
Do We Need a 37-Cent Coin? - mhb
http://freakonomics.blogs.nytimes.com/2009/10/06/do-we-need-a-37-cent-coin/
======
dbfclark
The story (picked up from Daniel Davies at
<http://d-squareddigest.blogspot.com>) goes that the way one argued with
Milton Friedman was to listen until he got to the part of his argument where
he said "let's assume x" and then say "no, let's not!" That is, the part of
the argument doing all the work tended to be hiding in some premise that
economists consider innocuous but is in no way representative of the world.

So here, premise (2): "probability of a transaction resulting in value v is
uniform." No! Not true! In reality, people price a disproportionate number of
transactions to make easy change with the coins we have, be easily divisible,
be .01 less than a larger number of dollars, and so on. The discovery that
cash transactions had a uniform distribution of change would actually be quite
weird.

But worse is the smuggling in of an unconsidered definition of the good in the
form of the efficiency metric -- fewest coins per transaction. Even granting
the uniform distribution, making change out of your pocket is still solving
the subset-sum problem in your head, which is of course NP-complete. The
existing setup of coins, including the first three powers of 5, makes this
problem very easy while almost all the proposed "better" solutions actually
make this aspect of the problem harder rather than easier. Who cares if I have
to handle a few extra tenths of a coin per transaction if it means I don't
have to spend two minutes puzzling out how to make change?

I suppose the lesson, as usual, is that business logic is lived experience,
not theory.

~~~
frgbhnmnjh
Not quite in the USA you buy three items that end in 99c, but two of them have
state sales tax, one of those has local sales tax and the other has a liquor
tax.

SO you can work out the change IF you know the random extra amount that will
be added at the checkout

~~~
chopsueyar
I've actually started using $2 bills for this reason.

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jerf
I rather suspect that if we consider "the ability for most of the population
to correctly and reliably perform mental math using the tokens provided" that
while our current system still doesn't _win_ it has a much better showing. And
yes, I'm willing to ignore the fact that people are already familiar with the
current system, but I can't come up with a much better one off the top of my
head.

By that metric, 37-cent pieces are just about the worst coinage possible,
11-cent pieces are a joke, and even 15-cent pieces which don't evenly add up
to a dollar are a suboptimal.

Even by economist standards, ignoring this aspect of the system is rather a
disappointment.

~~~
jjcm
Perhaps a good measure of whether or not the general populous can perform
mental math based on the value of the coins is to check and see whether or not
a single dollar is divisible by the value of the coins (as you hinted with the
15 cent coin). It allows for many mental paths to arrive at the correct answer
for what amount of coins are needed to make a certain sum. Take the nickel for
example, to make 50 cents you might think to yourself, "I just need to divide
50 by 5, which is obviously 10." Alternately one might think, "I know there
are 20 nickels in a dollar, if I halve this I'll have half a dollar, which is
50 cents. That means I need 10 nickels."

I'd say that the pool of coin values we can choose from then are 50, 25, 20,
10, 5, 2, 1. The two cent piece is already in use in Europe, and many
economists have suggested adding it to the coinage in the united states
(usually in replacement for the penny altogether). It'd be interesting to see
if the 20 cent coin would be a viable addition though.

~~~
daychilde
I very much agree that's the practical pool of possible coin values.

Seems to me if one wanted to simplify the system, a good solution would be (1,
5, 10, 50). This would really make the math simple.

But I don't think people would give up quarters happily; nor do I think fifty
cent pieces would go over well; and I think it's high time to lose pennies. So
if I was the evil overlord in charge, I think I'd just drop to (5, 25). Cash
transactions would round to the nearest nickel instead of penny. Getting back
four nickels instead of two dimes would be gotten used to quickly, I think.

------
martingordon
Jeez, the 37signals worshipping around here is getting a bit out of hand.

In all seriousness, how about vendors start pricing products with tax
included, rounding to the nearest quarter dollar? Say what you will about
movie theatre concession pricing, at least you're not going to walk out of
there needing a tub for your change as well as your popcorn.

~~~
decadentcactus
At least here in Australia, prices at the shops will include taxes. So getting
the correct change out while waiting in line is pretty simple.

~~~
points
Same in the UK.

