Do We Need a 37-Cent Coin? (2009) | Hacker News Reader

Do We Need a 37-Cent Coin? (2009)

freakonomics.com

61 pointsjawns164 comments

> Probability of a transaction resulting in value v is uniform from [0,99].

in reality, most of the transactions that use coins end up conforming to common existing coin combinations e.g. laundromats in US mostly price as multiples of quarters ($0.25)

The $X.99 price thing should be forbidden and I'm deeply disappointed in humanity/customerity that we don't shun them and refuse to deal with them

It's even uglier in jurisdictions where sales tax is not included in the $X.99 price tag. The total amount you need to pay becomes something like $X+1.07 and you end up with a lot of of unexpected change.

Edit: In the example, I meant X+1 dollars and 7 cents. Apologies for the ambiguous formula, it felt awkward to use parentheses inside of an amount.

$X * 1.07, or $X + 7% (of $X)

This certainly contributed to people preferring card over cash, making merchants loose ~3% per transaction.

That ship has long sailed, but it does male you wonder: if everything was priced at increments of, say, quarters, would enough people still use cash to offset the lost sales from the allegedly less appealing pricing?

I don't know, but I find I use cash much more readily when the price includes tax, because I can confirm ahead of time that the cash in my wallet is enough without breaking a 20 for a pile of coins.

> making merchants lose ~3% per transaction

Cash also has costs - mistakes in making change, forgeries, time to count/cash up, time to visit banks for cash deposit and/or getting change, theft - it’s been estimated that these can easily exceed any costs of handling credit/debit cards.

Cash indeed has a high handling cost. In my country and many others, withdrawing cash at the supermarket teller with your card is free (as in no ATM fees) because it reduces the amount of cash handled and transported by branches. They'd rather eat the cost of a card transaction than pay cash handling costs.

It's been estimated by card companies that these are higher.

Card companies say that cards are better? Who'd have guessed.

I run a business with lots of daily transactions. The cost of balancing cash drawers, getting change, making deposits and balancing those activities in accounting, all totalled, is still cheaper than to pay the credit card fees. Also it's kind of a fixed set of time regardless of how much cash it is. So more cash is more savings but there is definitely a point where if the cash amount gets to low it would be cheaper to go all card.

I think that cheaper propaganda is probably from theft in mostly places that hire minimum wage workers and treat them like slaves.

Could you elaborate? I have many years experience running a gas station. For five daily’s employees, handlung cash is about 4 hours labor a day. This is counting the till prior and after shift, validating voids and receipts, handling checks, cashiers checks, and bagging and dropping the cash. With cash there is always slippage, and it is never in the ledgers favor. So cash increases labor costs by 10% and incurs about 1% direct loss a day, prior to bank fees. Where as credit cards end up being about a 2.5% overhead.

Wait, you can still pay by check in stores in the US? That was phased out in the UK like 15 years ago. And even before then, I only ever saw old people do it.

The US is weird.

I think in part it's because its harder to transfer money between banks in the US - no equivalent of the faster-payments-scheme which allows a free transfer within a few minutes in the UK. Cheques do provide a layer of universal compatibility.

I think its also the reason behind the success of Venmo (and earlier PayPal) to allow for free/very low-cost money transmission.

It amuses me that venmo / cashapp (multi billion $ innovative startups that reimagined something) simply do what regualar banks do and have done for decades in the rest of the world.

I don't have experience with a gas station so mine could be very different. I'm at 1-3 daily employees.

For me it's:

- counting the till pre and post : It takes about 3-5 minutes a till. (money counters are awesome, and I setup all pricing increments to avoid anything below a quarter, which wouldn't be practical for an average gas station. But it could be done down to the nickle or dime) I don't count before and after, just after. The before till should already be done from counting the after and using for a shift the next day.

- validating voids and receipts : it's mostly fully automated via the POS. Maybe 10 mins when something odd happens but it's not common.

- checks and cashier's checks : we get almost zero of these.

- bagging and dropping cash : labeled bags and a drop safe, I don't count until at least the next day, all in one quick go. All the time is in the counting part.

- cash slippage - ours has usually been fairly close. Some times a bit over sometimes a bit under. If its a few dollars off every now and then I don't worry about it. If its consistently off, either way, it signals a problem, usually in training. But every now and then its nefarious and corrected.

So weekly time breakdown is probably:

- counting daily tills : 30-45 mins

- making the change request, deposit and going to the bank, Ill just say 1 hr as the bank is about 10 mins away. I also usually do this when already out for another reason and I usually go only once per week as cash is so low post covid. I used to go 2-3 times a week pre covid. But if we have a large cash day I will make an extra trip so we are not sitting on as much.

- misc accounting etc. : our QuickBooks auto syncs to the POS, with each day's sales recorded and the corresponding expected credit card and and undeposited cash account records created. So when the physical cash deposit is made it with auto match the record already created by the POS and I just click the match button. But other things always can happen in the chain so let's give another 10 min buffer here.

So I'm out 1.75-2ish hrs/week, which actually feels like more than I spend on it. So for quick math for each 10k sold per week at a 2.5% cc rate (ours is higher around 2.8ish). That's $250 in credit card fees. That's About $125/hr to handle the cash vs take the card. Looking up the average gas station sales of about 109k/month that is around $2,725 in fees. So even quadrupling the time I spend that would yield a savings rate of $340/hr spent handling the cash. Seems worth it.

I mean, the x.99 prices make more sense in places like the U.S. where state and local sales tax cause the final prices to be somewhat unpredictable anyway. It would be weird to advertise $9.99 when you know that that’s going to be the final price.

