With its usual impeccable timing, the Government has launched a campaign to increase social mobility at exactly the moment the economy falls off a cliff.

One of the few reliable ways of enhancing the lives of the poorest is to run the economy as close to overheating as we dare - labour shortages encourage employers to improve the skills of their existing staff and to hire workers they would otherwise not want.

But even if conditions were more propitious, there¡¯s a huge intellectual hole in the middle of its project. Actually, there are several holes.

Let¡¯s start with the relationship between equality and mobility. The Government¡¯s wish that people can make their way from the poorest estates to top jobs presupposes an unequal society.

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But Whitehall thinks this is part of its equality agenda, fudging the fact that there are two very different social models that you might decently embrace, but which satisfy different aspirations.

The first really is egalitarian, with a ¡°flat¡± or ¡°lozenge¡± distribution of income, education, interesting jobs, and whatever else you have in mind as the crucial signifiers for a happy life.

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Given that, social mobility in the Government¡¯s sense - some people rising from the bottom to the top of an unequal society, with others heading the other way - would be uninteresting. Flexibility in the sense of everyone having a fair range of choice in occupation and lifestyle would matter, but ¡°up¡± and ¡°down¡± would not.

The merits of such a society are obvious. ¡°Fear of falling¡± would not be a powerful social sentiment; although one might want a larger house and sacrifice something for it, or a more interesting job and sacrifice something for that.

Even with a flat distribution of income and wealth, there would be hierarchies of esteem that would make some people feel they were special and others that they weren¡¯t. But there wouldn¡¯t be many and they wouldn¡¯t make much difference. It is, to all intents and purposes, what R.^^?H. Tawney defended in Equality (1931), his manifesto for a fraternal society.

It might not be a very innovative society. It would not be one where clever young men invented financial instruments that not only their bosses, but they themselves, only half understood. It is the polar opposite of what Gordon Brown and Alan Milburn have committed themselves to.

That is a society in which the gap between the worst-off and the best-off is as wide as the market dictates. It is an open society - the worst-off are not worst off because they are foreigners, or female, or religious outcasts. They are worst off because their services are not in demand.

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It is, as the Marxists used to say, ¡°formally¡± equal, inasmuch as nobody faces legal or political obstacles to getting ahead. Predictably, it is unequal, because in a free market, the quick, clever, imaginative and entrepreneurial rake in whatever anyone is willing to pay for their services. It is a casino or lottery in which we all get a ticket; at the end of the day some will have prizes and most will not.

Less predictably, although not unpredictably, the system doesn¡¯t do what its defenders say it will do over time. In the first generation, there may be a lot of social mobility; but in the second, assortative mating, the urge of parents to see that their children do well, and our tendency to cut corners, or information costs, by choosing the people we know from experience will do the job we want, mean that the children of the less advantaged are handicapped from the start.

Give it time, and the least advantaged will be ghettoised, but there will be gains. This society will be unfraternal, but fast-growing; it will be innovative. The best-off may see the virtues of a relatively generous welfare state to ensure not only that the worst-off don¡¯t suffer too badly, but also to ensure that their discontent doesn¡¯t lead to revolution.

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If - perhaps only if - the game of chance that is an ideal capitalist economy can be run in such a way that advantage isn¡¯t passed on from one generation to the next, this would be a way of combining equality and mobility.

The young Herbert Spencer thought as much 150 years ago and wanted to abolish inheritance. But new Labour has been as eager as the Conservatives to help the prosperous pass on their advantages.

The Government doesn¡¯t really know what it wants. Most people would be happier in the first sort of society than the second. Brown and Co¡¯s final thought is that people should ¡°do better¡± than their parents; the answer to that is the first sort of society, with productivity gains evenly spread. If productivity grows by 2 per cent a year, children will do 50 per cent better than their parents.

But what has happened over the past 30 years is that almost all the gains have been hoovered up by a small and unrepresentative elite.

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All this is well known. What is inexplicable is that governments think that playing around with school-leaving examinations and university-entrance systems will roll back the capitalist counter-revolution of the past three decades.

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