The 17 members of the Eurozone share a common currency.  This is a problem, however, because their economies are fundamentally different.

If two fundamentally different economies share a currency, the uncompetitive economy will likely run up huge debts against the competitive economy.

This imbalance is unsustainable; the competitive lending economy cannot indefinitely lend to the uncompetitive borrowing economy.

This is the case of core Eurozone members like Germany (the lenders) and peripheral Eurozone members like Greece (the debtors).

The chart below from PIMCO shows the net international investment position of Eurozone members (as of September 2011).  A positive figure means a member is a lender to the rest of the world.  A negative figures means a member is a borrower to the rest of the world.

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The borrowing members have seen their international debt levels grow to about 80 percent of their GDP while the surplus members have seen their international financial claims grow to about 40 percent of their GDP.

These figures are astounding.

From 2000 to 2007, both sides of the Eurozone and the rest of the world were willing to play the imbalances lending game. 

Since the global financial crisis, however, the lenders are no longer willing. 

If the debtor countries had their own currencies, all they have to do in response is dramatically devalue their currencies, which would reduce their purchasing power and lower their cost to the rest of the world.

What usually results is an economic boom fueled by surging exports.   Their debt to the rest of the world would also be paid down because they would be less able to buy foreign goods/services and more able to export domestic goods/services.

However, because the Eurozone shares the same currency, countries like Greece are stuck with unrealistically high wages.  Their economies are therefore suffering from a double whammy of low exports and waning domestic consumption (from austerity measures), which causes high unemployment and slow economic growth.

Economic growth (i.e. growing income), of course, is the key to paying down debts.

Theoretically, wages could adjust to market equilibrium over time and achieve the same effect as currency devaluation.  (In countries like Greece, it is already happening through compensation cuts to public sector employees.)

Realistically, however, wages are sticky and do not adjust fast and far enough to prevent countries like Greece from taking a serious look at the alternative of adopting a newer (and devalued) currency.