First, a structured default on the Greek debt, giving creditors a major haircut, but compensating them with eurobonds of half the face value of the Greek bonds, guaranteed by the European Central Bank.
Second, a huge new European Financial Stabilization Facility of trillions of euros to recapitalize stricken banks and buy up the sovereign debt of Portugal, Italy, Ireland and Spain, should private investors flee their bonds.
Such a solution, however, depends upon Germany, the richest nation in Europe and major contributor to the ECB.
Hard-money Germans, however, do not relish bailing out the deadbeat nations of Club Med who have more generous welfare states than their own.
Politically, it may not be possible to cajole or coerce the Germans, indefinitely, into saving the eurozone, the collapse of which could bring on a depression and bring down the European Union itself.
There is another reason the European Monetary Union and EU may be headed for the boneyard: demography.
Looking over the 2008 World Population Prospects from the United Nations' Department of Economic and Social Affairs, one finds that the nation which is to carry Europe back to solvency is aging, shrinking and dying.
Every decade of this century, Germany will become less able to sustain its dynamism, let alone carry the continent.
Consider. In 2010, there were 82 million Germans. Fully 26 percent were 60 years of age or older; 20 percent were 65 or older; 5 percent were 80 or older.
Now, fast forward to 2050.
Between 2010 and mid-century, 12 million Germans will disappear. In 2050, Germany will be a nation of 70 million, whose median age will have risen from 44 today to 51. And the life expectancy of all Germans will rise from today's 80 years to 84.
The average German may enjoy four more years of life, but he or she will also require four more years of social security and health care provided by the taxpaying public. And that taxpaying public is also going to shrink.
By 2050, the percentage of Germans over 60 will have risen from 26 to nearly 40 percent. The percentage 65 and over will have risen from 20.5 to 32.5 percent, and the share over 80 will have tripled from the present 5 percent of the population to 14 percent.
By 2050, one in three Germans will be 65 or over, and one in seven will be 80 or over. That is a lot of old-timers for working Germans, whose numbers and share of the population will have been dramatically reduced, to support.
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