Making Change 1129
Roland Piquepaille writes "There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 10 cents, and 25 cents. But is it the most efficient way to give back change? This Science News article says that a computer scientist has found an answer. "For the current four-denomination system, [Jeffrey Shallit of the University of Waterloo] found that, on average, a change-maker must return 4.70 coins with every transaction. He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents." He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. Check this column for more details and references." The paper (postscript) is online.
Science v. Common Sense (Score:5, Interesting)
Me, I'm on the side of science.
Oh, that'll work well (Score:4, Interesting)
How the hell can we expect these people to handle 18 cent pieces when they can't even figure out what 25% of 20 is?
Minimize coins in pocket (Score:4, Interesting)
If something costs 77c I give them 1.02 - and get a quarter back. In the US, the tellers stare at me blankly, but then dutifylly enter the amount I give them - and then smile in amazement at the simplicity of the exchange.
In Japan, it is almost the other way around. The tellers come up with the most creative combinations that minimize my number of coins (and maximize theirs - this is in both of our interest).
Tor
Worst.... idea.....ever........ (Score:2, Interesting)
why did we ... (Score:5, Interesting)
easy, look
Measures of length
After 1959, the U.S. and the British inch were defined identically for scientific work and were identical in commercial usage (however, the U.S. retained the slightly different survey inch for specialized surveying purposes). A similar situation existed for the U.S. and the British mass unit pound, and many relationships, such as 12 inches = 1 foot, 3 feet = 1 yard, and 1760 yards = 1 international mile, were the same in both countries; but there were some very important differences.
Measures of volume
In the first place, the U.S. customary bushel and the U.S. gallon, and their subdivisions differed from the corresponding British Imperial units. Also the British ton is 2240 pounds, whereas the ton generally used in the United States is the short ton of 2000 pounds. The American colonists adopted the English wine gallon of 231 cubic inches. The English of that period used this wine gallon and they also had another gallon, the ale gallon of 282 cubic inches. In 1824, the British abandoned these two gallons when they adopted the British Imperial gallon, which they defined as the volume of 10 pounds of water, at a temperature of 62F, which, by calculation, is equivalent to 277.42 cubic inches. At the same time, they redefined the bushel as 8 gallons.
In the customary British system the units of dry measure are the same as those of liquid measure. In the United States these two are not the same, the gallon and its subdivisions are used in the measurement of liquids; the bushel, with its subdivisions, is used in the measurement of certain dry commodities. The U.S. gallon is divided into four liquid quarts and the U.S. bushel into 32 dry quarts. All the units of capacity or volume mentioned thus far are larger in the customary British system than in the U.S. system. But the British fluid ounce is smaller than the U.S. fluid ounce, because the British quart is divided into 40 fluid ounces whereas the U.S. quart is divided into 32 fluid ounces.
From this we see that in the customary British system an avoirdupois ounce of water at 62F has a volume of one fluid ounce, because 10 pounds is equivalent to 160 avoirdupois ounces, and 1 gallon is equivalent to 4 quarts, or 160 fluid ounces. This convenient relation does not exist in the U.S. system because a U.S. gallon of water at 62F weighs about 8 1/3 pounds, or 133 1/3 avoirdupois ounces, and the U.S. gallon is equivalent to 4 x 32, or 128 fluid ounces.
1 U.S. fluid ounce = 1.041 British fluid ounces
1 British fluid ounce = 0.961 U.S. fluid ounce
1 U.S. gallon = 0.833 British Imperial gallon
1 British Imperial gallon = 1.201 U.S. gallons
Measures of weight and mass
Among other differences between the customary British and the United States measurement systems, we should note that they abolished the use of the troy pound in England January 6, 1879, they retained only the troy ounce and its subdivisions, whereas the troy pound is still legal in the United States, although it is not now greatly used. We can mention again the common use, for body weight, in England of the stone of 14 pounds, this being a unit now unused in the United States, although its influence was shown in the practice until World War II of selling flour by the barrel of 196 pounds (14 stone). In the apothecary system of liquid measure the British add a unit, the fluid scruple, equal to one third of a fluid drachm (spelled dram in the United States) between their minim and their fluid drachm.
