OK, the Euro, as a common currency, has probably not increased trade much, if at all. The basic logic -- separate fiscal authorities, and less-mobile labor markets in the US -- mean that it's clearly less desirable to have a common currency than in the US.
And yet, is this factor at the core of the European problem now? See Krugman's latest.
I tend to think this is just a small part of the problem, albeit larger for the smaller countries within Europe... Since those are higher risk countries, they get double-whammied having their currency float with Germany, meaning that they can't save themselves by devaluing in times of trouble.
But, the real problem, make no mistake, is that Jean-Claude Trichet and other European central bankers are complete fools. His big fear over the past few years has been inflation, a fear which has proven to be unfounded. Had the smaller, poorer countries been able to devalue, then Germany would be doing comparatively worse. But Germany isn't doing well, even though their currency has been much cheaper (thanks to being pegged to troubled countries), which isn't what we'd expect according to the Euro-was-a-bad-idea-and-is-at-the-heart-of-it mess...
The Euro might have been misguided, but the real idiots are Europe's monetary authorities...
Contrast this with Japan. Japan is also not doing well. Hasn't done well for nearly a generation. Should we therefore conclude that Shikoku and Tohoku, heck, the entire Inaka secede from the Yen? Actually, might not be a bad idea... But yet, that the Kanto and Kansai regions, and Japan's economy over all, have not done well imply that a good bit of the blame lies with Japan's foolishly conservative central bank, not the monetary policy decision of Chiba.
Links for 04-26-17
55 minutes ago