Gordon Brown has saved the world yet again. Until the Prime Minister arrived in Davos, the businessmen, political leaders and central bankers at the World Economic Forum reminded me of prisoners on death row, wandering aimlessly around an airless indoor exercise yard while awaiting news about their final appeal.

For once, even the professional economists were unanimous: every economist who spoke officially on the Davos panels began with the axiom that “we are all doomed”. The dominant view was that the slump would last for at least a decade and bankrupt every major financial entity and government around the world. This was the firm prediction of Nouriel Roubini, the economics prophet whose apocalyptic visions raised him to the status of Davos Oracle this year.

While such strong intellectual leadership can be important in a crisis, it can also produce disaster — just ask a lemming. And the more I listened to the one-sided “debates” at Davos — with business leaders unanimously recommending cutbacks in public spending and predicting doom for every business but their own — the more this lemming analogy came to mind. Indeed, I had resolved to leave the business “leaders” to their dreams of lemming-heaven and head off to the ski slopes, when the atmosphere was suddenly transformed. Flash Gordon swirled into Davos.

In a panel discussion of less than an hour, Mr Brown did something that had seemed impossible only minutes before — he offered a way out of the crisis. While the oracles and lemming-leaders were unimpressed by Mr Brown's message, the lemming-followers had adulation written on their faces as they filed out of the Congress Hall.

How did he do it? First, Mr Brown explained that recessions were a natural feature of capitalism and that they rarely lasted for more than a year or two. But surely this recession felt different? Yes, but mainly because this one was “the first crisis of the global age”. As a result, global solutions were required. He added that a certain British economist had explained why such recessions happened and how they could be overcome. His name was John Maynard Keynes, and the Prime Minister described poignantly how he had seen a document in the Treasury archives in which the young Keynes's proposals for saving Britain from the Great Depression were dismissed by the Chancellor in only three scribbled words: “inflation, extravagance, bankruptcy”. Finally, Mr Brown moved on to a three-stage response from governments around the world. The first stage was to stabilise the financial system and prevent bank failures. After Henry Paulson's catastrophic blunder in bankrupting Lehman, this had been achieved. The second stage, now in progress, is to counteract the collapse of private economic activity triggered by the near-failure of every bank in the world with huge doses of monetary and fiscal stimulus. The third stage will be to restore the growth of credit by forcing banks to increase their lending.

This may be technically the most complex part of the recovery plan, but it should be the least politically problematic and expensive. The question is whether Mr Brown and other genuine world leaders have understood that a comprehensive plan for credit recovery should be far less expensive to implement than the tens of trillions of dollars divined by Dr Roubini.

While I cannot vie with the Davos Oracle for the clarity of my crystal ball or the tastiness of my chicken entrails, I can draw attention to five statistical facts that will govern the cost of the recovery process — and wonder why these indisputable facts are largely overlooked. The first is that public money invested in supporting credit growth costs taxpayers nothing. Taxpayers pay only if borrowers default on their loans. This means that guarantees on capital injections designed to revive bank lending do not add trillions to national debt burdens — only the likely losses on these investments should count.

The second fact is that these probable credit losses bear no relation to the current market prices of mortgages and other assets. Market prices are governed primarily by the liquidity of these assets, not by their default risk. The “mark-to-market accounting” that assumes that market prices automatically reflect true economic values has been discredited by the illusory profits it created in the credit boom — and should be ignored in valuing bank assets for the new guarantee schemes that governments are rolling out. These schemes should instead use what Ben Bernanke has described as the “hold to maturity” valuations of assets, which use transparent and reasonable economic assumptions about house prices, inflation and so on to assess the long-term probabilities of default.

The third simple fact is that banks can increase their lending to non-financial companies and households even if their capital continues to decline. This is because, as I explained in last week's column, 70 per cent of the growth in their lending has been to other financial institutions and this part of their balance sheet should now be aggressively reduced, leaving plenty of capital available for lending to non-financial borrowers.

My fourth observation is that even if additional bank capital must be injected, the pricing of this public support is unimportant, because the true returns to taxpayers will come not from capital gains in bank shares but from the vast additional revenues that will flow into Treasury coffers if economic activity can be revived.

Finally, suppose that, despite all these mitigating factors, significant public money does have to be permanently invested in banks. Much of this investment could — and should — be financed by printing money at no cost to taxpayers at all. To see what I mean, consider the two charts. They show a continuous reduction in the amount of cash and bank reserves circulating through the British and US economies, the so-called base money that is printed, essentially free of cost to taxpayers, by the central banks. This increase in velocity of circulation has been driven largely by the reckless growth of the financial sector. If more prudent liquidity management now results in a return of velocity of circulation to the levels in earlier decades, then central banks can and should print far more money to support economic growth — and the seigniorage profits from issuing this new money offers taxpayers huge gains.

Ultimately, of course, such a tightening of bank liquidity requirements would be equivalent to an indirect tax on bank profits, but that is an objection that somehow doesn't seem very potent today. At Davos last week I put this argument to three Nobel laureate economists who happened to be in a room at the same time. They looked at each other in bafflement and then responded in unison: “That's a good point.”

Why, then, I wondered, had no professional economist ever mentioned such an obvious idea? I may not like Gordon Brown much as Prime Minister, but I would gladly back him against any academic economist for the next Nobel Prize.

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