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.
A chemist, a physicist and an economist were stranded on a desert island when they discover a crate of canned food. The chemist says that they should leave the cans in the salt water for a while and then try opening them. The physicist says they should try banging them open with rocks. The economist says "Let's assume we have a can opener."
I am totally stealing this joke for the next faculty meeting. But, we have to make some assumptions in life. Until we get that cranial recording unit running.
>making change out of your pocket is still solving the subset-sum problem in your head, which is of course NP-complete.
Generally speaking, that's true. Most currencies however are designed, so that the greedy algorithm always works and produces optimal solution. The coin systems given in the linked article do not have this property, so they are actually inferior to real systems.
edit: come to think of it, they in fact do, but it requires ridiculous amounts of pennies, so my argument still holds.
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
This actually makes the non-uniformity worse, not better -- things priced at an even number of dollars don't factor into the calculation before tax (and there are lots of those), but after, change amounts get disproportionately weighted to the amounts of change produced by even numbers of dollars. Argh.
Also, his most efficient system of coins in one in which every denomination is a prime number, so no denomination but the penny factors evenly into any other.
In our current system, the only one that doesn't work is breaking a quarter into dimes.
(And I presume you mean "first three multiples of 5".)
Nope, powers: depending on indexing, the first three multiples of 5 are either 0,5,10 or 5,10,15, and we have neither a zero-cent coin nor a 15-cent one. The first three powers of 5, on the other hand, are 1, 5, and 25.
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.
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.
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.
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.
Same in Japan. 6-7 years ago a law was passed that all posted prices must have the sales tax figured in. I think it makes things much clearer to know exactly what you're paying.
Also, something of interest, I have a lot of friends who come over here to Japan and complain at how expensive food is in restaurants. What I noticed is that while the price on the menu is much more expensive than in the States, your final cost is pretty comparative.
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.
I used to share your confusion, so I asked some Americans and was partly converted. One reason is that having taxes "added on" means people are more aware of the tax rate and how it affects prices at the cash register.
Since there are sales taxes at multiple levels (another reason - taxes can change frequently and are far from national) having a feel for taxes comes in useful when voting since if you feel you're getting nothing for your local taxes, you can make an informed decision at the ballot box.
Why go to the effort of eliminating small coins? Why not just go ahead and switch to an electronic currency? Or at least an electronic replacement for coins and bills like they do in Japan:
Subsantial new infrastructure would have to be built to accommodate person to person transactions. When I deal with an established vendor, I use a credit card almost 100% of the time and while not electronic currency it is close.
When I buy orsell something of craigslist right now it is almost always cash and the infrastructure available would have to change substantially for that to change.
Yes credit cards are more prevalent in the US, but they have a 3% overhead, retailers eat the cost. With value points and clubs you can recover 1-2% of those fees. I think a fee-free anonymous electronic cash system like Suica would be a great alternative.
You can buy and recharge Suica cards at train station ticket machines, so they're effortless to obtain. Having been to Tokyo twice in the past 3 years, the Suica cards are a godsend. I used them only for transportation purposes, but I saw stores that accepted them.
I had a Suica card that I bought the first time I went in 2008. I didn't use up all the money that I put on the card and kept it when I came home as a souvenir. When I returned in 2010, I brought it with me, figuring that there was a time limit on the validity of the card, or that I would have to get the card re-activated first. No, it worked just like it did when I bought it in 2008. When it ran out of money, I went to a Suica-issuing ticket machine and put more money on the card. So, don't throw these cards away.
For what it's worth I just came back from a week and a half in Japan and never knew these things existed (well, I knew there was some sort of smartcard system for the subway I wasn't using, but had no idea it extended further than that). Japan is still the most cash-heavy culture I've visited.
The US, on the other hand, is the most plastic-heavy culture I've visited. It's the only place where it's socially acceptable to pay for a $1.50 cup of coffee with a credit card.
Yeah, you definitely need to have cash with you. Plan on visiting the ATM often while there, especially during Golden Week. The Suica card makes it effortless to travel on Tokyo Metro and the JR lines.
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...
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.
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.
The irony here is that anonymous digital cash protocols, while complicated, are also basically built around digital tokens or "coins", so efficient change-making is still relevant! (although the coins would be handled by software, so 11 or 37 unit coins would be acceptable; generally systems have used coins in the powers of two sizes, to reduce number of coins per transaction, at the expense of total number of denominations).
