Rome is home to the three sprawling United Nations agencies that deal with the world’s food problems and, at a time of rising prices, it was a natural choice to host a summit on the threat of hunger and starvation, if incongruous that the city has also been synonymous for 2,000 years with eating well.

The present alarm about prices is largely the temporary result of several unfortunate coincidences. To that extent the summit will produce some good fixes. But it doesn’t look like touching the tangle of perversities that make up farming and trade policy. There is a genuine problem in working out which trade rules would help the poorest countries but, even so, some reforms that should be made now will be ignored.

In Rome this week all the numbers are huge and the warnings are bleak. Robert Zoellick, the President of the World Bank, has said that soaring food prices threaten 100 million with hunger and 30 countries with social unrest. Ban Ki Moon, the UN Secretary-General, called for world farm production to rise by 50 per cent by 2030 to meet demand.

Some of this reflects one-off problems. Biofuels have played a part in siphoning off grain otherwise used for food, although they have got too much attention; Zoellick rightly called for the issue not to dominate the summit. So have storms. So have rigidities in World Trade Organisation rules (for example, preventing Japan from reexporting extra rice without permission from the original producer). So have fuel costs, which have passed through to food prices.

Population growth plays a part but Malthusian fears that the planet cannot feed 6.7 billion people look misplaced. It can, and could, feed more; this year’s problem is that the food is in the wrong place and costs too much. The technology that would boost yields further is there already, such as genetically modified crops. One hope is that this crisis prompts European countries to be less precious about these inventions.

Some suggestions are outright disastrous. One is the spontaneous chorus in Rome – from assorted rich and poor countries - calling for national self-sufficiency in the name of “food security”. They would do better to look at the trade barriers that make supply of food so lumpy, costly and sometimes unpredictable. They might start with the Doha trade round, struggling to survive after seven years of talks, which was billed as the “development round” of trade liberalisation because it put so much weight on agriculture and helping poorer countries.

Yet Doha has become so mangled in the process that it is hard to say blithely that its passage would be good for all poor countries. Indeed, the World Bank has produced recent studies showing that it is facile to assert that all freeing up of farm trade helps poor countries (although, on balance, its conclusion is that it does). But two recent moves are outright harmful: the groteque new Farm Bill that the US is about to pass, subsidising the mere two million people who still run farms in the US, and the EU’s recent decision to tinker with its own absurd system of farm support but not really to change it.

The billions of dollars in aid that the chieftains in Rome have demanded are a good quick fix for a problem whose worst aspects are temporary but they offer no solution at all to its other causes.

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