The Italian shortage of small notes

Thomas Kaminski, a loyal MR reader and current resident of Italy, writes to me:

There doesn’t seem to be enough currency in small denominations in circulation.  Wherever I buy something, the merchant or cashier seems to ask for smaller bills or coins.  Back home in Chicago, if I go into a Starbucks, I don’t give it a second thought if I give the cashier a twenty dollar bill for a $2.50 purchase.  They always have plenty of change.  Here, even in some supermarket chains, the cashiers constantly ask for exact change or at least for notes in smaller denominations.  And when I go to a museum, they often seem to have no change at all…My wife, who is not as familiar with the currency as I am, says that she hates carrying any bill larger than a 10; she constantly gets dirty looks or has to endure sighs of frustration if she tries to buy a cup of tea and doesn’t have small change.  And you should see the complications if you try to buy something from a street vendor and don’t have exact change.  What is equally annoying, whenever I go to a cash machine, all I get are 50-Euro notes.

I had the same problem in the old days of the Lira, but I am surprised it continues to plague the Euro in Italy and yes I’ve had the same experience here in Venice.  Is the Italian central bank simply refusing to print up the right denominations?  If so, given Eurofication why don’t the proper size notes flow into Italy where they are most needed?  Or should I assume that Italians do not carry socially optimal cash balances at hand?  Is there a heavy tax on cash registers and other forms of monetary storage?  I remain puzzled.