It happens in Europe where we have inclusive pricing in almost all, if not every nation.

(apart from very rare circumstances like bottle deposit costs (which are refundable) not being included)

At least the bottle deposits (€0.15 or €0.25) are listed with tax included and can be payed with 2 coins (10+5 or 20+5)

That would be a reasonable argument if sales tax fluctuated more often than the prices of goods. In reality, it’s the other way around.

I'd rather we outlaw the ridiculous "and 9/10 cents" that is appended to every single gasoline price in the US, and that everyone ignores when reading.

Funny enough it is there because of the tax law, not in lieu of it.

https://amp.cnn.com/cnn/2022/06/14/energy/why-gas-prices-fra...

At the very least there should be a browser extension that round up all prices ending in .99.

I'm deeply disappointed in humanity/customerity that it works.

It doesn't even cost $X+1 - it must be a bargain.

Humanity did shun it and get rid of it in nearly every country.

The US must be one of the last that still has the stupid penny

This makes the rest of analysis irrelevant. Kind of like most mainstream economics, where they start from some convenient but wrong assumptions, then build an edifice on top of those and make strong statements inferred from said edifice.

The article isn't about transactions that use coins but transactions that return coins.

If you go to the grocery store and buy 8 or 12 items then the distribution of change will actually be pretty uniform.

Just a single item sold by weight will do it. But also so many prices like $3.19 or $2.59 will mix up the second-to-last digit of your total, and your total item count mixes up the last digit.

Not to mention the items which get sales tax applied further scramble any pattern that might have existed previously.

Laundromats seem like more of the exception then the rule. Besides vending machines, I can't think of any other service priced evenly in coins -- especially after sales tax.

We should better introduce $50, $100, $500, $1000 and $5000 coins. I'd love my entire salary to come in coins and to be able to pay for any purchase in coins conveniently.

And easier to bankrupt yourself because of a hole in your wallet.

It wasn't that long ago when it would be normal to be paid in cash (notes and coins) at the end of the week or the end of the month.

Depending on the job sector, this could be the 1970s or 1980s in Britain, for example.

perhaps if we reduce these coins to some units of digital currency so we don't have to physically carry them around, like bits, but for coins

How are you going to prevent fraudulent double spending of these digital coins? You'd have to invent some kind of Byzantine Fault Tolerant (BFT) consensus method.

Sure, but then you’d need a way for all participants to agree on which transactions are valid. Maybe like a chain of blocks that hold transaction data, and each block is cryptographically linked to the previous one. Sounds pretty difficult. I doubt that anyone would be able to create anything like that any time soon, if ever.

Few more years of AI investment and we can just ask GPT13 to create and run this model.

That actually sounds more promising than the way most altcoins are operated today. If only Sam Altman doesn't elope with all those GPT13 coins...

In the year 2045, the world had transformed into a sprawling metropolis of concrete and steel, where the sun rarely pierced the thick haze of pollution. The government, in its quest for absolute control, had implemented a system known as the KYC Protocol—Know Your Customer. It was a measure designed to eliminate fraud and ensure security, but it had morphed into a bureaucratic nightmare.

Every citizen was required to stand in line for KYC checks before making any purchase, no matter how trivial. The most mundane items, like a pack of gum, had become luxuries that demanded hours of waiting. The lines snaked around the block, a serpentine mass of weary faces, each person clutching their identification cards, biometric scans, and digital wallets.

Maya stood in line, her stomach grumbling as she watched the clock tick away. She had been waiting for nearly two hours, the fluorescent lights above flickering intermittently, casting a sickly glow on the faces around her. The air was thick with impatience and the faint scent of despair. She glanced at the digital screen mounted on the wall, which displayed the current wait time: 45 minutes remaining.

“Next!” barked a voice from the front, and the line shuffled forward. Maya’s heart raced. She had only come to buy a pack of gum, a small indulgence to brighten her day. But the KYC checks had turned this simple act into a test of endurance.

As she inched closer to the front, she overheard snippets of conversations. A man lamented about the time he lost waiting to buy a loaf of bread, while a woman recounted her experience of being denied a purchase because her biometric data had been flagged as “inconclusive.” The stories were all too familiar, a shared trauma that bound them together in this dystopian reality.

Finally, it was Maya’s turn. She stepped up to the kiosk, a cold, metallic structure that loomed over her like a sentinel. A screen flickered to life, displaying a series of prompts. She placed her hand on the scanner, feeling the chill of the glass against her skin. The machine whirred and beeped, analyzing her fingerprints, her palm veins, and her heartbeat.

“Verification in progress,” the screen announced, the words flashing ominously. Maya held her breath, the seconds stretching into an eternity. She could feel the eyes of the people behind her, their impatience palpable.

“Error,” the machine suddenly blared, and Maya’s heart sank. “Biometric data does not match records. Please step aside for further verification.”

Panic surged through her as she was ushered to a separate area, a sterile room filled with flickering screens and stern-faced officials. The line she had waited in for so long now felt like a cruel joke. She glanced back at the kiosk, where the next person was already being processed, oblivious to her plight.

Hours passed as she sat in the cold room, her mind racing with thoughts of what could happen next. Would she be denied the gum forever? Would she be flagged as a potential threat? The KYC Protocol had become a tool of oppression, a way to control the masses under the guise of safety.

Finally, a woman in a crisp uniform approached her, a tablet in hand. “We need to conduct a manual review of your data,” she said, her voice devoid of empathy. “Please provide your identification and answer a series of questions.”

