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The Big Problem of Small Change


  • Sargent, Thomas J
  • Velde, Francois R


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. The authors 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. They use the model to study the behavior of exchange rates between large and small denomination coins across periods of shortages. The authors 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.

Suggested Citation

  • Sargent, Thomas J & Velde, Francois R, 1999. "The Big Problem of Small Change," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(2), pages 137-161, May.
  • Handle: RePEc:mcb:jmoncb:v:31:y:1999:i:2:p:137-61

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    References listed on IDEAS

    1. Lucas, Robert Jr., 1982. "Interest rates and currency prices in a two-country world," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 335-359.
    2. Diaz-Gimenez, Javier & Prescott, Edward C. & Fitzgerald, Terry & Alvarez, Fernando, 1992. "Banking in computable general equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 533-559.
    3. John Kareken & Neil Wallace, 1981. "On the Indeterminacy of Equilibrium Exchange Rates," The Quarterly Journal of Economics, Oxford University Press, vol. 96(2), pages 207-222.
    4. Glassman, Debra & Redish, Angela, 1988. "Currency depreciation in early modern England and France," Explorations in Economic History, Elsevier, vol. 25(1), pages 75-97, January.
    5. Helpman, Elhanan, 1981. "An Exploration in the Theory of Exchange-Rate Regimes," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 865-890, October.
    6. Redish, Angela, 1990. "The Evolution of the Gold Standard in England," The Journal of Economic History, Cambridge University Press, vol. 50(04), pages 789-805, December.
    7. Thomas J. Sargent & Francois R. Velde, 1997. "The evolution of small change," Working Paper Series, Macroeconomic Issues WP-97-13, Federal Reserve Bank of Chicago.
    8. Sims, Christopher A, 1990. "Solving the Stochastic Growth Model by Backsolving with a Particular Nonlinear Form for the Decision Rule," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 45-47, January.
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