The new Government has, quite reasonably, put the welfare of claimants above the cost (over pounds I00 million) and the possible disincentive effects. This is an excellent example of the hard choices that have to be made.The fourth message is that all changes to the system will involve similar trade-offs; there is no getting round them. Increasing incomes in work at any point will mean withdrawing them later. Under this rule the benefit system would effectively no longer have paid for self contained accommodation for the single unemployed. The downside of this policy, though, is that more people would be caught on Housing Benefit in the first place.The new Government has already decided to reverse one Housing Benefit change announced by the last government – a reduction in the maximum benefit payable to single childless people over 25. That would mean lower Housing Benefit payments to tenants and less benefit to withdraw once they take work.

An alternative would be to reduce the 65p in the pound withdrawal rate of Housing Benefit so that more is gained from extra work. Perhaps the most direct thing he could do would be to increase subsidies to local authorities and housing associations so that they can charge lower rents – though this costs money. For some groups, especially single mothers, it has been shown to be modestly effective. But the picture illustrates how, for many people, its effectiveness is blunted by another part of the benefit system, namely Housing Benefit. Because much of what the state gives you with one hand in extra Family Credit, it takes away with the other hand by reducing Housing Benefit.So one place that Mr Brown might well look if he is interested in promoting work incentives is the Housing Benefit system. The third message is that this is a problem of the benefit system, not of the tax system – the Chancellor should forget about wasting money on reducing the lowest rate of income tax.The diagram also shows why this is such a difficult issue to resolve.

For people who can only earn pounds 3.50 or pounds 4 per hour but who receive benefits of more than pounds 150 if not in work, there is never going to be much of an incentive to be in work unless the benefit system provides an extra bonus for it.Family Credit is intended to provide just such a bonus. If she were to work 40 hours a week the 10p rate would make her just 65p better off than at present. It would reduce the marginal tax rate she faces from 92.65 per cent to 91.6 per cent. There is a small jump at 16 hours as she moves on to Family Credit and then another long flattish period as Family Credit and Housing Benefit are withdrawn as earnings rise.The potential problems are clear enough. There is relatively little to be gained from working at all, and once in work little to be gained from working more than 16 hours a week.Changing the current 20p rate of tax to a 10p rate would make absolutely no difference to her if she were to work 16 hours a week, since she would not be paying tax. It is particularly a problem when people have to pay high costs in order to work – for childcare for example.

As rents have risen, wages of the low skilled have fallen behind everyone else’s and the number of lone parents has increased exponentially, the case for action has become more urgent.The problem, for a particular type of person is illustrated in the graphic. It shows, for a lone parent with two children, the income that she would enjoy at any hours of work from none up to 40. We assume she earns pounds 3.50 an hour and has a rent of pounds 50 a week. Each of these figures matters.Having a relatively high rent is a problem – though this is not a high rent for a council flat in London. Having a low wage is a problem, though pounds 3.50 an hour is not unusually low for a low-skilled woman.