inflationary consequences.

      France was tempted to copy the Spanish experiment, but ultimately refused. In France, the realization that mechanized minting allowed a fiduciary coinage dawned at the same time as in Spain. Before 1575, France’s small denomination coins had been made of billon. The French had set up the Mill Mint, a mechanized mint, in 1552 (see chapter 4). In 1575, it produced the first pure copper coins, with an intrinsic content worth...

    • Chapter 16 England Stumbles toward the Solution
      (pp. 261-290)

      This chapter and the next describe the mixture of experience and theorizing that eventually led England to adopt the standard formula. Experience held the upper hand. During the seventeenth and eighteenth centuries, England used privately issued tokens and counterfeits for much of its small denomination coins. In 1661, Sir Henry Slingsby propounded the standard formula. The government did not implement it, even after 1787, when Boulton’s steam press made Slingsby’s proposal practical. But private firms quickly exploited Boulton’s technology to make redeemable tokens that were difficult to counterfeit. For a generation after 1787, these private tokens supplied small change for...

    • Chapter 17 Britain, the Gold Standard, and the Standard Formula
      (pp. 291-305)

      With the Great Recoinage of 1696, Britain withdrew from its earlier experiments with token subsidiary coins and reaffirmed the medieval idea of a full-bodied commodity money throughout the denomination structure. It thereby arrested its earlier substantial progress toward the standard formula. Nevertheless, in the eighteenth century, market pressures and a government policy neglecting subsidiary coinage propelled Britain again toward the standard formula. These developments contributed to the gradual process by which Britain approached the gold standard in the early nineteenth century, when it explicitly made its subsidiary coins into tokens that it promised freely to exchange for gold coins.¹


    • Chapter 18 The Triumph of the Standard Formula
      (pp. 306-319)

      This chapter describes how the standard formula spread beyond Britain in the course of the nineteenth century. While Britain adopted the standard formula along with the gold standard, in 1838 the German Monetary Union implemented the standard formula but remained on a silver standard. When Germany unified in 1871, it switched to a gold standard. Meanwhile, the United States and a group of countries led by France put in place important features of the standard formula while maintaining bimetallism. All eventually followed Britain onto the gold standard.

      By the early nineteenth century, shortages of small change of the type we...

    • Chapter 19 Ideas, Policies, and Outcomes
      (pp. 320-332)

      James Laurence Laughlin (1931, 87) concluded his textbook exposition of the standard formula as follows:

      It might seem at first blush that, as subsidiary moneys play only a secondary part, the principles governing them are not of first importance. On the contrary, the questions raised in early monetary experience down to the present day of necessarily combining different metals of varying relative values in one monetary system have led to the evolution of general principles of far-reaching influence.

      Laughlin cited the role of these principles in managing the silver money stocks in formerly bimetallic countries, and also in maintaining “the...

  11. Part V: A Formal Theory
    • Chapter 20 A Theory of Full-Bodied Small Change
      (pp. 335-336)

      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 lay vulnerable to alternating shortages and surpluses of small coins.¹ 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. As in the Sargent-Smith model, for each type of coin, the supply side of the model determines a range of price levels...

    • Chapter 21 The Model
      (pp. 337-349)

      In a small country there lives an immortal representative household that gets utility from two nonstorable consumption goods. The household faces cash-in-advance constraints.¹ “Cash” consists of a large and a small denomination coin, each produced by a government-regulated mint that stands ready to coin any silver brought to it by household-owned firms. The government specifies the amounts of silver in large and small coins, and also collects a flat-rate seigniorage tax on the volume of newly minted coins; it rebates the revenues in a lump sum. Coins are the only storable good available to the household. The firm can transform...

    • Chapter 22 Shortages: Causes and Symptoms
      (pp. 350-365)

      This chapter computes some sample equilibria and uses them to highlight key operating characteristics of the model. We utilize the back-solving strategy employed by Sargent and Smith (1997) to describe possible equilibrium outcomes. Back-solving takes a symmetrical view of endogenous and exogenous variables.¹ It views the first-order and other market equilibrium conditions as a set of difference inequalities putting restrictionsacrossthe endowment, allocation, price, and money supply sequences, to which there exist many solutions.

      We use back-solving to display aspects of various equilibria. For example, we shall posit an equilibrium in which neither melting nor minting occurs, then solve...

    • Chapter 23 Arrangements to Eliminate Coin Shortages
      (pp. 366-372)

      This chapter describes two money supply mechanisms that, within the context of our model, prevent shortages of small coins. We scrutinize these mechanisms in terms of how they incorporate some or all of the ingredients in Cipolla’s recipe, and study whether some ingredients of the recipe are redundant.

      We change the supply mechanism to implement a version of Cipolla’s standard formula, retaining the demand side of the model. It is as if the government tells the mint to set up a “pennies department” that operates like a currency board for pennies. The rules for supplying dollars are not changed from...

    • Chapter 24 Our Model and Our History
      (pp. 373-374)

      We designed our model to help us understand problems with the arrangements for minting more or less full-bodied coins that prevailed for centuries throughout western Europe. Our model ascribes rules for operating the mint that copy historical ones, and focuses on the difficulty those rules create for simultaneously maintaining two commodity currencies. The model extends insights from single-currency commodity money models,¹ where minting and melting points impose bounds within which the price level must stay to arrest arbitrage opportunities. In those one-commodity money models, when the price level falls enough (i.e., when currency becomes scarce), new coins will be minted;...

  12. Glossary
    (pp. 375-376)
  13. References
    (pp. 377-392)
  14. Legal Citations Index
    (pp. 393-394)
  15. Author Index
    (pp. 395-398)
  16. Subject Index
    (pp. 399-406)