A 10p tax rate will not banish the poverty trap

`The problem is a fundamental one. Give people money when they are out of work and you have to take it away again when they move in to work. Where people can only earn low wages, and when their benefits are relatively high to cover the costs of children and a high rent, the problem is severe'

We hear a lot from politicians about work incentives. Concern about incentives was one of the main reasons put forward (publicly at least) by the last Conservative government for reducing rates of income tax, though the suggestion that small reductions in the basic rate of tax help incentives has tended to give discussion about incentives a bad name.

Nevertheless the new government too is talking about incentives. They are less concerned about rates of income tax as they affect higher earners, and more concerned about people nearer the bottom of the earnings distribution. Quite right too. For this is where really high marginal tax rates now bite. But what can the new Chancellor do about this in his first Budget on Wednesday?

The truth is that the problem is a fundamental one. Give people money when they are out of work and you have to take it away again when they move in to work. Where people can only earn low wages, and when their benefits are relatively high to cover the costs of children and a high rent, the problem is severe. 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. For people with higher wages and lower rents or without children this picture would look very different. The first message is target help where it is most needed. The second is remember that the tax and benefit system is not the only thing that matters.

The height of each bar shows the total income at each level of hours. The subsections of each bar show the income sources at each point. At zero hours she has some Child Benefit, but the bulk of her income comes from Income Support and Housing Benefit, leaving her with a total of pounds l.57.

The general pattern after that is of a flat area up to 16 hours of work as extra earnings are accompanied by an equal reduction in Income Support. 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. 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. 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. 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. 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. 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. 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. Under this rule the benefit system would effectively no longer have paid for self contained accommodation for the single unemployed. 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. Reducing income out of work will leave the poorest people worse off.

And wheezes like integrating the tax and benefit system don't help. Recently there have been clear signs that the Government is interested in the American Earned Income Tax Credit. This is effectively a scheme like Family Credit, administered through the tax system and paid as a tax refund rather than as a social security benefit.

There are arguments in favour of such a change, but they have nothing to do with altering the return from working. In fact the main argument in its favour is a presentational one. Politicians are impressed by a system in the US which makes big increases in the Earned Income Tax Credit popular because they can be sold as an income tax cut, not as a benefit increase. Many people believe that support for children would currently be more generous if it was still provided through child tax allowances, since increasing them would have been sold as tax cuts. But presentation doesn't change the fundamentals.

All of which sounds very gloomy. Partly this is because the tax and benefit system cannot provide the answers by itself. One of the biggest problems is the very low level of earnings that many people can command. So the final message is that the new Government is quite right to be concentrating on other things as well - education, training, workfare and, possibly, childcare. The challenge is to put all this together into an effective set of policies, and to find the money to fund it when receipts from the windfall tax run out. Mr Brown needs to spend money where it will be effective, not waste it on introducing a new 10p rate of income tax.

Paul Johnson is deputy director of the Institute for Fiscal Studies.

Gavyn Davies' column will return next Monday to assess this week's Budget.