Sales tax in the US is just ridiculous. I've never understood why they would
prefer things that way.

~~~
hugh3
As mentioned elsewhere, it's because sales tax varies from state to state and
from county to county. So if you're going to advertise something for a given
price, you either have to exclude sales tax or accept that you'll be making
significantly less profit selling it in California than in Oregon.

It's a crazy system, but state and local governments are dependent on sales
tax revenue so it's impossible to dislodge.

The system in the UK isn't exactly sane either though, as I recall from the
fact that everything at Pret is advertised with an "eat in" and "take away"
price since the two scenarios are taxed differently. If you say you'll take it
away but then change your mind and eat it in, you're presumably in serious
(theoretical) trouble.

And then you've got the Australian system which is at least invisible to the
consumer but is still annoying and inconsistent to the merchant. It _was_
going to be a consistent 10% applied to everything, but the minor left-wing
parties insisted at the last minute that it needed to exclude some but not all
forms of food. Meanwhile feminists have been agitating for years to get
tampons excluded as well... not because any analogous male or unisex product
(toilet paper?) is excluded but because they have apparently run out of any
serious problems to complain about.

------
BerislavLopac
Actually, the search for "the most efficient coin system" is kinda pointless
-- if you are as advanced to discover and implement such a system, you are
certainly advanced enough to implement and use a cashless system based on
digital payment transactions...

~~~
gregpilling
The cash system will be hard to get rid of in the US. Many people want to be
able to hold their real money, not just have it on a bank statement. With
these same people - for fun - have a few drinks with them and try to explain
to them that the dollar bill they are holding is also not 'real' in the sense
that it is only a piece of paper and has no intrinsic value of its own.

~~~
xyzzyz
Cash is also useful for anonymous transactions. The anonymous cashless
protocols are very complicated compared to cash, and I don't even know if
anyone implements them at all.

~~~
m_eiman
It would be awesome to track every transaction in an economy, though. We'd
finally be able to tell exactly what our taxes are used for, and who's paying
the CEO's bonus. Not to mention the benefits when combating organized crime..!
I can see how some people might think it's worth sacrificing anonymity :)

~~~
limmeau
You'd still not know which of the incoming payments to an account is causally
connected to which outgoing payment.

~~~
m_eiman
You could, if the system is designed for it. Lots of little digital "coins"
that are shuffled around between different accounts, with traceable history.

~~~
uxp
Dollar bills have serial numbers, so it is already possible to track incoming
and outgoing transactions to an extent.

The problem would come in assigning a static serial number to a pool of bits.
If I spent an electronic dollar, did that dollar come from the few bucks my
neighbor gave me for gas after he borrowed my lawn mower, or from my paycheck?
It's not like I care which one gets spent, since they are the same, but how
would you determine which one get priority. I guess the same argument applies
to dollars sitting in my wallet, but its something one would have to consider
designing such a system.

~~~
xyzzyz
>The problem would come in assigning a static serial number to a pool of bits.

I don't really see it. There are cryptographic protocols designed just for
this kind of things. The real thing is it would be more awkward than just
cash.

~~~
limmeau
If for every dollar you spend, you have to be aware of its history ("Oh,
sorry, I can't buy cigarettes now, I only have two research-grant-dollars and
three from my non-smoking mom, neither of which may be used for tobacco"),
then the money ceases to be money (in the meaning of uniform tokens of value)
and you're back at some later stage of bartering economy.

------
pmjordan
I quite like the idea of 1/3/10/30 cent denominations. The even more efficient
combinations would be mainly a social experiment: would people adapt with
better mental arithmetic, would they revolt or would they rely on automation
(cash tills, computers) even more?

The Euro/cent has far too many denominations with 1/2/5 at each power of 10 up
to €500 (split between 8 coins and 7 notes). Combining 2s & 5s into 3s would
reduce that to 10 denominations total, and I think it would be reasonable to
drop single-digit cents from cash transactions entirely. IIRC Finland has
"banned" 1 & 2 cent coins already. (they're in circulation obviously, but no
prices require anything below the 5 cent coin)

~~~
sethg
I like the idea of a ternary currency: redefine the dollar¹ to be worth 81
pennies², and then issue 1p, 3p, 9p, and 27p coins. (cf.
<http://en.wikipedia.org/wiki/Balanced_ternary>)

Of course no country other than Geekistan would actually do this, so I would
settle for a 1/3/10/30 system.

¹Or pound or euro, of course.

²We couldn’t call them “cents” any more, could we?

~~~
pmjordan
_Of course no country other than Geekistan would actually do this_

You do know about pre-decimal Pound Sterling, right?
<http://en.wikipedia.org/wiki/Pound_sterling#Pre-decimal>

I particularly like the insanity of the Guinea denomination (1 Pound + 1
Shilling = 21 Shillings). My girlfriend's mother apparently was still
nominally paid in Guineas as a legal secretary in the early 70s. Reminds me of
volume controls that go to 11.

