Q: Have BREXIT and Trump increased the probability of a breakup of the eurozone?
That Britain voted for BREXIT, even under the false pretense of an extra 350 million pounds a week for the health service, is a strong indication that the tide of globalization and integration is not irresistible. That Americans... well, Americans did not vote for Trump--they voted for Clinton. That the quirks of the electoral college have made Trump president-elect is a strong indication that the tide of globalization and integration is not irresistible.
Ambitious politicians can now see that mobilizing aggressively "we need to go it more alone" sentiment is a potential road to power. That was not clear before BREXIT. That was not clear before Trump.
Now it is.
In every country there are politicians with few principles seeking a road to office. And if they see a plausible road, they will follow it.
For example, consider Boris Johnson: I certainly do not believe that Boris Johnson wanted BREXIT. I believe he wanted to campaign for BREXIT, lose, and then use that loss to advance himself within the Conservative Party as the advocate of Englanders rather than of the City and the global system.
There will be politicians like Boris in every country looking forward. There are bunches of countries. Some will call for exit from the euro.
This door was not known to be unlocked and open before. Now it is. And so some people will try to walk through it.