There is a curious development in the Eurozone: since Thursday, April 14th, there are now Euros circulating in Northern Europe, which are not legal tender in Southern Europe. There may be more examples of that sort, but this is the first I am aware of (mea culpa). This raises fascinating issues, at least in principle.
The step taken is a modest one. On Thursday, April 14th, the Bundesbank has started to issue 5-Euro coins, that are legal tender in Germany only. A link to a video (in German) is here: http://video.tagesspiegel.de/funf-euro-munze-ist-da.html . And it makes one wonder: could the Bundesbank issue 10-Euro coins as well? 20-Euro coins? 100-Euro coins? Conversely, could perhaps the Soutern European Central Banks get together and issue southern versions of these coins, which are then legal tender only in Southern Europe, and not in Northern Europe?
And what should be their exchange rate? There is no reason, a priori, that 5-Euro coins will be traded at par. Indeed, given that they are intended as collectors items, it may well be possible that it will be trading above par soon. That's interesting: Euros issued by the Bundesbank will then be more valuable than Euros issues by the Italian Central Bank.
Perhaps that is an experiment worth extending far beyond its original intention, cautiously, one step at a time. It may be entirely reasonable to feature "Northern Euros" and "Southern Euros" and have them trade at some exchange rate. It could induce some much-needed flexibility into the price system, and could dislodge some of the thorny misalignment problems we now see in Europe. At a later point, as things are returning back to normal, the Northern Euros and the Southern Euros could be sucked out of the market again, at the appropriate exchange rate at that time.
I know: this idea is a bit crazy. But monetary policy these days is stuck in a rather crazy corner in the first place. So, tossing around crazy ideas might help to formulate policies that have the chance to do lots of good, in the end. Let this be a contribution to that end.