Greece's public debt crisis makes daily headlines. The government led by George Papandreou and the country are engulfed by political uncertainty that threatens the acceptance of the rescue package being offered by the EU.

This is the worst crisis ever to have hit the eurozone. We could be at the beginning of an upheaval leading to an exit from the euro of first Greece and then Portugal and Ireland, the three countries most hit by public debt problems. If that happens, the continued eurozone membership of Spain and Italy will be in doubt.

Alternatively, the crisis could lead to recognition by the core eurozone countries that keeping the peripheral countries on board will require much larger transfers of taxpayers' money than have so far been contemplated.

In short, the eurozone is bound to change, but nobody can forecast in what direction.

In recent weeks, all the attention has focused on the public debt crisis, to the exclusion of the ultimately much more important competitiveness crisis. This arose because the eurozone founders imposed a common currency on countries with very different historic inflation rates. They hoped it would, by itself, force convergence of economic behaviour and, in particular, of inflation rates.

Those hopes have not been fulfilled. Since joining the eurozone, Greek inflation has outpaced German, causing a 28 per cent loss of competitiveness. The recession has reduced the balance of payment deficit, which was nearly 15 per cent of GDP, because recessions always reduce imports. But there remains a large structural deficit of more than 10 per cent of GDP.

One way for Greece to solve its problems would be to engineer a major devaluation, making its exports competitive again. The ensuing export-led growth would generate the tax revenues it needs to resolve its public debt crisis. Indeed, the only long-term solution to Greece's debts is to cure its competitiveness problem. All the much-discussed rescue packages are only sticking plaster on this festering wound. This solution is ruled out by Greek membership of the eurozone.

The only alternative is for Greek inflation to fall, say, to 3 per cent below German inflation and remain below it for 10 years. If you think that sounds implausible, you are right. Though theoretically possible, it would entail an unparalleled period of hardship for the Greek population. Austerity programmes imposed from abroad are always hugely unpopular politically, as the history of Latin America shows. Sooner or later, there will be a popular revolt, either at the polls or, worse, on the streets. Remember, Greece was ruled by a military junta as recently as 1974.

So, of these two ways of restoring competitiveness, a Greek exit from the eurozone may come to seem the less unlikely, and reputable commentators are now discussing it as a possibility. But if we start to think through how Greece might actually leave the euro, it quickly becomes apparent how huge the difficulties are.

Suppose its government decrees one day that euro deposits in banks on Greek soil be exchanged for new drachma at a conversion rate that restores competitiveness – a devaluation of at least 28 per cent, plus, if they are wise, a substantial safety margin. This would imply that deposits in Greek banks lose 30 to 40 per cent of their value overnight. But this will be known in advance, not least because the government will have had to print and distribute the new drachma, something difficult to achieve with the swiftness and secrecy of an old-fashioned devaluation. So all sensible Greeks, wishing to preserve the value of their bank deposits, will seek to forestall that loss. They will do so either by withdrawing their cash, in euros, as soon as they can, or by asking their bank to transfer their funds to another European branch located in, say, Germany. So, an expected exit from the euro is likely to cause both a run on Greek banks and a flight of capital.

Capital flight can be prevented by imposing exchange controls. But these run sharply counter to EU law, which upholds free movement of goods, labour and capital. And there will surely be Greek citizens, angry at the sharp capital loss imposed on them by their government, who challenge the replacement of euro by new drachma in the European Court of Justice. After all, they put euros into their Greek bank. Are they not entitled, under European law, to get euros out?

It is hard, given these facts, to see how Greece can leave the eurozone without leaving the EU itself. On balance, it seems more likely that the Greeks will ultimately accept the austerity regime as the necessary price for staying in the EU, and the German and French governments will accept a long period of fiscal transfers as the necessary price for preserving the eurozone.

That outcome would not address the problem of Greek competitiveness. It implies that Greece becomes a permanently impoverished region of Europe, unable to earn its way and dependent on regional subsidies. That may not seem a beguiling prospect, but that is what happens in large currency unions. Wales and Scotland might be more prosperous if they could devalue the Scottish or Welsh pounds. Naples is still suffering from joining a currency union with Milan when Italy was unified in the 19th century.

As for Portugal and Ireland, their public debt problem (a debt to GDP ratio of around three-quarters) is much more manageable than in Greece (where debt is nearly 1.5 times GDP). The Irish have made astonishingly rapid progress in reducing their public sector deficit. These are small countries and the necessary transfers are affordable. The Portuguese and the Irish are strongly committed to the EU as a counterweight to their large neighbours, Spain and England. They will probably remain in the eurozone even if Greece departs.

Spain and Italy are different. Over the past year the public debt crisis has caused the yield on Greek debt to increase by 53 percentage points and on Portuguese debt by 17 percentage points. This is a crisis of a very different order of magnitude from Italy, where the increase has been 3.5 percentage points, or Spain (2.2 percentage points). Italy and Spain do not have a balance of payments problem, or a competitiveness problem, on the same scale as Greece. The crisis may bring down the Berlusconi government but Italy or Spain will not leave the euro.

Bill Robinson, a former special adviser to the Treasury, is head of economics advisory at KPMG