Bhattacharya, Kaushik (2009): Demand and Supply of Currencies of Small Denominations: A Theoretical Framework.

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Abstract
The paper presents theoretical framework of demand and supply of currencies of small denominations. In our framework 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 demandsupply 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 cobweb 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.
Item Type:  MPRA Paper 

Original Title:  Demand and Supply of Currencies of Small Denominations: A Theoretical Framework 
Language:  English 
Keywords:  Small Change, Denomination, Currency Management, Poisson Distribution 
Subjects:  D  Microeconomics > D0  General E  Macroeconomics and Monetary Economics > E5  Monetary Policy, Central Banking, and the Supply of Money and Credit E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates 
Item ID:  27334 
Depositing User:  Kaushik Bhattacharya 
Date Deposited:  09. Dec 2010 13:41 
Last Modified:  12. Feb 2013 13:47 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/27334 