Maya nodded, her heart heavy. She had come for a simple pleasure, but now she was trapped in a web of bureaucracy. As she answered the questions, she realized that the world had become a place where even the smallest joys were overshadowed by the weight of surveillance and control.

After what felt like an eternity, she was finally cleared. The official handed her a slip of paper, a token of her victory. “You may now proceed to purchase your item,” she said, her tone flat.

Maya stepped back into the bustling world outside, the slip clutched tightly in her hand. She made her way to the nearest store, where the shelves were stocked with brightly colored packages of gum. As she reached for a pack, she couldn’t shake the feeling of unease that lingered in her chest.

In a world where freedom had been traded for security, the simple act of buying gum had become a reminder of the chains that bound them all. And as she walked out of the store, the taste of mint and sugar on her tongue, she vowed to remember the struggle it took to reclaim that small piece of joy in a world gone mad.

Wot

LLM I am guessing.

It likes to talk about Maya's various organs. Alot!

Ahhh. A VISA card then :)

You say that, but it used to be a common criticism Americans had of British currency, that large denominations (up to £2) were exclusively coins.

They cited that coins are in compatible with nearly all wallets, being weighed down, and somehow never actually having exact change.

Background: I'm British and live in the UK but have spent a fair amount of time in the US over the years.

I love the dollar bill. I'd really love to have a £1 and/or £2 note in the UK. The moment you need any reasonable number of coins to buy anything they become unwieldy in your pocket and you can carry enough dollar bills to be useful without there being a chunk of metal digging into your leg.

I've hears arguments against relating to durability but those are all predate the new plastic notes we have.

For some reason I get a load of pushback when suggesting that a £1 or £2 note would be nice to have.

On the other hand, coins are pretty neat.

They are also far more durable than bills, specially lower-denomination bills like the $1 note that wears out quickly because it is used more than higher-denomination bills.

I am curious what the cost difference is to manufacture a coin vs a banknote. Certainly the penny is probably going to not be worth much more than a penny in melt value, but for stuff like quarters if I can make 5 bills that each last 5 years that may be more preferential than a single coin that lasts 25 years because it gives better control over the money supply.

In our household we call them “parking tokens”. We use cash for little else.

I use them almost exclusively as collectors items for whatever country I visit. And nothing else. America is mostly cashless nowadays anyway. My thought is that at least in America, we will not be rid of coins for another few decades at least . Because gauging by the current climate it looks like the only way we start to phase some of these denominations out is when inflation makes them impractical and useless.

Being in Europe, I'm surprised you can get anything with coins in the States. I'd struggle to find much under €1.

They are mostly relegated to a jar that you take to the coin exchange once every X years. I honestly don’t remember the last time I actually carried coins and paid for something with them (aside from receiving them as change and dumping in said jar) but it was over a decade ago that I used to actually carry change in my pocket for use. Could have probably been two decades ago almost.

Probably the most actionable use I have for coins in todays era is having a quarter for the deposits for the carts at the Aldi lot.

I think with polymer notes, they might last until withdrawn by UK standards, but that's a unique factor of how fast they cycle their banknotes out. I think even 5 year old English notes (the paper GBP50 with Watt on it) are at the phase where you have to take them to a bank and replace them with polymer ones.

America has always tried to avoid calling back old notes, likely to avoid creating an upset in places where they're a store of value overseas. This means the old ones can circulate basically forever. I can recall my brother getting a $10 note of the 1934 type in a normal transaction in about 2015, and 1977-series $100s seemed strangely common into the 1990s and 2000s. So the survival rates at 10 and 20 years are relevant for American paper in a way that maybe don't apply in the UK.

Isn’t it because the US supports large scale money laundering and tax evasion whereas more civilized societies try to get rid of it?

I think its meant as not spooking the people in countries with unreliable currencies that hoard USD like one might gold bars

So, money laundering. ;-)

Its not laundering to buy gold and store it, same with stashing USD

Why is it a problem then to take it and have it replaced by newer and safer bills?

In countries that do introduce newer standards, you can still take old bills to the central bank and convert them.

I don’t buy that argument. It doesn’t make sense, especially compared to the immense damage of fraud.

The Bank of England don't manufacture £1 notes, but the Royal Bank of Scotland still make them.

Perhaps you can help popularise them, so they make even more!

You can still create a massive wad of cash to impress the ladies with 5's and a 20 for not such a high cost.

And maybe, instead of common metals and assigning them arbitrary value, we could make them out of rare metals (with a little bit of alloying for hardness) and people can trade them for their relative abundance or rarity!

I can only get behind this if there’s a fixed exchange rate between two coinable metals that doesn’t change with their relative scarcity.

Let'em Lithium coins roll!

Let’s adopt CR2032 batteries as a currency

The values of nickel, zinc, and copper are far from arbitrary, and oftentimes the metal value of a coin is higher than its face value. The US penny is >2¢ of zinc and copper.

Besides, metals like lithium corrode too easily, and other rare metals like zirconium/niobium/tantalum/REEs are intrinsically scarce so minting coins from them would be wasteful. Arguably using zinc, nickel, and copper for coins is wasteful, and all coins should be some sort of stainless steel or aluminum. (Like the aluminum Japan 1 yen piece.)

Then your cash becomes a store of value. Exactly what the government doesn't want. Not least as people will make a living melting down coins as the governments expense.

As long as they have prepunched holes in the middle so I can hang them on a chain around my neck like a maester.

