Eurozone membership is a privilege for EU member states, not a right.
Actually, membership in the Eurozone is not a privilege, it is mandatory.
EU member states are obliged to join once the convergence criteria are met and there are no legal provisions that make leaving the Eurozone possible. Unless you have an opt-out like United Kingdom or Denmark.
That's also the reason why it will be interesting to see how the EU is going to organize a Grexit without breaking any treaties and without Greece seeking legal action against a Grexit before the European Court of Justice.
Exactly, Greece is staying in the Euro indefinitely because of Game Theory
Greece's existing treaties prohibit leaving the Euro, and any new agreement that supersedes that prohibition has to be ratified by Greece to come into effect. Because of that, Greece doesn't quit the Euro in any situation where they just keep using it (of course this might be difficult in practice)
Using the euro will become virtually impossible if the ECB completely turns off the tap. So w/o an agreement on sunday Greece will eventually have to issue its own currency regardless of what the treaties say.
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