In Great Britain, the yard, the avoirdupois pound, the troy pound, and the apothecaries pound are identical with the units of the same names used in the United States. The tables of British linear measure, troy mass, and apothecaries mass are the same as the corresponding United States tables, except for the British spelling "drachm" in the table of apothecaries mass. The table of British avoirdupois mass is the same as the United States table up to 1
Re:Instead... (Score:3, Interesting)
In the netherlands (and most, if not all, of europe), consumer prices must always be advertised including VAT. This includes pricetags in the store itself and commercials on TV and such. It is illegal to advertise prices without VAT to consumers.
Consumers never have to deal with prices without VAT included. The price isn't even mentionned anywhere.
Because VAT is tax deductable when you buy a product for commercial use, you can get a receipt which shows how many VAT you have paid.
It actually never occured to me that this would be different in other countries. It makes absolutely no sense to me ;-)
Bring back LSD (Score:2, Interesting)
For those who don't know what I'm talking about, British currency up to the 1970s was counted in pennies, shillings (12 pennies), twenty of those to a pound, with a guinea at 21 shillings (lend a pound, get a guinea back in a year, see, works for interest too).
Semi-Log; Diameter; Thickness; Mass (Score:4, Interesting)
Euro 1,2,5,10,
When I was in Europe recently I noticed their semi-log scale change system of 1,2,5,10,20,50,... and really liked it compared with the US system, which has quarter dollars, but not $2.50 bills.
Evidently two bits are indivisible anyway these days, so Americans don't seem inordinately hooked on using powers of 2 to divide up their money all the time.
The US should have its monetary system go the same direction as the stockmarket which recently abolished fractions (down to what, 1/64, 1/128?) in favor of decimal stock prices.
Also, the US treasury needs to push $1 coins (and perhaps $2 and $5 coins) because the paper money wears out so much faster and costs more to replace than coinage.
And, while we're on the subject of monetary redesign, coins should be monotonically increasing in diameter, thickness, and mass to make it easier for people with poor vision.
In fact, if the weights were done nicely, it might even be possible to start weighing heterogeneous buckets of coins to obtain value (assuming no rocks, counterfeits).
Or to measure linear thickness of heterogeneous coin stacks and still have $/inch be as good a measure as $/weight, again, to avoid explicit counting.
Ahh, if nerds were running the world, things would be so damn efficient...
Re: I hate math... (Score:2, Interesting)
> Let's face it; can you imagine the average cashier at WalMart giving back 98 cents change with an 18-cent coin?
When I need to hand over, say, $1.47 I'll give $2.02 if I have a couple of pennies in my pocket, to get a nice even $0.55 change. You can't imagine how badly that confuses most clerks whose registers do not calculate the change for them. (Or more likely you can imagine it.)
I suppose I have an unfair advantage, since I practice it regularly and most of them probably don't have to deal with anal retentive geeks like me on a regular basis.
Re:Instead... (Score:3, Interesting)
Why not round prices to dimes ? Or even quarters ?
Because retailers use the fractional part to encode information. Did anybody here ever work at a Target? (or perhaps a wal-mart, etc?) Do you still remember what a price ending in ".97" means?
Re:I hate math... (Score:2, Interesting)
They have a hard enough time when I hand over $3.12 for a purchase of $2.87. They'd need the register to say "give the customer X of these coins and Y of those coins"...but then what happens when the till runs out?
Pirates (Score:5, Interesting)
Re:I hate math... (Score:3, Interesting)
I'd probably still go with 3 dimes and a penny, cause I can do that in my head without even really thinking about it. 2 eighteens would give back a dime though, but how long would it take most people to remember 18x2 is 36?
How about most 10 year olds?
Re:Instead... (Score:3, Interesting)
Give it up, you will never ever see logical pricing that doesn't require loose change.
$19.99 may not fool you or me, but subliminally many people perceive it quite differently from $20. It begins with a "1". "In the teens" seems easier to justify psychologically than $20 for an impulse buy. Everyone knows about the trick but it still works in spite of that. It's very obvious but at the same time very subtle, and it works because most people think with their emotions rather than logic. Marketeers know this, and we will see this trick done until the end of time. And then there are gasoline prices - I don't recall ever seeing one that didn't end in 9/10 of a penny.