I'd love to find your $5000 coin on the sidewalk!

Sounds terrible to me, coins are so much harder to keep track of!

The back of the sofa would be worth digging through.

You tend not to walk around with coins on you that are worth a lot. Same thing with cash; most people aren't walking around with wads of $100 bills. That's something you keep in a safe until you need to exchange it for smaller units.

I understand the romanticism of coins and the nostalgia of coin collectors, but the experience of actually using them is just so much worse than bills. When I go to Canada I immediately relinquish my loonies and toonies to my Canadian friends because they're such a pain to deal with.

A well-designed set of coins is nice to use, but this is unfortunately rare.

Canada and the USA certainly don't have it. The Euro doesn't, which is odd as the currency is so new -- why are the 10, 20 and 50 cent coins so similar?

The Pound Sterling is generally well-designed, with sets of coins in copper-silver-gold materials, and easily distinguishable sequences of shapes and different sizes. The Danish and Swedish coins also work, in the Danish case with a hole to distinguish some denominations.

I found Danish and Swedish coins to be just as annoying as American coins. They are difficult to tell apart immediately. The Pound and its denominations, I agree, are the best I've encountered so far in real world use.

I wish America would get off its butt about getting rid of the penny. It's such a waste of resources. We don't need it. In fact, Ecuador uses USD as well and they, a country with much lower GDP and prices, don't use our penny. They round up.

    > just as annoying as American coins.  They are difficult to tell apart immediately.

Which American coins are difficult to tell apart immediately?

Penny (1c) is a different color (copper).

Nickel (5c) is fat.

Dime (10c) is small.

Quarter (25c) is large.

Are dollar coins (Susan B. Anthonys) used heavily now?

I agree about the penny. I am pretty sure that Australia no longer has a penny, and rounds up everything to the nearest 5c. (Can any Aussies confirm?)

Only a certain subset of people would think that universally, a coin that looks bigger would be half the value of the smaller one.

In Argentina back when coins were worth anything, from 1c to 50c they would grow in size, also would have the value in big clear numbers, and varying colors. The 1 peso coin would be a big smaller in diameter but substantially heavier and different with two colors.

Coins in the US from this “obviously the smallest one is the least valuable” mindset didn’t make sense. Also seems like no one cares about any coin but the quarter for anything other than trading them. Any coin operated machine I’ve seen takes 25c

>why are the 10, 20 and 50 cent coins so similar?

...have you ever used the coins?

All different sizes and the border of 10 and 50 are similar but the 50 is x2 the size and the 20 is totally different

I don't think anyone would say they are similar

I'm British and I fully agree that Euro coins are too similar. It always irritates me when I'm travelling in the Eurozone. The coins are different sizes but they're not different enough and it always takes me a moment to confirm which coin is which. A short moment, but a moment nonetheless.

British coins aren't like this. They're all extremely distinct, with big differences in size, colour, weight, and even shape (the 50p and 20p coins aren't circular). It's completely impossible to mistake one coin for another, even at a glance. Maybe I'm biased but I think they're exceptionally well designed. Rule Britannia!

The 50c isn't double the size of the 10c, it's 18% wider. It has the same edge texture as the 10c coin. It's 1mm larger than the €1 coin, and 1.5mm smaller than the €2 coin.

The 20c coin has 7 subtle indents, and is only 1mm larger than the 5c coin. Can you tell the difference when your hands are cold, or if you're wearing gloves? (I understand people lose their sense of touch in old age.)

Meanwhile the 20p and 50p are heptagonal, with a similar 20% size increase.

The 5p and 10p have a 26% size increase. They have milled edges, unlike the 1p and 2p.

What are you talking about? The Euro coins were designed for and with the blind community.

I can grab any coin blindly and know exactly which one it is?

Same with the bills and their relative sizes. I still think the EU messed up the bills; they’re super ugly and feel plastic, but for the blind the Euro is insanely well designed.

I think it might be easier for the blind to differentiate them than people with normal vision tbh. The designs on the face are all quite similar, but the designs on the edges are all unique.

That’s a fair point

The heptagonal shape of the 20p and 50p make them much easier to distinguish from other coins by both sight and touch. I can see the different coins in a heap, and I feel the difference even through gloves.

The copper and gold-coloured Euro coins all look very similar.

I find Polish coins to be very easily distinguishable too.

A bill could never replicate the gratifying "plunk" of putting a dinner plate sized 10kg coin worth $5000 into the Carvana vending machine

the coin purse market in such a world would be a sight to behold

Wealthy people would hire someone whose only job is to carry a wheelbarrow full of change.

let alone the satisfaction of plunking in 10 of them, one after another, muscling them up from my Weimar®-brand currency wheelbarrow.

Iportant first comment in the blog:

> Just to summarize how commenter, Jeffrey Shallit, addresses the (1, 3, 11, 37) solution: this is the best way to use the Greedy algorithm to select coins. However, (1, 5, 18, 25) and (1, 5, 18, 29) are tied for the actual solutions. [...]

I thought it was going to be about how there was 3700% inflation since coins were actually a useful concept.

It's probably just better to go for eliminating the cent and the nickel and making a 2.5$ coin.

I’d go farther and eliminate all but the quarter.

And make it illegal to sell any service or product that isn't ending in 0.25, 0.5, 0.75, and 1.00. Tax must be included and listed in advance for all sales prices.

A few tiny pieces of candy? Sell more at once. Want to charge a dollar for something but tax makes it 1.07? Either eat the tax yourself and offer it for 1.00 post tax, or raise the price and charge 1.25 for it.

