FOR all you know, Angela Merkel is even now contemplating how to break up the euro. Surely Germany’s long-suffering chancellor must be tempted, given the endless euro-bickering over rescues that later turn out to be inadequate. How she must tire of fighting her country’s corner, only to be branded weak by critics at home. How she must resent sacrificing German wealth, only to be portrayed as a Nazi in some of the very countries she is trying to rescue.

But for this very practical woman there is also a practical reason to start contingency planning for a break-up: it is looking ever more likely. Greece is buckling (see article). Much of southern Europe is also in pain, while the northern creditor countries are becoming ever less forgiving: in a recent poll a narrow majority of Germans favoured bringing back the Deutschmark. A chaotic disintegration would be a calamity. Even as Mrs Merkel struggles to find a solution, her aides are surely also sensibly drawing up a plan to prepare for the worst.

This week our briefing imagines what such a “Merkel memorandum” might say (see article). It takes a German point of view, but its logic would apply to the other creditor countries. Its conclusions are stark—not least in terms of which euro member it makes sense to keep or drop. But the main message is one of urgency. For the moment, breaking up the euro would be more expensive than trying to hold it together. But if Europe just keeps on arguing, that calculation will change.

Grexit, pursued by a bear

Begin with Greece. There is a common fallacy, not least in Germany, that dropping the Greeks would be a fairly costless way to teach a useful lesson. In fact the European Central Bank (ECB) owns Greek bonds with a face value of €40 billion ($50 billion), which would be converted into devalued drachma and which Greece might not service. A further €130 billion or so of loans that Greece has received in the bail-out would have to be written down, or written off. The €100 billion of the temporary debts Greece has stacked up in the ECB’s payments system would crystallise into a loss. Add in a one-off grant of say €50 billion to tide Greece over—call it conscience-salving “solidarity”—and the bill might come to €320 billion. Estimating the price of a “Grexit” is guesswork, but Germany’s share might reach €110 billion of this, about 4% of the country’s GDP.

At first sight that is a bargain, because it would save German taxpayers from an open-ended commitment to Greece. And yet proof of the euro’s reversibility will throw markets into a panic. Ireland, Portugal, Cyprus and Spain also all owe investors abroad a net sum of 80-100% of GDP (the gross debt is much larger). One reason why these foreigners have hung on is the belief that the euro cannot break up. Greece’s defenestration would turn that calculation on its head, triggering soaring bond yields in southern Europe. Stampeding domestic savers would cause runs on banks. With the single market in peril and depression looming, Mrs Merkel would come under huge pressure to pay whatever it takes to save the rest of the euro zone. She would have no time to negotiate the pan-European federal discipline that she has always demanded as the price for German aid. A rescue would be a blank cheque.

A bolder Plan B would amputate well above the site of infection, cutting off Spain, Ireland, Portugal and Cyprus too. Italy, which has net foreign debt of just 21% of GDP, would probably escape the chop: even with its heavy debts and chronic lack of competitiveness, Mrs Merkel would reckon that the euro zone could not function politically without it. The cost of a bolder Plan B would be high. When you add up the ECB’s holdings of their bonds, the temporary debts in its payments system, written-off rescue loans, and a care package to soften the blow of being chucked out, the total for Spain, Ireland, Portugal, Cyprus and Greece comes to perhaps €1.15 trillion. Germany would also have to put money into its own banks, hit by losses in the five departing countries. Altogether, this might cost Germany getting on for €500 billion, or 20% of GDP. But the blank cheque to defend the other four weaklings after a chaotic Grexit might exceed that; and the broader break-up would establish a more co-ordinated, defensible euro zone.

I’m a chancellor, get me out of here

If neither break-up looks attractive, is there a better way? This newspaper has argued that the euro zone’s members should use their combined strength to create a banking union and to mutualise a chunk of the outstanding debt (as well as introduce policies to temper austerity and promote growth).

This more federal Europe would also involve costs. Recapitalising banks and financing a euro-wide deposit-guarantee scheme might cost €300 billion-400 billion, perhaps a third of it paid for by Germany. But this would be a one-off and might be reclaimed from the banks. Mutualising a slug of debt would lift Germany’s interest costs by €15 billion or so a year. The numbers are rough, but, even allowing for some extra loans to the south, rescue would be cheaper than break-up. And that is before you factor in the enormous political costs of disintegration, with, say, Greece departing into a new Balkan hell.

Our solution, then, is broadly the same as Mrs Merkel’s appears to be. But a prescription is useless if it is never applied—and our doubts that this one ever will be are increasing.

The euro could have been saved a long time ago, had the politicians agreed on who should pay what or on how much sovereignty to surrender. Rather than push forward, Mrs Merkel has waited, hoping that fiscal adjustment and structural reform will lead to economic growth in southern Europe and that the politicians could sort out their differences. The ECB has once again bought her a bit more time (see article).

The evidence, though, is that time is not on her side. Southern Europe’s economic rot is deepening and spreading north. Politics is turning rancid as the south succumbs to austerity fatigue and the north to rescue fatigue (see article). Populism only makes a grand bargain more elusive. For the moment, breaking up the euro would be riskier than fixing it. But unless Mrs Merkel presses ahead, the choice will be between an expensive break-up sooner and a really ruinous one later.