Curiously, another pricing trick that is done in some cases - especially "wholesale" or "factory outlet" type places - is to do the opposite - price it at some oddball amount _other_ than $19.99, like $18.54 or $21.43. This appeals to bargain-hunters who are looking for "deals" and are suspicious of the .99 trick. An oddball price can give
them the psychological impression that the vendor is cutting the price to the bone, down to
the last penny they can trim.
Yet another ploy, that works with rich people buying luxury items, is to purposely price something with round numbers. You don't often see a painting in an art gallery, or a high-fashion designer dress, priced at $2399.99 - it would almost make it seem "cheap" to some of these people. A round number like $2400 makes it seem more sophisticated, and nitpicking about price or using cheap pricing tricks is beneath these people.
"Taxes not included" is done to make things seem cheaper and more competitive, again a subtle psychological trick to get the customer to cross that fragile threshold of deciding to purchase while maximizing their profits. Once at the cash register, when the real amount hits home, that borderline psychological decision has already been made and the customer is now emotionally committed to the purchase. And the listed price is going to be $19.99 anyway, whether it cost the vendor $10 or $12, taxes included or not, so why should the vendor forfeit the extra tax money?
And then there are those "deals" in TV ads or web sites that seem cheap until they add in the shipping and "handling" charge. That's a whole discussion in itself.
There is one thing I've always wondered about - taxes are always including for certain items like gasoline, alcohol, or cigarettes. In Massachusetts I recall it is or used to be $.47 per gallon. So I wonder why gas stations don't advertise "$1.09 9/10 plus tax" instead of "$1.56 9/10". Is there a law prohibiting this or something? I would almost like to see it done this way because it would make people painfully aware of the money they're paying to the government.
Re:Instead... (Score:3, Interesting)
Consider the following typical purchase:
- You walk into the store.
- You find yourself a bag of CheesyPoofs, which cost $0.99USD (hey, they're that expensive thanks to the constant free advertising the get on SouthPark!), and head over to the counter.
- The cashier looks up from their magazine (sneers) then rings up the price on the till, and asks for 99 cents.
- You hand over a dollar, and grab your bag of CheesyPoofs
- The cashier opens the register, puts the dollar in, grabs a cent and hands it to you, then says, "Have a nice day!" (sarcastically)
- You then leave the store
Now think how different this'd be if everything matched the common notes. You'd hand over a dollar, but then as you've paid in full you've got no reason to hang around anymore so might just walk out with the goods. This kinda 'breaks' the transaction - you may've made a mistake and under or overpaid, or maybe you have something in your hands which you forgot to pay for, but the cashier can't correct this 'cause you've already left. Equally, they don't get to check you out, or say "Have a nice day!", which, as much as people hate it, is a typical part of customer service/interaction and may encourage you to shop at the same store again ('cause that cute chick behind the counter smiled at you as she gave you your change). It's also a signal that the transaction is complete and you can leave.So, without having to wait for some token amount of change, an essential part of completing a monetary transaction is removed, and things become a lot more difficult. I think *that* is why prices are always XX.99 (as well as the obvious marketing "looks cheaper" aspect).
Re:I hate math... (Score:4, Interesting)
Once Again... (Score:3, Interesting)
I believe that what the researcher failed to take into account is the way that the human mind works. Adding 1's, 5's, 10's and 25's is definately easier than adding 1.37's or 83's for us.
Sure, it may make the handing out of change more efficient by lowering the average amount of change given from 4.x to 3.x coins, but that efficiency will be more than lost when the clerks at the local mini-mart -- who already have problems giving out the correct change -- have to figure out that my $0.72 in change will be two 29-cent coins, two 5-cent coins and four 1-cent coins.
Not to mention the increasing size of cash drawer shortages caused by less-than-mathematically-inclined clerks.
Is it just me, or does it seem that the less "rounded" education becomes, the more one-dimensional "solutions" appear? Guess it is more true than ever: when all you have is a hammer, everything looks like a nail.
Simpler Solution: Get Rid of the Penny (Score:3, Interesting)
* Counting in 5's, 10s, and 25's is a lot easier.
* Saving pennies, rolling them up, going to the bank, and then driving home is a pain-in-the-ass, and honestly isn't worth my time, e.g. 2 hours of work to get $10 of pennies?!?!?. It's more economical to throw the friggen ugly coins in the trash, but I can't do that out of principle.
GET RID OF THE PENNY!