Most efficient would be to start rounding purchases to the nearest five cents (if is isn't electronic) and get rid of the penny which costs more to produce than the penny is worth.

But an average one cent coin is involved in more than a single transaction - if you amortise the cost of the coin over every transaction it is involved in, then it’s much less than one cent.

If the cost of metals in a coin is more than its value, you do have a point.

In the Netherlands we've been rounding to 5ct intervals for 20+ years now, and 1ct coins were abolished long ago. With the introduction of the euro, the 1ct and 2ct coins returned, but all shops still round to 5ct for cash transactions.

Every time I return from Germany I have a handful of 1 and 2ct coins though, since they haven't done this, and most prices are X.99.

In Australia the 1 and 2 dollar notes were removed from circulation decades ago too. $1 in 1984 and $2 in 1988.

With respect to the 1c and 2c coins, isn't the metal in them worth more than the currency value?

Cost in metals and manufacturing cost. (just to clarify)

People need to be able to quickly do the math in their heads to make change. More efficient use of coins but harder for everyone involved is not a functional improvement.

Some of the proposed schemes seem acceptable from that point of view, in particular 1, 3, 10, 25.

I love thinking about problems like that. Yes it is impractical and unlikely to result in any change but it also helps illuminate relationships (like # of coins in your change) that you might not otherwise see.

Of course, as an economist Patrick (the person asking the question in the article not the author) ignores what is most important about choosing coins "Can the teller give you change quickly and accurately?" That is the important question because GDP depends on transaction flow, and anything that hinders transaction flow is a net negative on GDP[1].

Using the Suica card in Japan I was reminded again of how useful it would be if the government would just bless a pure stored value cash card. Yes, I understand the arguments against it (mostly based on surveillance IMHO) but still it would be a useful thing in terms of getting us to 0 coins per transaction. :-)

[1] Yes, I subscribe to the theory that GDP is inherently a time based numbers "value per unit time"

OTOH I liked that I could buy a meal with a single coin.

The other doesn't discuss the 'prices' vs 'currency' question which would relate to your sentiment. Recently visited Japan where they have a lot of different coins, 1, 5, 10, 20, 50, 100, 500 yen. We don't talk a lot about dollar coins, but they were there to replace the $1 bill which gets worn out. A $5 coin (like the the 5 L coin in the UK) would be the 'you can get a meal with one coin' coin.

In ideal world, I would prefer coins to be powers of 2.

It requires 7 coins in [ 1 .. 64 ] range to reach 100, but the average of popcnt( 1 .. 99 ) is only 3.19 coins per transaction, way better than 4.1 coins.

Now account for the amount of mental overhead required for the average person to calculate change or coinage of a random amount in base two coins, as opposed to multiples of 5 or 10, and see if your 3.19 coins per transaction really saves you time.

One could simply switch to a base 16 numbering system as well!

I think the amount of mental overhead with base 2 coins is still less than with the proposed [ 1, 3, 11, 37 ] solution.

Great idea! Let's also make them double in diameter and density each denomination increase.

Two obvious problems: the fractional part of the price is not uniform over [00..99] and the system has 5 coins, since in 2021 minting for the half-dollar coin was restarted.

At some point, that we are possibly near to, doesn’t the value of a dollar become so small that the fractions of a dollar that coins represent aren’t even worth dealing with?

If so, and transactions just rounds to nearest dollar the we are basically expecting that over our lifetime it will nearly balance out without the need to think about it too much.

I currently have 0 coins and 0 bills on me. I had to borrow $10 from my wife to tip the bartenders at a wedding this past Saturday since I didn't want to go to an ATM. Cash (and coins) have their place but it's not worth the effort to make them more efficient anymore.

I believe the young economist mentioned in the article is simply wrong in his analysis. The most efficient 4-denomination set is {1,5,18,25} (tied with {1,5,18,29}) at 3.89 coins per transaction, better than the economist's {1,3,11,38} at 4.10. This result is from a 2003 paper by Jeffrey Shallit called "What's This Country Needs is an 18¢ Piece". Just before posting, I verified Shallit's result with a Python program.

[1] https://graal.ens-lyon.fr/~abenoit/algo09/coins1.pdf

> The chance you have 43 cents in your pocket is equal to the probability that you have 29 or 99 cents in your pocket (in addition to any bills).

This was something I found fascinating when I first visited the US. I'm not sure if it's common across the entire country, but it definitely happened everywhere I shopped: I always received the exact change. If something cost $1.97 and I paid $2 in cash, I would get 3 cents back. And so on, no matter how many coins would be necessary. How thoughtful. I'm more used to rounding off and leaving the change behind, no questions asked.

Why not just re-index the dollar so that coins are useful amounts of currency?

Canada got rid of the penny for cash transactions. Problem solved

All transactions, actually. They're rounded to the nearest 0.05

> As pennies are gradually withdrawn from circulation, price rounding on cash transactions will be required. This will have no impact on cheque payments or electronic payments, such as credit and debit cards, only cash transactions will be affected.

https://www.canada.ca/en/revenue-agency/services/forms-publi...

I paid $2.88 for something the other day by card. Only cash transactions (should) round.

Odd, I distinctly remember gas prices on some machines behaving that way in 2012 or so.

I was curious what the theoretical distribution of digits might be, did not know that there is an extension of Benford's law for later digits which suggests the uniform assumption is quite nearly right: https://en.wikipedia.org/wiki/Benford%27s_law#Generalization...

Of course in real life, 50 cents and 99 cents are way more common.

