Those current account imbalances are the result of imposing a single currency on 17 eurozone countries. If their exchange rates were free to vary, normal market pressures would cause the currencies of Italy, Spain and France to decline relative to Germany’s, stimulating exports and reducing their imports while also shrinking Germany’s trade surplus.

The politicians who planned the euro generally did not think about future current account imbalances or other economic problems. They wanted the euro as a means of accelerating political integration.

Although the exchange rates at which countries entered the eurozone were negotiated to avoid initial trade imbalances, different future rates of wage increase would inevitably lead to trade imbalances. Those politicians and bureaucrats who recognised this problem believed that the single currency would somehow eliminate it by causing productivity trends to converge.

But convergence clearly has not happened. Productivity in Germany rose much faster than it did in Italy, Spain and France. Germany also placed limits on wage growth. Those two factors mean that labour costs in Germany’s tradable sector have risen some 30 per cent less since the start of the euro than labour costs and prices in those countries with slower productivity growth. The result is that Germany has a current account surplus of 5 per cent of gross domestic product while Italy, Spain and France each have current account deficits of about 3.5 per cent of GDP.

Some economists and officials in countries with trade deficits argue that Germany should expand to increase demand for their products and allow a faster rise in wages to reduce its trade advantage. Not surprisingly, Germany rejects these suggestions.

German officials and the European Central Bank argue that the trade deficit countries need an “internal devaluation” – ie, cutting wages and prices to make their products competitive. Estimates differ but many suggest this would require a 30 per cent wage cut followed by permanently slower wage growth than in Germany. This would mean a decade or more of high unemployment and declining GDP – an economically wasteful and politically dangerous strategy.

An alternative proposal might be to reduce consumer spending in countries with trade deficits, since each nation’s current account balance is the difference between its national saving and investment. But reduced consumer spending would just cause GDP to decline unless there was also a fall in the exchange rate to stimulate net exports – something precluded within the eurozone.

So this brings me to the action that can shrink the current account deficits of Italy, Spain and France without austerity, internal devaluations, or German expansionary policies. The solution is a lower value of the euro leading to an improved trade balance with countries outside the eurozone.

The overall trade-weighted value of the euro has already declined 12 per cent since the beginning of 2010. Although fundamental factors imply that the euro should eventually appreciate relative to the dollar(primarily because of overweight dollar positions of most sovereign wealth funds and large US current account deficit), concerns about the euro and the European economy more generally have caused the currency to decline relative to the dollar by 10 per cent in the past six months.

Further declines of the euro’s trade-weighted value would cause the exports of all eurozone countries to rise and the imports from outside the region to decline. More specifically, the lower value of the euro would help Italy, Spain and France because about 50 per cent of their imports and exports are with countries outside the eurozone. Germany’s export surplus would rise, giving Germany the opportunity to increase financial or real foreign investment or to increase domestic consumption.

It is not clear how much further the euro would have to fall to eliminate existing current account deficits, but it might take a trade-weighted decline of 20 per cent or more. That could imply a euro-dollar exchange rate below its initial value of $1.18 per euro.

What might cause such a substantial decline of the euro? The recent momentum alone might cause that to happen. So also could the ECB’s increased supply of euros to deal with credit and banking problems. Even statements by Mario Draghi, ECB president, expressing a lack of concern about the declining euro might cause the financial market to drive the currency lower.

A decline of the euro cannot be a permanent solution to differences in productivity trends within the eurozone. But it would give those countries time to improve productivity growth before the euro’s fundamental strength returned. If those relative improvements in productivity do not happen, there may be no choice but to end the eurozone as we know it today.

The writer is professor of economics at Harvard University and former chairman of the Council of Economic Advisers and President Ronald Reagan's chief economic adviser.