It has become the new paradox of European economic policy: There is no saving the euro without saving Italy, and there is no saving Italy without saving the euro.

Which perhaps explains why Mario Monti, Italy’s new, “non-political” prime minister, hosted the leaders of France, Germany and Spain in Rome on Friday as part of his increasingly desperate effort to force a resolution to a euro crisis that is dragging Italy, Europe and possibly the global economy back into recession.

If you have been following this long-running financial soap opera, you know there are those who argue, with good reason, that because it was a monetary union without a real fiscal and economic union, the euro zone was always doomed.

The counter-argument is that even the United States didn’t emerge fully formed as an economic and political unit with the ratification of the constitution — that it took time to evolve, often in response to difficult crises just like the one Europe is going through now. Those in this camp — and I count myself among them — are not so foolish as to believe that a success is inevitable, and neither is failure.

It should be no surprise that Monti has emerged as a key figure in this process. It is not simply that Italy’s huge debt load (120 percent of gross domestic product) makes it exquisitely sensitive to a crisis whose severity has come to be measured in interest rate spreads on sovereign bonds. He’s also a Yale-trained economist, the former rector of Italy’s leading economics and business university who spent a decade pushing European economic integration as the European Union’s top antitrust official in Brussels.

Now, he’s technocratic turnaround artist brought in to clean up after the clownish former leader Silvio Berlusconi, and free to do what he thinks best for Italy without any concerns about winning the next election. It also helps that he has the respectful ear of President Obama.

Most significantly, Monti is well-positioned to act as the honest broker between France’s new socialist president, Francois Hollande, who wants to shift the focus of European policy to pro-growth fiscal and monetary stimulus, and German Chancellor Angela Merkel, a stubborn champion of hard money, tight budgets and market-friendly structural reforms. As the leader of an economy shrinking at the annual rate of 2 percent or more, Monti is determined to put growth back at the top of the European policy agenda. At the same time, his tough moves to raise taxes, cut spending and reform Italy’s notoriously uncompetitive labor and product markets have won him credibility with Merkel and investors.

In truth, there is no simple Keynesian solution by which the euro zone could borrow-and-spend its way back to growth. With the notable exceptions of Germany and a few of its smaller, northern neighbors, borrowing costs for most of the continent are simply too high, and if those two countries were to try to stimulate with tax cuts or increased government spending, the spillover effects on the rest of Europe would be modest at best.

What would work would be if Europe as a whole could borrow money not to spend it for the sake of spending, or on unsustainable welfare payments, but to invest it in genuinely Europe-wide energy, transportation, education and environmental projects that would enhance the efficiency and productivity of the region’s economy over the long run. Money from such euro bonds could also be borrowed, as well as raised from private investors, to expand the existing European Investment Fund, which makes investments in the innovative small and medium-size firms that account for much of the job growth in Europe and which have been starved for capital as a result of the ongoing financial and banking crisis.

On Friday, Monti and his three colleagues talked about committing 1 percent of Europe’s GDP to this purpose — about $175 billion. At a time when governments are cutting several times that much from their operating budgets, and private capital is constrained, surely that’s at the very low end of the range they should be considering.

At this point, however, the bigger impediment to European growth is not the insufficient level of government spending and investment. It is the insufficient level of private spending and investment due to the loss in confidence caused by the twin banking and government debt crises. The two crises, in effect, are now one and the same. Troubled governments are borrowing to bail out banking systems while their banks are trying to help their governments by loading up on government bonds — a process likened by Martin Wolf of the Financial Times to two drunks remaining upright by leaning on each other.

Two things should be obvious. The first is that European governments cannot, and should not, be called upon to bail out shareholders and creditors of banks that have made bad loans or taken bad risks. The other is that European banks cannot, and should not, be called upon to use their depositors’ money to bail out governments that can’t control their spending. Each bank and each country has to be allowed to stand and fall on its own, subject to its own market discipline and pricing of risk. The only ones who should be protected are retail bank depositors, through properly priced deposit insurance.

Everyone pretty much agrees on that — the problem is getting from here to there. And, once again, the answer is for European countries to borrow money collectively — that’s those euro-zone bonds again — to recapitalize the European banking system. This investment will largely pay for itself in terms of restoring investor confidence, restoring consumer confidence and putting the European economy back on a growth path. The best recent evidence we have of that comes from the much-maligned Troubled Assets Relief Program in the United States, which did just that and wound up costing taxpayers almost nothing.

Why should German and French taxpayers put themselves on the hook to recapitalize banks in Spain and Italy?

For starters, it may turn out that some of those weak banks might not only be in Spain and Italy, but in Germany and France, where there is a long history of bankers and regulators conspiring to hide problems. The important intellectual hurdle for Europeans to get over is that these are not French or Spanish or Italian banks — they are European banks that have on their books large amounts of bonds from multiple European countries. It’s also important to understand that the recapitalization of these banks would be done in the context of creating a Europe-wide bank regulation and deposit-insurance program that would create a stronger and more efficient European banking system.

Moreover, in most cases this need not be about “bailing out” banks, in the way most people understand that term. It should be about buying them, the way JPMorgan Chase bought Washington Mutual and Wells Fargo bought Wachovia. Yes, a bit of borrowed euro-zone money might be necessary to grease the deals if the banks turn out to be insolvent. But the amounts are likely to be modest and, as the United States proved, can be recovered once the economy has rebounded through minority stakes in the combined entities. To reduce the political fallout, shareholders and creditors in the weak banks could be forced to take haircuts and bank executives could be sent packing.

Solving the banking crisis, I suspect, would go a long way toward solving the sovereign debt crisis in most countries. But in the short term, it may also be necessary for Europe to prop up the bonds of countries that, like Italy, have demonstrated that they have done what is necessary to put their fiscal house in order. That’s why Monti is pushing to authorize the new European Stabilization Fund to act as the “sovereign buyer of last resort” when financial contagion strikes.

Once again, however, the key point is that the Fund should be financed not by separate borrowings by the Spanish government, and the Italian government, and the Portuguese government, all which have to pay rates of 6 percent or more. Instead, it should be financed at half the cost by the E.U. as a whole, which would be able to borrow at rates closer to the German rates of less than 2 percent. To do otherwise is to simply double or triple the cost to preserve a political figleaf.

And who is standing in the way of Monti’s plan for using European bonds for genuinely European purposes? Germany’s Merkel, who as one official put it to me this week, seems to believe that economics is a branch of moral philosophy. Her attitude is rather ironic coming from a former resident of East Germany, which was literally pulled up to Western living standards by the taxpayers of West Germany after the fall of the Berlin Wall. And it is stranger still coming from the leader of a country that, just 75 years earlier, was rebuilt from the rubble of war with investment funding from the United States.

In private meetings, Merkel claims that German voters will simply not accept anything that smacks of subsidizing lazy and profligate southern neighbors. But what is also very clear is that the German chancellor and her colleagues have done nothing — and I mean nothing at all — to educate Germans that their own economic success over the past 20 years has been due not just to their hard work and efficiency, but also to the fact that their largest trading partners were allowed and encouraged to live beyond their means. Nor have they explained that, at this point, the cost to Germans of fixing the problem will be less than the cost of letting the recession and the market contagion spread.

Merkel has made her point: European assistance must be offered only to countries such as Italy, Ireland and Spain, which have genuinely committed themselves to changing their ways and getting their economic acts together. But at this point, by preventing reasonable collective action to end the euro crisis, Merkel is on the verge of proving the Euro-sceptics right. What she demands is that everyone else in Europe start to think and act like Europeans while Germans continue to think and act like Germans.