Do We Need a 37-Cent Coin? - https://news.ycombinator.com/item?id=1694075 - Sept 2010 (137 comments)

Freakonomics: Do We Need a 37-Cent Coin? - https://news.ycombinator.com/item?id=864838 - Oct 2009 (50 comments)

There's a question on SE cstheory site that addresses the more general problem [0]. I wonder if this problem is still open.

[0] https://cstheory.stackexchange.com/questions/5861/asymptotic...

It's quite surprising to me how the US still has the penny. Like its value is less than the cost of carrying it around.

Canada gave up on it over a decade ago (https://en.wikipedia.org/wiki/Penny_(Canadian_coin)).

I've said before, I'll say again:

We should have the $0.1 and $0.5 coins and everything should be rounded to that.

There's no reason to have $0.01 or even $0.05 precision. The value of the dollar, these days, has inflated to the point where there's simply no practical difference between $0.01 and $0.03 or $0.08 in everyday life, when dealing with cash transactions.

You could certainly track $0.01 in digital account tracking, but the coin is silly.

And -- with payment processing fees, places dealing with cash or card processing would still see less cost in "rounding down" than paying for card processing.

Prices in America are wired. Bought a beer yesterday waiting for the train. Claimed it was $7, actual price $7.62 (which Amex coincidently converted to exactly £6.00)

If I’d paid in cash I’d have to pay with at least a 2 cent coin (and likely need a 1 or 3 in change), despite the nice round number

Until America changes to advertise things at the actual price rather than a partial price, I don’t see how getting rid of 1 cent coins works.

It'd cost $7.6 if you pay in cash and $7.62173451123 if you pay via a card?

(and, if I were to pass the "small change" bill, I'd, by fiat, make it so that it'd still be "$7.6" even if it was $7.68 -- and the vendors would still come out ahead because the $0.08 lost from rounding down is much less than the $0.23 in card processing fees that comes with a 3% surcharge from your payment processors.)

Does the UK include VAT in all listed prices? I don't recall it working that way in continental Europe, and it certainly doesn't work that way in Canada with our equivalent (nor in the US, as you discovered).

That said, advertised prices are commonly not "round" in the first place. In Canada, we simply round the figure on the bill when paying cash.

Yes, prices advertised to consumers must include VAT. UK advertising laws mandate that the price must include all non-optional taxes, fees, etc. Prices advertised exclusively to businesses can exclude VAT.

UK and EU law requires advertised prices to include all taxes.

The most common exception is things aimed at business buyers, who won't pay tax -- so the Dell consumer website shows laptops prices including tax, and the business site shows them without, but labelled as such.

It means if I buy for business from a consumer site, and I'm logged in with my business account, I see 'ugly' prices like 5119.20, as the marketing-friendly number of 6,399.00 is chosen including tax.

People are superstitious about math, and fearful that rounding to the nearest nickel, or dime, will result in them getting ripped off. Also, it's an admission that the government has given up on inflation.

This is the country that gave up on the metric system because it involved too much math.

I'd suspect they rejected the metric system because it would have cost money to change everything over. The argument would presumably have gone something like "we can't have the federal government imposing a cost on the citizens / corporations".

Exactly. It had nothing to do with "too much math" -- I think everyone appreciates metric uses less math, and we all learn it in school anyways for science classes.

It's the cost of change. Replacing every speed limit sign, spending decades where half the cookbooks you own use oven temperatures in °F and half use °C. Years of confusion where someone says they were going 60 and you have to ask if they mean mph or kph.

Not to mention changing the size of every milk container, and so forth...

I'm not sure I buy that excuse. For packaged goods and so on, you don't have to change any sizes of things. Just pick a date and change to a different package design. So nothing in your factory that produces 1 gallon milk jugs has to change except the graphic design needs to start saying 3.8L Milk instead of 1gal Milk. At that point, you can transition to change the physical size of things whenever it is convenient.

For cars, most of them in the US already show mph and kph, so the switch should be easy. Leave old signs alone, but whenever new signs get built, build them in both units for a few years (65mph / 105kph) allowing you to gradually transition to metric.

Repeat for everything else. You can gradually make the switch. Heck, some products (like soda and bullets) are already in liters and millimeters.

I agree with the OOP. We refuse to even take the first steps to switch because of good ol stereotypical American paranoia: "If we switch to metric, all the companies will use it to make everything smaller and rip us off!" as if shrinkflation wasn't already a thing.

> Leave old signs alone, but whenever new signs get built, build them in both units for a few years (65mph / 105kph) allowing you to gradually transition to metric.

Road signs last around a decade. So you're talking 10 years to replace with dual-unit signs (which are more confusing) and then another 10 years to replace again with metric-only signs.

Is it worth it? Is it really that important to change driving speeds to metric? What's the benefit?

And how does it help to say "hey can you pick up 3.8L of milk?" If packaging sizes don't change then we'll still call it a gallon and we won't have "converted" at all.

Conversion is a massive, confusing, expensive effort, and it's reasonable to wonder whether it's actually worth it.

I was thinking 50+50 years, but ok 10+10 years is even better. I mean, if you do it gradually enough, the cost approaches zero, so is it worth "almost zero" to have a standard measurement system across the globe? Maybe?

Nothing stops us from enacting generous legislation mandating the switch to metric by the year 2125 or something. You'd have to have intermediate milestones of course, or everyone would just do nothing and wait until 2124 and then complain endlessly about how the transition is so costly and we can't possibly do it in a year, and so on.

