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Demand and Supply of Currencies of Small Denominations: A Theoretical Framework

  • Kaushik Bhattacharya


    (Indian Institute of Management Lucknow)

Economic history reveals that different countries over different time periods suffered from severe shortage of currencies of small denominations. Due to the frequency and severity of these incidents, first Cipolla (1956) and later Sargent and Velde (2002) named this phenomenon as ``the big problem of small change''. The paper presents a theoretical framework to understand ``the big problem of small change''. It specifies demand and supply equations of currencies of small denominations. Both demand and supply equations emerge out of an optimization framework. Demand functions for small denominations are obtained from a linear expenditure system. Our main contention is that economic agents would like to hold a fixed number of small changes, independent of their respective total cash holdings. However, in our model the fixed quantity is influenced by the probability that in a currency transaction, the counterparty would be able to provide the small change if needed. The supply function is derived from an optimization problem where the central bank balances its operational cost with the probability that an individual would be able to carry out ``small'' transactions independently, without the help of counterparty. In this demand-supply framework, the probability that a randomly chosen individual in an economy would hold certain currency combinations is interpreted as ``price''. We attempt to show that in a dynamic environment, such interaction could be understood by specifying a cob-web type model where expectations are formed based on previous period's experience. As an operational rule, it is proposed that the central bank should increase the supply of small denominations at a rate marginally above the growth rate of economically active population and stop minting as soon as some of the small denominations start return in the currency chest. We also suggest how demand for ``small change'' could be estimated from the ``lifetime'' of the ``smallest'' denomination.

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Article provided by The Indian Econometric Society in its journal Journal of Quantitative Economics.

Volume (Year): 9 (2011)
Issue (Month): 2 (July)
Pages: 123-139

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Handle: RePEc:jqe:jqenew:v:9:y:2011:i:2:p:123-139
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Order Information: Postal: Managing Editor, Journal of Quantitative Economics, Indira Gandhi Institute of Development Research (IGIDR), Gen. A.K. Vaidya Marg, Goregaon (E), Mumbai 400 065 , INDIA

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  1. Cramer, J. S., 1983. "Currency by denomination," Economics Letters, Elsevier, vol. 12(3-4), pages 299-303.
  2. Sumner, Scott, 1993. "Privatizing the Mint," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(1), pages 13-29, February.
  3. Laurence Ball & N. Gregory Mankiw, 1993. "Relative-price changes as aggregate supply shocks," Working Papers 93-13, Federal Reserve Bank of Philadelphia.
  4. Wallace, Neil, 2003. "Modeling Small Change: A Review Article," Working Papers 9-03-3, Pennsylvania State University, Department of Economics.
  5. Manjong Lee & Neil Wallace & Tao Zhu, 2005. "Modeling Denomination Structures," Econometrica, Econometric Society, vol. 73(3), pages 949-960, 05.
  6. Wallace, Neil, 2003. "Modeling small change: a review article," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1391-1401, September.
  7. Kaushik Bhattacharya & Himanshu Joshi, 2002. "An Almon Approximation of the Day of the Month Effect in Currency in Circulation," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 37(2), pages 163-174, July.
  8. Kohli, Ulrich, 1988. "A note on banknote characteristics and the demand for currency by denomination," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 389-399, September.
  9. Telser, L. G., 1995. "Optimal denominations for coins and currency," Economics Letters, Elsevier, vol. 49(4), pages 425-427, October.
  10. Kaushik Bhattacharya & Himanshu Joshi, 2001. "Modelling currency in circulation in India," Applied Economics Letters, Taylor & Francis Journals, vol. 8(9), pages 585-592.
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