Granted, Ireland also received fiscal aid. But that came much later, toward the end of 2010, and when it came, the internal devaluation stopped almost immediately. Twelve of the 13 percentage points of the Irish decline in relative product prices came before that date. Of the eurozone countries hardest hit by the financial crisis, Ireland will be the only one this year to see its G.D.P. surpass its precrisis level.

Greece’s devaluation started five years after Ireland’s, and by now has reached 9 percent. Analysis by Goldman Sachs researchers suggests that product prices would have to decline by another 13 to 22 percentage points for Greece to be competitive. (Wages in neighboring Turkey, Bulgaria and Romania, the latter two being European Union members, are only one-third to one-fifth Greece’s level.)

The better alternative is a Grexit accompanied by debt relief, humanitarian aid for the purchase of essential imports and an option for eventual return to the euro. Greece could reintroduce the drachma as the only legal tender. All existing prices, wages, contracts and balance sheets, including internal and external debt, could be converted one-to-one into drachmas, which would immediately decline in value.

The devaluation would induce Greeks to buy domestic rather than imported products. Tourism would get a boost, and capital flight would be reversed. Rich Greeks would return with their money, buy real estate and renovate it, fueling a construction boom. As the trade deficit gradually turned into a surplus, creditors would get some of their money back.

Greece would have the option to return to the eurozone, at a new exchange rate, after carrying out institutional reforms — such as public recording of land purchases, functioning tax collection, accurate statistical reporting — and meeting the normal conditions for eurozone membership. It could take five or 10 years.

It is true that Grexit would make it clear that membership in the eurozone is not irrevocable and could expose member countries to speculative attacks. But this is not very likely, as the markets’ calm reaction to Greece’s capital controls and the “no” vote in the referendum showed. More important, it would lead other countries to adopt more prudent financing and steer clear of the debt trap that caused the bubble in the first place.

Until Europe is turned into a federal state — as it should become, at some point — it will not have a currency like the dollar. Until then, what is needed is a “breathing” currency union, with orderly entry and exit options, coupled with an insolvency rule for member states. This would be a better compromise between the goals of avoiding speculative attacks and excessive debt accumulation than the current promise of eternal membership.