~~~
sethg
If I were a British subject I would _totally_ get behind a campaign to un-
decimalise the currency.

~~~
pmjordan
I wonder if anyone would notice - in the UK everyone but kids and old people
seems to use credit cards these days. And old people frequently still use the
pre-decimal terminology anyway.

Part of the reason for the widespread use of cashless payment might be that
for larger amounts cash is totally impractical; the largest de facto
denomination is £20, the £50 note gets you nowhere.

That said, I do really like the current design of the coins.

But weird currency experiments _would_ be cool.

~~~
arethuza
I rarely use cash these days - maybe once a month or so.

Edit: I'm in the UK - I use a chip-n-pin debit card for most things.

~~~
pmjordan
I don't know where you're from, but I can only compare to various other parts
of Europe as well as South Africa. The UK is definitely the most card-happy of
that lot.

------
impeachgod
Actually, in the Soviet Union you used to have 3-kopek and 15-kopek coins, as
well as 3-ruble notes.

~~~
listic
Clarification: late Soviet ruble (1961-1991) had the following coins: 1, 2, 3,
5, 10, 15, 20, 50 copecks and 1 ruble
<http://en.wikipedia.org/wiki/Soviet_ruble>

I think if you really want to minimize the number of coins per transaction,
you can always add more (than four) denominations of coins, up to some
reasonable number.

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z0r
Abolish the penny, use a uniform rounding rule to make the nickel the smallest
denomination. I hate pennies.

~~~
decadentcactus
Read somewhere that $1 notes account for almost 50% of paper money in the US.
To me it also makes sense to get rid of them (replace them with $1 coins).

~~~
delackner
Not holding my breath, but:

The Japanese solution works very very well. the 100 yen coin (their system's
$1 equivalent) is smaller than a US quarter and much lighter than a british
pound coin. The 500 yen coin is about as big as a Susan B. Dollar coin, yet is
still quite light. I often have as much as 2000 yen in coins in my pocket at a
time, and it doesn't feel particularly heavy. Paying a transaction under 1000
yen is generally quick and pleasant.

Contrast with US $1 dollar bills, that are for some reason almost always
falling apart, crumpled rags, and with the Quarter being the largest coin in
_common_ circulation, paying for something under $10 inevitably means fishing
out a mix of disintegrating bills and small change.

~~~
harisenbon
I know what you mean. I cleaned out my sofa and found 5000 yen worth of 100
and 500 yen coins.

My friend had a 500 yen coin bank, which when full held over 50,000. It was
not a large coin bank.

------
frgbhnmnjh
Can i suggest splitting the $ into 20 equal parts and then each of those parts
into 12cents.

Then you could have 1,2,3,6 cent coins and 1,2,10 part coins.

For anyone that can manage the calculations for feet/inches/yards/miles,
drams/ounces/pounds/tons it should be simple.

~~~
blahedo
Brilliant! But perhaps we could go with a 2.5 part coin instead? There's just
something that feels right about that.

~~~
frgbhnmnjh
A sterling suggestion - I award you half-a-crown

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Aron
The negPenny! Anyone want to write a quick script to check combinations that
include negative values?

~~~
limmeau
Joking of which, complex currency would also be an interesting toy.

The imaginary part could represent some orthogonal aspect of worth, e.g.
consumption of scarce resources.

~~~
jerf
Interesting, but since there's no reason to multiply two money values together
(what use is a square dollar?), it doesn't really do anything. It ends up
trivially degenerating into two currencies with some exchange rate between
them.

~~~
Dove
I already consider food to have costs in two currencies: one in dollars and
one in calories. There is no conversion between them; I must meet both
budgets.

~~~
jerf
What on Earth are you talking about "there's no conversion between them"?!?
You can't trade dollars for food? You can't trade food for dollars? What are
dollars good for if there's no conversion between them and food?

The lack of an abstract market selling and buying abstract "calories" at some
price doesn't mean there isn't a conversion between them, just that it isn't
clean and has a lot of other moving parts, just like everything else in the
real world.

Hie thee hence to a microeconomics textbook forthwith, I've been enjoying
[http://www.daviddfriedman.com/Academic/Price_Theory/PThy_ToC...](http://www.daviddfriedman.com/Academic/Price_Theory/PThy_ToC.html)
but heck anything would do.

