# Penny facts and optimal denominations

\$10.5 billion in small change sits around people’s homes.

The average U.S. transaction produces 4.7 coins in change.

Eliminating the penny would lower this figure to 2.7 coins.

The average Canadian transaction produces 5.9 coins in change (Canada has a dollar coin), this would be 3.9 coins in a pennyless world.

A mathematical technique known as Diophantine equations can be used to calculate the coin denominations that would produce the least amount of expected change per transaction. If we replaced the dime with an 18-cent coin, the average number of coins per transaction would fall from 4.7 to 3.89. If we must keep the dime, adding a 32-cent coin would give us a figure of 3.46. The best solution of all would be to combine an 18-cent piece, and actually use the half-dollar coin, for a figure of 3.18 coins per transaction. N.B.: These calculations do not consider the limited ability of Americans to do math in their heads.

These facts are taken from the October issue of Discover magazine, although only a small fragment of the article is available on-line.

Thomas Sargent’s excellent The Big Problem of Small Change (co-author Francois Velde) provides a fascinating historical look at how our denominations evolved, and why we use fixed denominations rather than monies with floating exchange rates against each other, as in medieval times. Imagine having a daily rate for how much a dime is worth, vis-a-vis a quarter. Sargent and Velde claim that fixed rates, combined with a willingness of the central bank to trade at those rates, offers the best possible mix of denominations. They stress that this solution requires good safeguards against counterfeiting.

According to one poll, seven percent of Americans use coins to stabilize table legs, seventy-three percent to scratch off lottery tickets.

One individual wisecracked: “Actually the United States does have an 18-cent coin…It’s called the Canadian quarter.”

Addendum: About \$600 worth of coins pass through the hands of a typical American each year. Using pennies may make an average cash transaction three seconds longer.

Second addendum: Professor Bainbridge tells us that the penny will never be abolished, and that sales tax is the reason why. He also cites this link on why abolishing the penny would raise government expenditures by more than a billion dollars, due to CPI effects.

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