Estimating Optimal Denominations

34 Pages Posted: 24 May 2012

See all articles by William J. Luther

William J. Luther

Florida Atlantic University; American Institute for Economic Research

Date Written: May 24, 2012


Two distinct approaches have been taken in the literature to consider the optimal denominations of coins and banknotes. One approach reduces the problem to determining the smallest set of denominations capable of handling a given range of transactions. Another approach argues the optimal denomination structure would minimize the number of coins and banknotes used in the average transaction. Both are ultimately concerned with the optimal spacing of denominations. In contrast, I estimate the average range of denominations for coins and banknotes conditional on real income and the monetary unit employed. To illustrate the practical application of this approach, I use the estimates as a benchmark for evaluating the payment system of Somalia emerging after the state collapsed in 1991. I show that the surviving 1000 Somali shillings note is too small for conveniently making large transactions, but too large to make precise change in small transactions.

Keywords: Banknotes, Coins, Currency, Denomination, Denomination Structure, Monetary Regime, Monetary Standard, Monetary Unit, Money, Payments, Payment System, Powers-of-Three, Powers-of-Two, Somalia, Somali Shilling

JEL Classification: E41, E42

Suggested Citation

Luther, William J., Estimating Optimal Denominations (May 24, 2012). Available at SSRN: or

William J. Luther (Contact Author)

Florida Atlantic University ( email )

777 Glades Road
Boca Raton, FL 33431
United States


American Institute for Economic Research ( email )

PO Box 1000
Great Barrington, MA 01230
United States


Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics