Why do the €200 and €500 notes exist? From what I read, they are mainly popular in organised crime. Most currencies do not have such large notes. Some eurozone predecessor currencies did — is that the only reason, or are there some legitimate uses for such large notes?
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Large banknotes can be used for two things mainly: large transactions like buying a car (it happens both in the eurozone and in other countries like Switzerland) and as a store of value.
If you live in the Netherlands or France, all this might sound surprising but there are huge differences in the way people use cash in the various countries of the eurozone. That's also why, while the authority to issue new banknotes legally rests with the European Central Bank, only National Central Banks actually handle cash.
In a way, it's related to your point about large banknotes in predecessor currencies but in many cases it's not a mere historical curiosity. It's something that's embedded in those countries' payment system and people use and expect banknotes with a relatively large face value.
A few facts to illustrate this:
- In this ECB survey, 10% of Austrian and 0% of French respondents report using cash “always or often” for purchases above €10k like a car (in France, it's actually forbidden in many cases). For purchases between €20 and €100, the proportion is above 60% in Italy, Germany or Spain compared to 20% in the Netherlands.
- From the same source, more than a third of Spaniards and Italians never withdraw money from an ATM compared to 4% in the Netherlands. 25% of Spaniards withdraw money over the counter at a bank at least every two weeks, compared to 2% in the Netherlands (84% of Dutch respondents never do it, the highest proportion by far, compared to 30-50% in most countries, 59% in France). Average amount withdrawn is €89 in France, €214 in Germany.
- The proportion of respondents who report having a €200 or €500 banknote in their possession at least once a year is 45% in Luxembourg, 39% in Italy, 37% in Austria compared to 9% in France and 8% in the Netherlands (there, 70% of respondents never had one).
- Only Germany, Austria, and Luxembourg commissioned new €500 banknotes since 2002. Belgium, France, Portugal, and the new members (Greece, Cyprus, Malta, Latvia, Lithuania, Estonia, Slovakia) never commissioned anything above €50. Before the 2008 crisis however, many €500 banknotes were found in Spain, which never commissioned any!
These figures also put the numbers regarding organised crime in perspective: It's perhaps true that most of the value is in the hand of criminals, especially outside of the eurozone (Wikipedia mentions a lot of concern about this in the UK) but a large proportion of the population does use €500 banknotes at least occasionally. Still, according to the same survey, a third of all euro banknotes are used for transaction purposes and 20 to 25% are held abroad. That leaves a bit less than half as store of value in the eurozone but not circulating.
There are also subtler differences beyond the use of banknotes with a high face value. It's anecdotal but based on my travels in both countries, I have the feeling that German ATM are mostly stocked with €50 banknotes, sometimes not even offering multiples of 10 or 20, whereas in France it's much more common to receive €20 notes, even if you withdraw €100 or €200.
Incidentally, the Netherlands might be an exception in another way: There was in fact a 1000 Dutch guilders note but it seems the country has moved away from cash to a much larger extent than almost all other eurozone countries except perhaps France, which did not have very large banknotes before the euro (since 1960, the largest note had a 500 Franc face value, about €75 at the time the euro was introduced). So the large Dutch banknote now looks like a curiosity in a way that Austrian or German banknotes do not.
It may be as simple as a combination of 2 things. An aversion to credit/debit cards, as well as checking. These people are often called "the unbanked." That, and the need to transact more than €500 on a regular basis.
I am in the US, and deal with people paying their rents. $1000 rent, and a pile of $10 and $20 bills to count. I'd prefer 10 $100 bills, but would be happy to see the $500 bill back in circulation. It's valid currency but hasn't been in circulation for some time.
Why do the €200 and €500 notes exist? From what I read, they are mainly popular in organised crime.
While it does make sense that organized crime may prefer large denominations of the currency in question, I don't see how not having these denominations will help in preventing organized crime. After all, there's a whole lot of US$ (where the largest denomination is $100) in the hands of organized crime as well*. And even if that wiki rumour of Bin Ladin having had a 500 € note sewed into his clothes - I guess 5 100 € notes wouldn't have been that much more difficult. (tongue-in-cheek: though the official statistics will look better if organized crime has to move to denominations that are anyways popular: then a smaller percentage of the notes of that denomination is in the hands of organized crime - even if it is the same amount of money...)
* Does anyone know whether withdrawing the larger denominations in the 1970 had any effect on organized crime?
are there some legitimate uses for such large notes?
Yes, of course.
Euro notes are legal tender, and this includes the large denominations. Which means that if you want to repay debt, your creditor must accept these notes. In contrast, there's no legal requirement to accept a wire transfer, cheque, or whatever else.
(You can establish a contract beforehand, though, that establishes how the payment has to be done, e.g. gas-stations do this by putting up a sign that they don't accept those large denominations).
Note that there seem to be different perceptions of what this means in different countries. E.g. in Italy (AFAIK, and according to notes I read in a hotel) cash transactions > 1000 € are not allowed any more.
@Relaxed already mentioned the purchase of a (used) car. In Germany it is perfectly normal to do this by cash, because it can save some runnig back and forth: you'd anyways want to test-drive the car. Ideally, if you're satisfied with the car, you can just pay, receive the papers, go to the closest license plate office and get temporary license plates - that's it, you can drive home with your new car. The advantage of saving ways is of course larger if the car in question is several 100 km from your home.
Although I'd use more normal smaller (100 €) notes which you can withdraw from an ATM, and which are easier to use for everyday purchases (see gas-station example above). The survey @Relaxed linked asked in a 1000 to 10000 € category: this is not too bulky in 100 € notes.
Similar for other things like e.g. used machines, tools, etc. where you're reasonably sure that you want to buy it, but will always look/test it beforehand, and where things are too big for sending by post back and forth. And where you don't want to wait until the wire transfer is processed, and the seller doesn't like the uncertainty nor the fees that come with cheque payment.
Notes have two purposes. One, their obvious purpose, is the exchange of goods and services.
However (some "rock-solid" currencies) can be used for another purpose: storage of value. This is especially visible on 100USD bill (which is still quite small): it's average lifetime is whopping 7.5 years (compared to mere 2.5 years average of other USD notes) and Federal Reserve estimates that between 25-60% of all 100USD notes are physically outside USA. This all clearly show that 100USD bill is used as a long-term storage rather than everyday money. This happens because US Dollar is perceived as a stable, "benchmark" currency and 100USD bill just happens to be the biggest denomination it has. And it's not just because 100's are unpopular: quite the contrary. 100USD is the SECOND most issued US Dollar bill (after the 1USD)!
Another currency perceived as most unlikely to undergo inflation is Swiss Franc (CHF). Switzerland prints probably the most valuable bill ever: the purple 1000CHF note. This note also serves the storage purpose (excluding the fact that Swiss use 1000 bill quite frequently and getting a change from 1000CFH bill in Switzerland is apparently much easier than getting a change from 100USD bill in USA. Perhaps because Americans are bit crazy about their 1USD "greenback" bill, but that's another story.)
Now, your question was: what's in it for the state? The answer is: money. People withdrawing notes from circulation are basically buying 0 interest bond from the emitent. Printing large denominations makes it easier for people to store large value in small package. I've already said that 100USD is the second most common bill, there were 8.631 bills as of 2012. That's 863 billion USD in 100s. Let's assume that only 25% of them are kept under the mattress - that's 215 billions frozen. AFAIK current interest on 1-year USA bonds is 0.25% - this means half a billion USD saved every year.