I’ve been weighing up a very elegant treatment for the banking crisis that has been buzzing around the economics blogs – so elegant, in fact, that it took me several days to convince myself that it wasn’t just a logical sleight of hand, the kind of subtle fallacy that mathematicians use to “demonstrate” that 1+1=1.

One way to understand the banking crisis is that the banks cannot raise new money and lend it to people who could use it. This is not because there is no money, or no deserving investment projects. It is because the banks, whose assets are worth less than they hoped, are now weighed down by their existing promises to repay depositors and other creditors. They cannot raise fresh money because nobody wants to lend money to a near-bankrupt bank.

So far, governments have been trying to raise or at least stabilise the value of bank assets, but an alternative is to reduce the burden of their liabilities.

The elegant approach I’ve been examining has been developed by long-time collaborators Jeremy Bulow and Paul Klemperer. They suggest splitting crippled banks such as Citigroup or RBS into a good “bridge” bank and a bad “rump” bank. The bridge bank gets all the assets, even the so-called “toxic” assets. These are not truly toxic, simply worth less than everyone hoped. The bridge bank also inherits sacred liabilities such as deposits. The rump bank gets no assets, only the debts the old bank used to owe to creditors.

With a leap and a bound, the bridge bank is well-capitalised and capable of raising new funds to lend out to good projects. Depositors feel secure and the economy acquires a functioning bank. The rump bank, of course, is a basket case, so one might think that the shareholders and creditors in the rump bank have suffered expropriation. They have not: Bulow and Klemperer propose giving all the equity in the bridge bank to the rump bank – this is full and fair compensation. The rump bank may well go bankrupt and the creditors will have to see what they can salvage – which will include shares in the bridge bank. But the bankruptcy process will not damage the bridge bank, nor prevent it from raising new money and making fresh loans.

The plan may not work, for a number of reasons. The most serious objection is that everything is now systemic, and that allowing creditors to lose a percentage of their claims – despite the fact that they lent money to the banks without any government guarantee – may cause further bankruptcies. Even so, the Bulow-Klemperer plan allows the government to pour further money into the banks in a more transparent way: to the bridge bank if the concern is to ensure well-capitalised banks; to the rump bank’s creditors if the concern is to prevent a chain reaction of bankruptcies. Transparency, of course, may be the last thing governments want, given the possible sums involved.

If you are still blinking at the idea that one can produce a healthy bridge bank like a rabbit from a troubled-bank top hat, without injecting new funds and without resorting to expropriation, you should be. But it is true. The confusing thing about the financial crisis is that the physical economy is in the same shape as ever, but it can be paralysed if investment money cannot flow from those who have it to those who can use it. A tangle of – unpayable? – claims against the banks is, like some modern-day Jarndyce and Jarndyce case, stemming that flow. Bulow and Klemperer try to set the tangle to one side to be resolved while the banks continue their business. Put like that, the idea does not seem like such a conjuring trick.

Tim Harford’s ‘The Logic of Life’ is out now in paperback

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