
What This Country Needs Is an 18¢ Piece [pdf] - jdleesmiller
https://cs.uwaterloo.ca/~shallit/Papers/change2.pdf
======
s0rce
Interesting idea, however, it seems like it would be slower for people to
calculate what change to give, also Americans won't even use the $1 coin, I
can't see the 18c coin gaining wide acceptance.

~~~
wcummings
IMO we should simultaneously introduce a new dollar coin _and_ a two-dollar
coin. Once you have two-dollar coins, you're able to conveniently make small
purchases exclusively using coinage.

~~~
semi-extrinsic
FWIW, both Switzerland and Japan have coins that are about $5 (5 CHF = $5.14
and ¥500 = $4.5 right now).

~~~
Symbiote
Perhaps a more interesting measure is how many coins it takes to buy a Big
Mac, or whether the coins are worth so little it would normally be done with
paper money.

For example, the Big Mac index of the UK is £3.09, which is fairly reasonable
for coins (£2 + £2 + 10p).

For Switzerland, it's 6.50Fr, so 5Fr + 1Fr + 0.5Fr.

But for the US, it's $5.06, which needs the paper $5.

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Humphrey
Australia solved this problem back in 1990 by removing 1c and 2c coins. When
paying in cash, transactions are rounded to the nearest 5c. No rounding occurs
for digital transactions.

Have just spent a month in the USA for the first time, I found that the only
reason coins < 25c were used were when change was given. And this was only the
case because adding tax to the price made most prices having unrounded final
amounts. In Australia, all prices are quoted including tax, which means that
prices can be rounded, and so the need for coins in minimised.

I love the mathematical slant of this paper, but it'd make much more sense to
try and get rid of the need for coins.

Perhaps, the USA could remove all coins except for quarters?

~~~
froindt
I've sworn for years if I ever own a store, all prices will either include
tax, or will be to a round dollar or quarter.

The US got rid of the half cent when it couldn't be used to buy anything of
worth. Inflation adjusted, it had the value of 14 cents. I've started to leave
pennies, nickels, and dimes in the "leave a penny, take a penny" holders.

~~~
Humphrey
Yeah, although if you did that, everybody would subconsciously think that your
prices were higher. Perhaps just show the inc. tax and ex. tax prices. AirBNB
and Uber do this nicely already.

Half cents! ha ha... I find it funny how US petrol stations quote gas to the
tenth of a cent. Such as $3.39 9/10 a gallon.

I also found it really difficult having all the paper notes the same colour.
I'd look in my wallet and I couldn't tell whether I had hundreds of dollars,
or just ten one dollar bills. The poor shop keepers who had to wait for me to
look at each bill and coin individually before handing them over :-p

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forinti
In 2010, after reading an article similar to this one (but lighter on the
maths), I wrote a Perl script to calculate what would be the best combination
of 4, 5, or 6 coins.

I did not look into the actual distribution of prices and just supposed that
every value was equally probable.

[http://alquerubim.blogspot.com.br/2010/09/otimizando-
niquele...](http://alquerubim.blogspot.com.br/2010/09/otimizando-
niqueleira.html)

[http://alquerubim.blogspot.com.br/2010/09/otimizando-
niquele...](http://alquerubim.blogspot.com.br/2010/09/otimizando-niqueleira-
ii.html)

------
dizzystar
It's interesting from a purely computational perspective, but I'm pretty sure
most people would have some difficulty counting out in denominations that
aren't mod 5.

Noting that this is from 2003, before many stores introduced the automatic
changer, I'm not sure if the 17% increase in efficiency would make a huge
difference.

Humans themselves aren't efficient, and many registers across America aren't
designed to be an assembly line with no niceties.

One would think the 50c coin would be in wider circulation than it is, so I'm
assuming the authors are correct that the odd denomination wouldn't see large
acceptance.

~~~
pandaman
USSR had 2 and 3 cent coins along with 3 rouble bill, I don't recall people
having any difficulty with these.

~~~
chch
As did the United States, for the coins [1][2]!

[1] [https://en.wikipedia.org/wiki/Two-
cent_piece_(United_States)](https://en.wikipedia.org/wiki/Two-
cent_piece_\(United_States\))

[2] [https://en.wikipedia.org/wiki/Three-
cent_nickel](https://en.wikipedia.org/wiki/Three-cent_nickel)

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nayuki
Currency denominations (coins and bills) are usually based on numbers like 1,
2, 5, 10, 25, 50, 100, 200, etc.

An extreme example is that Japanese yen are denominated as 1, 5, 10, 50, 100,
500, 1000, 2000(uncommon), 5000, 10000. But I noticed that it takes a lot of
1's to pay or make change, whereas the 5's are less used.

What if we use denominations like 1 and 3 instead? The benefit is that the
ratio 1:3 is similar to the ratio 3:10, so they are more evenly spaced on a
logarithmic scale. Specifically, I'd like to explore what happens if the
denominations are 1, 3, 10, 30, 100, 300, 1000, 3000, etc...

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grenoire
Reminds me of McNugget numbers
([http://mathworld.wolfram.com/McNuggetNumber.html](http://mathworld.wolfram.com/McNuggetNumber.html)).

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protomyth
I would rather we scrap this whole base 10 and have the Dollar divided into 12
pence (like the old pence to shilling). That given a nice 2, 3, 4, and 6 for
divisibles instead of 2 & 5.

I would bet that 18c would get labeled a devil's coin by some.

Of course, I'm one of those folks who would like to to see the $1, $5, and $10
bills replaced with coins. Might be nice to follow the example of some of the
Chinese coins and have a hole in the middle for convenience.

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paulcole
> For people who make change on a dailg basis, it is desirable to make change
> in as efficient a manner as possible

Is it though? You're going to save a few random seconds here and there, not
big chunks of time. Plus it's not like the change making process is hugely
slowing down checkout lines.

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andrewstuart
Transactions are rounded by default in Australia.

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jstanley
"This country"? The author is at the University of Waterloo, but the Abstract
talks about the USA.

It should be called "What THAT country needs is an 18c piece"!

~~~
deanmen
Canada has the same coin denominations as the US, except that it has now
eliminated the penny.

~~~
rspeer
The article already accounts for a difference between Canadian and US currency
-- the US has no $2 coins and nearly nonexistent $1 coins, and the smallest
bill in Canadian currency is $5.

They suggest "optimizing" Canadian change with an 83-cent piece... which of
course makes no sense once the penny is eliminated, so now there must be a
different optimal coin.

~~~
uiri
The author could easily base calculations off of cost(100; 1, 2, 5, 20, 40)
and multiply the result by 5 to find the new optimal coin. This avoids unduly
weighting values which are impossible without a penny which is what cost(500;
5, 10, 25, 100, 200) would do.

