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What This Country Needs Is an 18¢ Piece [pdf] (uwaterloo.ca)
39 points by jdleesmiller 120 days ago | hide | past | web | 45 comments | favorite

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.

In case it isn't clear, this is a bit of mathematical play, not an actual proposal.

"Assuming each amount of change between 0 and 499 is equally likely"


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.

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

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.

In other words... copy Canada. We have proven that it works already!

Basically. England, too.

I never understood this. They start printing $1 coins and complain that nobody uses them. Then they stop printing them.

Of course nobody uses them. Their wallets are filled with bills. That they keep printing. Then they announce a coin that will surely be cancelled in a few months, and collectors jump on it.

Americans would use a $1 coin if the deployment strategy wasn't garbage, condemning them to collector status almost immediately.

So what's the argument for the government forcing people to use a coin they have repeatedly chosen not to use voluntarily?

In any case, at this point in history, it would seem to make little sense to overhaul currency denominations.

The problem is that the coins won't be useful unless the entire country adopts them together. By signalling that they're not really serious about it, the Treasury ensures that they won't be adopted. Transforming the currency is a fairly big project:

  - banks have to introduce the new coins in quantity
  - banks have to collect the old bills for return to the treasury
  - cash registers have to be redesigned and replaced
  - vending machines need to be updated to accept the new coins
  - businesses have to stock the new coins to give out as change
  - pricing and accounting may have to be updated to handle new rounding rules
That's a lot of work. People will do it if they think the change is here to stay, but otherwise it's not worth it. And of course, society won't reap the benefits of the change if all this stuff doesn't get done.

Speaking for myself I don't want dollar coins. And I expect a lot of others agree. And would vote against it given the opportunity.

Honest question. What benefits?

Especially with so many transactions going electronic, it also seems an odd time to make an expensive and disruptive currency shift even if there were some small net positive.

Wouldn't the effort be better spent on stored value cards? (Though I wonder if even the time for that is getting past given smartphone payments.)

I can only speak for myself, but I (an American) tend to any away from using coins at all just because they're rather unwieldy compared to bills or credit/debit cards, which are light, easily stored in a wallet, and useful in much smaller quantities.

That's because American coins aren't worth anything. I'd like to see $5 and $20 coins, and the elimination of the penny and nickel, which would mean I don't have to carry around paper money any more.

Traveling to Europe I found the euro coins to be much more convenient.

Just got back from Europe. Can't stand those 1 and 2€ pieces. The worst part is when we got back to change our leftover euros back to dollars, the bank wouldn't take the coins. Now I have a stack of them sitting on my dresser.

Worthless coins is a feature, not a bug for me. I can toss them somewhere and eventually redeem them in a Coinstar machine. I don't like the bigger Euro coins. It means I actually need to be aware of spending the coins when I travel to Europe. Much prefer only bills, touchless cards/phone, credit cards.

Euro coins only go up to 2 euros, does that really make such a difference?

Here in the Netherlands we don't really use the 1 and 2 eurocent coins anymore. It was decided that they're just annoying, so (almost?) all shops always round prices to the nearest amount that can be divided by 5 cents (Only when you pay with cash, electronic payments are not rounded. Naturally you can still pay with 1 and 2 cent coins, you'll just never get them back as change). I visit Germany a couple of times a year and it always surprises me they're still bothering with those 1 and 2 cent coins.

"Dime and quarter" is awkward -- it's a benefit to have the smallest positive difference between any two piles of coins to be a coin value. Either get rid of the dime, or replace the quarter with a 20 and/or 50 cent piece.

If we got rid of the 1c penny and 5c nickel, then the dime would be the smallest/thinnest coin... having change in $0.1 increments seems as reasonable to me as having the current (e.g. gasoline) pricing in $0.001 mils.

Just shift up an order of magnitude for physical payment. The FED is targeting 2% inflation a year so every century or so we should shift an order of magnitude in value.

Interesting! Out of curiosity, what aspects of coins do you find more convenient than paper money?

In the US you pay in paper money and you're almost always going to get some change in coins. Pretty much that means you're always carrying around both bills and coins. The coins have so little value most people pay with bills and then just pocket the coins without counting them. At the end of the day the coins go into a jar, and eventually you have to lug that twenty pound jar to the bank or one of those coin machines.

Why not carry usable amounts of cash in coins instead? You pay in coins and you get coins back in change. Of course that doesn't work if need to carry larger denominations, but if you're going to buy lunch or pop down to the liquor store it's more convenient, IMO.

I'm the opposite. I carry a wallet-like thing anyway for cards and other misc paper. Paper currency is just a few more pieces of paper. Coins are another pouch or something that I need to carry. Although, to tell the truth, I pay cash so seldom in the US these days that it doesn't really matter.

My wallet includes a pouch for coins; I think that's fairly standard for a wallet sold in Europe.

Coins are easier to tell apart, and I never like the grubby $1 bills I get in the USA. But, I don't often use cash either -- mostly when splitting the bill in a restaurant, since it's easier to hand the waiter 200kr than have everyone use the card terminal in turn to pay their exact 194.23kr share.

One of the issues with coins for me is weight/volume. It wouldn't be too much work for me to have $20 in $1 bills in my wallet, but carrying around $20 in quarters (or even $1 coins, to be honest) seems like it would be much more effort, since it would take up a large amount of the space in my pocket and likely be fairly uncomfortable for my leg.

That's why I want a $5 and $20 coin.

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?

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.

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

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.



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.

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

Hey. I forgot about those things. I wonder when they went away.

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...

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

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.

> 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.

Transactions are rounded by default in Australia.

"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"!

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

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.

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.

*Also we have loonies and toonies

If you look at the bottom of the first page, you'll see it's a play on this: “What this country needs is a really good five-cent cigar.” T. R. Marshall (US Vice-President), New York Tribune, January 4, 1920

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