But this is the USA, where we can't seem to do anything that takes longer than a quarter, and our entire country's major priorities change every 4 or 8 years.

So if everyone knows everyone will be whining, you could just as well announce the transition tomorrow and get it over with in a year.

As if Americans don’t find a reason to whine every bloody day.

> And how does it help to say "hey can you pick up 3.8L of milk?" If packaging sizes don't change then we'll still call it a gallon and we won't have "converted" at all.

I'm with you on everything but this. The imperial system allows retailers (and/or consumer good manufacturers) to take consumers for a giant ride. I have lived in both USA & EU, and in the USA I just give up entirely on comparing goods in a supermarket. With the metric system there's nowhere to hide, and I can compare all products, whether you use ml or l, mg or g or kg. In the USA different manufacturers will use any odd denominator they can come up with and after about two weeks of normalizing fractions every time I went shopping, I gave up.

Even the little tags supermarkets add to try and help you, aren't enough. Many shops use a different denominator, and even a single shop will vary internally. Something as simple as comparing the price of bacon becomes a middle school math problem.

I hate corporate greed, I am partial to pointless mental exercise like math, and I am very stubborn. I don't want to speak for other people but something tells me I'm not the only one who has given up on this battle. Retail customers have more power in the metric system.

For everything else though yes I agree who cares. Except °F which is actually better. :)

> The imperial system allows retailers (and/or consumer good manufacturers) to take consumers for a giant ride.

That's a really interesting point. However, ultimately I actually don't think it has anything to do with imperial vs. metric, but just consumer culture.

In Europe, when you order a drink the menu tells you how many centiliters it is. In the US, it's just small-medium-large-XL, which every location defines however they want. And in the US, the difficulty in comparison doesn't have anything to do with imperial units -- it's that one package of tomatoes is defined by volume while another is by weight, and the loose bell peppers are priced per pepper while the packaged ones are priced per weight, and so forth.

Switching to metric wouldn't change any of that.

That's a problem that can seemingly only be addressed by legislation -- e.g. that strawberries and tomatoes must be sold by weight not volume, or that selling produce by the item must also accurately list the average item weight.

Your post reminds me of the additional problem of "The Serving" which is a unit of measurement entirely conjured up by the food manufacturer to serve as the denominator when listing required nutritional information.

A normal 50g bowl of your sugary breakfast cereal too unhealthy? Just define a "serving" as 20g and cut all your bad numbers by 2/5! Problem solved! Is your bag of chips full of salt? Just invent a "Serving Size" of three chips and you don't have to draw attention to yourself on the nutrition label.

Letting companies define their own units of measurement seems to be a totally preventable regulatory mistake.

Indeed, it's something the EU prevented. There are regulations on what the standard serving size is, and other regulations specifying how the item must be priced -- so all the milk says "per litre" under the price tag in the supermarket, even the fancy one in a tiny bottle.

There were also preferred size regulations, which was meant to make it even easier. Breand could only be sold in multiples of 400g. I think this was relaxed, but it's still present for some things. A standard bottle of wine is always 75cL, for example.

There UK still used miles per hour for speed limits, and I’ve debated how we may change with my partner.

I think the battle here is now lost - if you want to use km/h a sufficiently advanced modern car will show you the current speed limit and convert from imperial to metric for you. In the ten-to-twenty years a full change would take to complete we’ll proabably have cars which are close to self driving, so who cares what value they use for speed limits?

But for everything else - please do look to the UK as an example. We converted in the 1970s and it’s still a bit messy today, but it’s mostly worked.

Beer at a pub/bar is mostly sold in pints, but to sell in litres is legal. Bottles of beer are often 330 or 500 ml. Wine is sold in millilitres, as are spirits.

Basic milk is in pint sized containers (sizes in litres are shown). ‘Fancy’ milk is often sold directly in litres.

You get the occasional container which is a weird size - like golden syrup is still sold in a 454g (1 lb) container.

Ovens can be dual calibrated, and English language recipes often already will give both metric and imperial units for readers in the UK, AU, NZ, CA, etc.

When cooking - if I find an American recipe with unconverted values I will just use Google (“what’s 6oz in grams?’), etc. In fact a bigger problem for me is that American recipes tend to use volumetric units (e.g. 4 cups of flour) where I’m used to weight (e.g. 500g of sugar).

It's the cost of change, and also the fact that the people you need to convince to switch don't benefit. If you're an adult in the US, you already know the conversions you need to do everyday tasks (e.g. 12 inches to a foot, etc). You also have calculators absolutely everywhere to do the math for you, so it isn't like you benefit from being able to do it in your head more easily. So, if we switched to metric most of the country would have to incur significant costs, and reap no benefits. That's never going to fly.

>"we can't have the federal government imposing a cost on the citizens / corporations"

same kind of moronic non-argument for why the US gov can't invest in healthcare, or housing, or education; none of these things are "costs" and all of them are very high ROI investments, but Americanoids are incapable of thinking more than one fiscal quarter into the future

Government spending on those items is >$3 trillion per year in the US.

There is something to being wary of rounding up. For example when you get food from a drive-through or buy groceries and they ask you to round up to the nearest dollar, with the rest of the exchange going towards a charitable cause. They do that because at scale it's enough for them to get a tax incentive for charitable donations via other people's action. I refuse to help an international corporation cheese tax law.

But for something like me handing the shawarma guy a tenner for an exchange that comes out to $9.39, it's not anything to even care about. It's a rounding error.