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 :)
You could, if the system is designed for it. Lots of little digital "coins" that are shuffled around between different accounts, with traceable history.
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.
>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.
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.
People always use this as an example, but I don't think it's true. Next time you're in line at a retail store, or even a coffee shop, pay attention to how many people use cash. It's probably down to 50% or less these days, people already use a credit card for pretty much everything if only for the value points, convenience, and high ATM fees.
Who said global? A localized loss of power or connectivity for a substantial time period is not necessarily catastrophic. But there still has to be some exchange of goods and services both within this locality and between it and the outside world.
Without some accepted medium of value exchange between an electronically disconnected region and the outside world, it becomes much more difficult to establish or restore connectivity. So the purely cashless system is actually much less robust with respect to physical failures.
Maybe not catastrophic, but personally I can't stay where I live (in the city) with more than about 48hours without power, as I can't safely store food and I can't really get new food (unless the loss of power is only at my place).
I'm guessing you eat a lot of meat and/or fresh produce? There are plenty of foods out there which keep for longer than 48 hours: canned foods, crackers and other dry goods, and so on. They might not be as tasty, but keeping a decent food supply doesn't really require constant refrigeration.
The point about cities I'll give you to some extent: a city with very high population density is generally dependent on a much larger total rural area which supplies them in exchange for economic support. If the loss of power also kills all transportation, you're doomed. But our current transport infrastructure generally includes autonomous non-electric options even where public transport is primarily electrical (trains etc). You can pay someone to bring you food from outside the city without needing a network connection.
Really this reinforces my point above about currency though: absent an uncompensated intervention (ie government), a city which loses its power and connectivity must have some medium of exchange to pay for its food supply to be transported in, and to get itself back on its feet. Some non-electronic medium (ie cash) is essential in these cases.
Two weeks? You are making the common "predict the future" mistake of assuming people will not try to do anything, and will just sit around. In actuality if there was a global loss of power people will figure out many many things to help.
After working with payment processing of credit, debit, EBT, and gift cards for the past few years, I have started using cash more.
For most transactions, a merchant is charged between 2-3% of the purchase price. This means that whatever you are buying could be 2-3% cheaper if cash were used instead. (However, for high-volume stores this may not be true since credit transactions take less time than getting change from cash.)
Furthermore, if someone steals your credit card number, you call them and have the charge removed. Does your credit card company take the loss with this? Not usually. The merchant that accepted the stolen card will pay. This in turn, makes the price of goods go up again.
These things take some toll on the overall economy. The real question becomes, how can we make cash transactions more efficient so that it improves commerce for individuals and improves the profits of businesses?
One way would be to get rid of any rules which prevent retailers from passing through the cost of credit card charges to credit card users in an obvious way. Like by saying that credit card transactions will cost 2-3% more than cash transactions. I think this is either discouraged or prohibited by credit card issuers.
ATM/debit bank cards? Often only a flat .25 a transaction, PIN only, and you can't chargeback just like cash. Online transactions need a PIN interface although.
That'll require a fundamental re-ordering of a lot of the financial system. How do you pay the poor, whether working or on the dole (many of whom are refused bank sevices, which is currently a perfectly legal practice in most jurisdictions)? What level of loss per transaction would be unacceptable, and who gets to draw the line? What happens to garage sales, flea markets and charity bazaars? Can you lend me twenty bucks until Thursday, or do I need a bank loan?
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)
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.
A neat example from Joyce (early in Ulysses) of how to calculate the milk bill when a shilling is 12 pence (in case it's unclear, the bill is two shillings and two pence; the boys end up paying a florin (24 pence) and owing 2 pence):
-- Have you your bill? We had better pay her, Mulligan, hadn't we?
Stephen filled the three cups.
-- Bill, sir? she said, halting. Well, it's seven mornings a pint at twopence is seven twos is a shilling and twopence over and these three mornings a quart at fourpence is three quarts is a shilling and one and two is two and two, sir.
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.
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.
Officially it's a "banking note" and retailers are within their rights to refuse them (which they're more likely to do because lack of familiarity means staff are less likely to be convinced of the note's authenticity and it also requires giving more change)
Of course it was necessary for the Guinea to be worth more than the pound, since it was made of gold, not of silver. There is a method in the insanity.
If you were going to do the dollar redefine, why not have 1 dollar = 12 "coins". Only mint one coin and 12 has a lot of nice divisors. It would also have the advantage of no minted coin really being practically worthless.
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.
