You asked the question That is a question I have heard many times and only got the answer because of the pandemic! Like many, with in-person activities cancelled, I turned to online opportunities.

I learned the answer in a Zoom meeting presented by the Hobby Club in New Delhi, India. The simple answer is our culture. Explaining it is much more complicated. The culture that I am referring to is not high culture like old paintings, the symphony or opera. This culture is created by a blend of tradition, politics, convenience, superstition, religion, science, mathematics, anatomy, language, humor and many more factors. I think of culture as those things that everybody knows but nobody is taught. One example is the expression We all know it and we all believe it, but it is not taught in school.

First, a look at coins through the lens of our culture. Because of our culture, we think of coins as commodity money. That is to say, coins are worth the value of the metal, or they have intrinsic value. Logically, we know that today this is not true of our coins, but cultural beliefs are very deeply rooted and take many decades to go away if they ever do. Commodity money can be divided or split. The easiest split for the human mind in to divide into halves. So, we have 1/2 dollars, 1/2 dimes and 1/2 cents. Splitting the halves in half again and we have 1/4 dollars. Historically we have split these in half again and gotten pieces-of-eight. We have other fractions of a dollar. One tenth of a dollar is not called a it is called a dime. One hundredth of a dollar is not called a it is called a cent. This is because splitting into 10 or 100 equal pieces is harder for the human mind to consider. So why do we have a 25-cent piece? The answer is culture.

Next a look at banknotes. Our culture has always thought of them as fiat money. That is to say, banknotes are only backed by the belief in the issuing authority. We do not split fiat money. Almost never have banknotes been torn in half to make lower denominations. It is created for convenience. Convenience in paying with the fewest number of banknotes. Convenience in receiving change in the fewest number of banknotes. Also, the issuing authority wants to print the fewest number of banknotes for lower printing costs and transportation costs. To achieve these advantages of fiat money an efficient scheme needs to be used.

Analyzing various schemes can easily be done empirically. Pick the proposed banknotes in the scheme. Then count the minimum number of notes needed to pay amounts between 1 and 10. The lower the total number, the more efficient the scheme. Here is an analysis of a $1-$2-$3 scheme.

This analysis applies for the issuing $1, $2, and $3 banknotes and issuing $10, $20, and $30 banknotes and issuing $100, $200, and $300 banknotes.

The analysis can be done for any other combination of banknotes that the issuing authority is considering. For a $1-$2.50-$5 scheme the total is very high at 27. So, the $25 banknote is out of the question. I have done this analysis on many schemes. There are two schemes of three banknotes with a total of 19. These are the most efficient schemes, a $1-$2-$5 scheme and a $1-$3-$7 scheme.

So, the final question is which scheme to use, the $1-$2-$5 scheme or the $1-$3-$7 scheme? Culture makes this decision too. With human anatomy, we start counting with one finger, we have two hands and five fingers per hand. The $1-$2-$5 scheme is the obvious winner. And by extension to $10-$20-$50 and $100-$200-$500 if we choose to go that far. Of course, the $2 banknote is not popular because of superstitions in our culture. So why do we have a $20 banknote? The answer is culture.

To read the earlier E-Sylum article, see:
PEARSON: MORE DESIGNS FOR U.S. PAPER MONEY(https://www.coinbooks.org/v24/esylum_v24n39a14.html)