That's not how tax law works in the US. See https://taxpolicycenter.org/taxvox/who-gets-tax-benefit-thos...

The corp is acting as a collection agent on behalf of the charity, they don't get to deduct it as a charitable donation. Even if they did, they would have to then count the money as income, which would offset any tax deduction they would get, giving the corp 0 net tax benefit.

...Though they may get some publicity benefit from it, which is why I don't go out of my way to donate using corps as a proxy. If its a small amount that I may not otherwise make, for a good cause, sure. But for my more deliberate giving, I would avoid corp proxies. So I don't give through my employer (unless they are offering to match it with their own funds).

> They do that because at scale it's enough for them to get a tax incentive for charitable donations via other people's action. I refuse to help an international corporation cheese tax law.

This is a myth. They can’t claim this on taxes because they don’t have the associated income. To get that using your money, they’d have to claim your donation as income and pay taxes on it, making moot any tax savings (and committing fraud against you to boot).

What they do use your money for is marketing. All the money goes to the charity but they get to say things like “Our program raised a gazillion dollars for those in need.” Which has the effect of positive associations of a giving company which hasn’t actually given.

In countries with cash rounding (Denmark, Sweden, Australia, etc) there are strict rules on how that rounding works.

9.39kr will be rounded here to 9.50kr if I pay cash. 9.24kr would be rounded to 9.00kr.

If I pay electronically it's 9.39kr.

I assume your "kr" example is the Danish kroner here? If yes, for others, the current FX rates is 6.79 DKK to USD. So 0.25 DKK is about 0.0368 USD, or less than 5 cents in US.

It's the Danish crown as I live here, so yes, you lose or gain up to 3½¢.

In Sweden they round to the nearest whole crown, so you gain or lose up to 4.8¢.

When the US half-cent coin was withdrawn, it had purchasing power equivalent to 16¢ today.

Is any of that still true though?

I think it was 30 years ago. I don't think it is anymore though.

I think people just mostly stopped caring about getting rid of the penny because they use cards and apps for everything now.

On the one hand, I absolutely think we should get rid of the penny. On the other hand, I couldn't care less because I literally haven't used a coin or a bill for a single thing in years.

It's true that things have changed over the passage of time, and I think that people have also stopped caring about the metric system.

Industry has converted. CAD software lets you switch between US and metric with the flip of a switch. Things like the spacing of pins on a microchip are just arbitrary decimal numbers anyway. The car industry has standardized on metric fasteners. Most US households don't even need non metric tools any more.

A few things like building materials are still US, but once again, for industry, they're just decimal entries into a CAD program, and if they need different sizes, they can order custom sizes from the mill.

Some weird units remain, like spark plug threads, but those things are so unique that there's no reason to switch. The only use for a spark plug wrench is to loosen a spark plug.

As an amusing aside, I still use cash, because of my side occupation as a working musician. I often get paid in cash. It piles up in my house and I have to remember to use it. Also, there's an old tradition of drinking establishments letting the musicians have a free drink, so I keep some small bills in my instrument case to tip the bartender.

> On the other hand, I couldn't care less

Sounds like you should be in club "Ditch the penny" - because you don't use cash, the only effect it will have is lower taxes (or more efficient use of what you pay now), because of how much it costs to make pennies.

> This is the country that gave up on the metric system because it involved too much math.

You say laziness, I say efficiency. More math than necessary is always too much math. It will always be more important to divide things by halves and thirds than by halves and fifths. I would apologize to the French for that, but I'm not going to apologize for always preferring multiples of sixty to multiples of fifty, to a people who count by twenties. If you don't count in decimal, you don't get to be judgemental.

Except it's 8 ounces to a cup, 3 teaspoons to a tablespoon, 1760 yards to a mile...

Why is a 11-cent coin ridiculous? With nine of them you could pay for these X.99 products and not get a penny in return.

Yes, we should totally revamp our coins to suit the needs of retail marketing.

Because X.99 products are pre tax, so you really have to pay X.99 + X.99 * 0.0Y

This made me wonder about the origins of the 0.99 price. I had always thought it was largely to avoid theft, by ensuring the worker had to open the till for change on every transaction. Which makes sense if there's no sales tax, but if there is sales tax then you might as well round everything to the dollar.

Possibly sales tax wasn't a thing when this became a common practice.

Makes the argument for the psychological effect of 0.99 vs 1.00 much stronger these days though I suppose.

In the US, sure, but most of the world display prices inclusive of tax. (at least from my experience in EU and Asia)

The coins proposed are all prime, which makes sense to me intuitively. You'll always need a 1 coin. I'm curious if it's generally true that optimal coins for any given range starting at 0 will be primes?

I take issue with the assumption that you always need a 1 coin.

If we're going to go to such great lengths to minimize the number of coins, even at the cost of making real-life transactions more complicated, we could totally forgo the 1 coin and just have 2 and 5. If an amount ends in 1, you pay 5 and get two 2s back. Now you can have a coin system that is entirely primes!

not anymore :)

Personally, in the US, pennies, nickles and dimes should be eliminated.

I think we are at the point were paper money $1, $2 and $5 should be replaced by coins. But that would cause a huge uproar in this country.

I personally prefer bills (paper or plastic) because they are lighter weight than coins. I would very much like to see 25¢ bills.

Some countries use plastic rather than paper for bills of small denomination. They feel more pleasant and probably last longer. I also prefer these.

I think we need a 1337 cent coin!

While European Bank is striving for cash removal the coin is a nonstarter

Touching coins is icky.

Way less then banknotes... bacteria etc don't like metals

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