I strongly agree. This is the correct answer to the problem. That and adding sales tax to the tagged price (i.e. don't add sales tax at the time of the transaction).
The problem with adding sales tax to the price tag is that sales tax isn't uniform across the U.S., and residents from one state can buy something and have a different sales tax applied (I see this happen frequently with Oregon -> Washington travelers).
I suppose the first step would be to unify sales (or whatever) tax across the country.
Also, sometimes the sales tax might or might not be applied depending on the status of the purchaser. When I was a in college the campus stores would always have to ask us if were students, since only non-students paid state sales tax.
In Ontario specifically the tax can depend on the total purchase: fast food purchases under $4 (total) are taxed less than those over $4, so we have a lot of $3.99 value meals. If you buy two, it's 13%, if you buy one it's 5%.
Perfectly legal (although you're likely to draw intense ire from people behind you if you try it in a lunchtime lineup, since you don't actually have to leave the counter in order to create a separate transaction). Oh, and it won't work in a drive-through (not because there's anything wrong with it as such, but that ungrouping the orders makes fulfillment a pain in the butt, so restaurants usually won't do it as a matter of local policy.
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).
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.
Exactly. In every other country where coins have replaced notes, they've just said "OK, on such-and-such a date we're replacing the note with the coin, everybody come in and swap your notes for coins!" and a few months later you don't see the notes any more. I don't know why the US Mint has got the idea that they need to keep printing 'em both.
Of course there are two other factors that don't help:
a) Previous dollar coin designs have been ugly and filled with misguided feminism (I still don't know and don't care who Susan B Anthony was, and I only know Sacagawea from The Simpsons), and
b) Previous dollar coin designs have been damn near indistinguishable from quarters by feel. Make 'em bigger or thicker or give 'em flattened edges or a hole in the middle or something! Preferably all of the above so you can look at it and say "Wow, that sure looks like a dollar's worth!"
I haven't lived in (or been to, for that matter) the US for twenty years, but still...
I remembered the dollar coin as George Washington, silvery, larger than all others. And quite uncommon, especially compared to the dollar bill. Still really not something you'd confuse with quarters. Has it changed that much?
And what are those feminism attempts you seem to refer to?
The current dollar coins, with presidents on them, solve half of (a)--no feminism, but really ugly pictures. Instead of being profiles, they're portraits, with really deep eye sockets.
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.
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.
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.
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...).
If you also introduce imaginary time (as in some models of the big bang), then you can find funny definitions for what it means to possess a certain amount of money for a certain amount of time shortly after the big bang.
Perhaps something for interdisciplinary theoretical economist-physicists.
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).
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.
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.
Well for starters it would be a lot more expensive to print signs dedicated to the city/county of a store. Price matching becomes tedious too, requiring a calculator.
I had no idea that american sales taxes were so byzantine as to have individual city and county sales taxes in so many areas. Although I still contend that price matching is easier, because who really cares what the pre-tax price is, post-tax is what comes out of the wallet.
Well, America is large, and there's always been this struggle of Federal Government vs. State Government. And every state is run differently. The less competent ones require more taxes, or, on the other hand, should really be split into two states (e.g California).
Or retailers that don't do the .99 business when tax is already in place. For whatever reason, movie theaters in the US do this. They build the tax into the price and then use even units (it's still way overpriced, but at least you know the $6 pop-corn and $4 soda will mean you owe $10).
You're still ahead of the game because for a .99 purchase you'll get .01 back which is just one coin where if I'm using bills would need to pay with two singles and get .93 back (which for the US is at minimum 8 coins). It's no coincidence why I have tons of change collected.
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.”
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.
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.
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.
While you have a point, there is a flipside, specifically regarding cash v credit/debit cards.
1. Privacy
If you use a card for every transaction, then you can be tracked for every transaction. Simple as that.
2. Tangible spending
If you have digital currency, it is often hard to mentally understand the value of money. Everything is equal; be it $10 or $1000. I value an hundred dollar bill much more than an hundred dollars in my bank account, and consequently am less likely to spend the bill.
Digital currency has it's upsides. Let's remember there are real downsides as well.
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.
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.
From the government’s point of view, there is no reason to make it easier for citizens to anonymously and untraceably send money to one another. It’s politically impossible for them to eliminate paper/metal cash, but they’re not going to make cash transactions any easier.
(And any country whose central bank supports completely digital anonymous cash will suffer the fate of Nauru: first it will attract money launderers from all over the world, and then the world financial system will shut off all contact with it until it reforms.)
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.