Non-decimal systems have advantages (Score:4, Interesting)
Second, what is easy is what comes with practice. Currencies, like most other measurement systems, were not originally decimal, but duodecimal (i.e. using base 12) and various multiples thereof. Right up to the 1970s, the UK used a currency system which had 12 pennies to a shilling and 20 shillings to a pound. The US and UK still use duodecimal for weights and measures (think pounds and feet) and the whole world uses it for time (12/24 hour systems) and angles (360 degrees is 30 times 12).
Why were systems based on numbers like 6, 12, 24, 360 etc. so common, given that we tend to count in decimal? Well, they have large numbers of factors. In other words, while they might be harder to add and subtract in your head than decimal systems, they're much easier to do division with. And since division is much harder to do in mental arithmetic than addition, that's a big advantage.
For example, with 12 ounces in a pound, I can take a half, a third, a quarter, a sixth or a twelth of a pound and still be dealing in whole ounces. With a decimal system, 10 has only 2 factors: 2 and 5. So to buy a quarter of something devised in a decimal system you end up with 2.5.
Now that also has a knock-on effect when making change. Because of the limited factorisation of 10, most decimal systems divide things into 100s or 1000s.
Result: in a decimal currency, you end up not with 10 cents per dollar, but with 100 cents. And that's the real reason you have so much change in your pocket. If we had 12 cents to the dollar (or euro), then by copying the old british system -- with a 1c, 2c, 3c and 6c coin -- you'd never need more than 4 coins to make change from a shilling.
And would the cashier at WalMart be able to handle it? Well first off, maybe if as a result they had to think more as kids they'd be better off at maths to start with. And secondly, since they have to use a calculator now anyway, what would be the difference?
How does Walmart affect it? (Score:3, Interesting)
The writer TOTALLY doesn't get it. (Score:3, Interesting)
It's hard enough when you have to deal in 5's and 10's, but as soon as you start asking a cachier to add or subtract 18 from ANYTHING, you're going to have trouble.
The whole problem here is that the author doesn't realize that humans are (a) not computers, and (b) don't care about handing out one less coin. The system we have, as imperfect as it is, evolved this way through error and natural selection. Sure, perhaps no one considered printing an 18 cent coin, but that's likely because they knew people would have trouble dealing with them. Humans inherently have trouble with simple arithmetic, so a system evolved that was less ERROR-PRONE, completely ignoring minor improvements in efficiency.
So, of course, one has to ask the question: Could we make the system less error-prone? Probably. Maybe our esteemed computer scientist should develop a system to determine which coins we need to have in order to make it more likely for a cachier to give back correct change.
What's better, taking 2 seconds longer to give you correct change or two seconds less to give you incorrect change? I'll wait the extra 2 seconds.
Or maybe I'll just use my credit card.
Re:I hate math... (Score:5, Interesting)
Usually, the customer does not have exact change to pay the $x.99 (or can't be bothered to look for pennies) and it would force the cashier to open the cash machine to give change. Upon doing this, the sale is registered and the owner will know if you pocketed the money.
Re:I hate math... (Score:3, Interesting)
My emphasis:
Provided the key punching cashier monkey actually presses the right keys, yes this is true. But, how many times have you gone into a store, handed the cashier a $20 bill for example, and had them key in 2.00 <enter>, then get this confused look like "How do I get to $20 now?"
It's probably a good idea for someone who handles cash to be able to count change without having a register tell them what it is. I've also been in a store when the power acted up, and the cashiers were powerless (no pun intended) to help anyone until the registers came up, not because they couldn't write sales reciepts, but because they couldn't count change.
Re:I hate math... (Score:2, Interesting)
What is it with stories like this that prompt people to make-up (or pass one made up) stuff? "Our" (i.e. the US) coinage system was not specifically designed, it was the result of a compromise:
collectsource.com [collectsource.com]
It is a quasi-decimal system. For it to be a true decimal system, we'd have a 20 cent piece instead of a quarter, and a 40 cent piece instead of a half dollar. The quarter was retained because for over 100 years Americans had been using 2 bit and 2 reale coins. The half dollar was actually a useful coin, a day's wages for the higher paying skilled labor jobs back in the day.
Re:A "Scientist" wrote this!?!?!?!? (Score:2, Interesting)