~~~
Dove
I don't mean that I can't buy food. I mean that I can't trade between dollars
and calories. For example, a scoop of premium ice cream costs me $1.25 and 250
calories. The currencies are independant and inexchangeable; if there was an
exchange rate between them, I could get that same food for $5.00 and 50
calories.

Any food I contemplate has a cost somewhere in dollar-calorie space, so the
currency with which I buy food can be accurately modeled as a two dimensional
vector space (or perhaps as the complex numbers, though I guess I don't really
use the field properties...).

------
growt
Maybe he should take into account that in the real world most prices are
xy.99, this might change stipulation 2.

~~~
jonknee
Except there is sales tax, so your $xx.99 purchases usually don't end up that
way. For a $1.99 purchase in my city I end up paying $2.13 which would be
helped nicely by the $.37 cent coin.

I see your point, I doubt the distribution is completely uniform. But it's
probably not as clustered as you'd think (different taxation levels helps).

~~~
growt
Ok, I see. I live in germany, where the tax is already included (a 99 cent
coin would be really efficient here).

~~~
jasonjei
The problem as others have stated with including the tax is that if you have a
multi-state presence, the tax rates for different cities, counties, and states
are different, and sometimes are a huge difference (2-3%). I don't think it
should be up to the retailer to foot the difference. But I do think rounding
is an easier solution than a 37-cent piece.

~~~
winthrowe
Things are complicated when considering applying this to an online price list
for example, but applying to individual brick and mortar retail locations, I
don't see what the problem with the in store displayed price to be different
in different tax jurisdictions.

~~~
metageek
And online merchants don't take coins anyway.

~~~
winthrowe
I was thinking something more of large chain operations that have websites
referencing physical stores, like Walmart or Best Buy.

------
Anomaly775
I'm willing to use 0.60 more coins during transactions if it saves people from
actually learning how to count.

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nsfmc
Say what you will, at least the article has a sense of humor.

 _“How can you tell that Patrick is a young economist from the preceding
discussion? Because he finds that the current government solution for the
coins we use is 98 percent efficient and thinks this is inefficient.”_

------
ryanwanger
10 years ago, when I visited Australia, their currency was similar in value to
the US (I think an aussie dollar was worth roughly 65 cents US), and they had
no pennies OR nickles. It started at 10 cents.

They also had 1 and 2 dollar coins.

The best part was that the change in your pocket was worth enough to actually
allow you to buy things with it. Not like we have now, where people only use
it to avoid getting more change back.

------
julius_geezer
The novelist Anthony Burgess once wrote about the convenience of the old
British system of pence, shillings, pounds, and guineas: the pound was evenly
divisible to a value in pence if not shillings by 2, 3, 5, and guinea also by
7.

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JoeAltmaier
Who uses coins to pay exact change? I use bills, pocket the change (or leave
it in the dish), it piles up in jars at home.

Make the coins lighter! So my pocket doesn't wear out from carrying half a
pound of worthless metal.

------
vaksel
frankly I don't see why we even need coins at all. Talk about your waste of
resources minting all of those. It was fine when a can of coke was 25 cents or
when you could get a new car for 2 grand. But in this day and age? It's just a
waste.

should just switch to a digital currency already...disposable credit cards
that can transfer funds between each other.

~~~
protomyth
Well, some people really like cash, and I still run into places, particularly
in rural areas, where credit cards are only allowed on purchases over $20. The
credit card fees are a great incentive to keep cash / coins.

~~~
graywh
Visa and MasterCard don't allow merchants to impose a minimum purchase
requirement.

~~~
winthrowe
It may be against the terms of the merchant's agreement, but locally in
eastern Canada it's quite common (for both debit and credit transactions), and
(although I don't follow the issue closely) I've never heard of a lawsuit
brought forth over it. I'm sure the CC companies would be up in arms if it
were a national chain of some kind, but the little Mom'n'Pop restaurants and
convenience stores seem to fly under the radar, even if that category may be
large in aggregate.

~~~
graywh
I've heard of places that lost the ability to accept VISA/MC payment for
imposing their own minimum.

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saraid216
it would be a lot more efficient if we went to only 1 decimal place and got
rid of everything but the dime.

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jasonfried
Yes!

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code_duck
I hate economists.

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laut
I'm more concerned about other aspects of the U.S. economy. Such as inflation.
That's what made pennies worth so little in the first place.

These numbers are also more interesting than pennies:
<http://usdebtclock.org/>

