70 per cent of the cost of cutting the personal allowance goes to the richest half of society

Income tax is quite progressive; better to cut VAT or council tax.

Tomorrow is the beginning of the 2013/2014 tax year, and one of the changes that's going through is the latest rise in the Personal Allowance, which is increasing from £8,105 to £9,440. The Tories are making a big thing of it, launching this poster campaign:

That's going to sting for the Liberal Democrats, who are desperate to claim the increased personal allowance as their legacy from this government. But the phrasing is interesting, and worth examining.

For this poster, the Conservatives have dropped their favourite claim of "2.7 million taken out of tax altogether". That's good, because as the FT's Chris Cook explains, it's not exactly true:

The poorest families are paying a lot more in indirect tax (VAT, fuel duty, booze taxes) than in direct tax (income tax, NICs, council tax). In fact, direct taxes only overtake indirect taxes in size when you hit the fifth decile.

If you look at the second decile of households by income, just over 10 per cent of the taxes they pay are income tax. The other 90 per cent of their tax burden – still over £4,000 a year – comes from various other taxes, principally council tax and VAT. Between them, those two taxes account for almost half the tax burden on that decile.

But while it might not be the case that the tax cut takes workers "out of tax", it certainly is a tax cut for 24 million people. But rather than being a positive, this is actually the biggest flaw in the policy. This chart, prepared by the Resolution Foundation (pdf), shows the distribution of that tax cut amongst houses of different incomes:

As the chart clearly shows, the families with the biggest cash gain are the third richest tenth in the country, who get £210 each; and the families with the biggest proportional gain are the fifth richest tenth, gaining an extra 0.61 per cent of their income.

Meanwhile, the poorest families barely benefit from the rise at all. That's unsurprising; you need to be earning at least £8,105 a year for the rise to help you in any way, and at least £9,440 to gain the full benefit. And in a household, that needs to be true of both earners – otherwise half the allowance is wasted.

The chart also lets us get an idea of the distribution of the costs of the rise. Almost exactly 70 per cent of the revenue being forfeit for the increase in the allowance comes from the richest half of the nation. Less than 1 per cent of the money actually goest to the poorest ten per cent in the country.

The truth is that income tax in Britain is already one of the most progressive taxes we've got. The poorest in the nation pay little, while the richest pay most of their tax in income tax. As a result, if you want to cut taxes to help the poor, you would be better off returning VAT to its old rate of 17.5 per cent or increasing – rather than reducing – the number of people exempt from council tax. If you want to cut taxes to help the rich, going after income tax is the right way to do it.