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.

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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I believe only Yvette Cooper has the breadth of support to beat Jeremy Corbyn

All the recent polling suggests Andy Burnham is losing more votes than anyone else to Jeremy Corbyn, says Diana Johnson MP.

Tom Blenkinsop MP on the New Statesman website today says he is giving his second preference to Andy Burnham as he thinks that Andy has the best chance of beating Jeremy.

This is on the basis that if Yvette goes out first all her second preferences will swing behind Andy, whereas if Andy goes out first then his second preferences, due to the broad alliance he has created behind his campaign, will all or largely switch to the other male candidate, Jeremy.

Let's take a deep breath and try and think through what will be the effect of preferential voting in the Labour leadership.

First of all, it is very difficult to know how second preferences will switch. From my telephone canvassing there is some rather interesting voting going on, but I don't accept that Tom’s analysis is correct. I have certainly picked up growing support for Yvette in recent weeks.

In fact you can argue the reverse of Tom’s analysis is true – Andy has moved further away from the centre and, as a result, his pitch to those like Tom who are supporting Liz first is now narrower. As a result, Yvette is more likely to pick up those second preferences.

Stats from the Yvette For Labour team show Yvette picking up the majority of second preferences from all candidates – from the Progress wing supporting Liz to the softer left fans of Jeremy – and Andy's supporters too. Their figures show many undecideds opting for Yvette as their first preference, as well as others choosing to switch their first preference to Yvette from one of the other candidates. It's for this reason I still believe only Yvette has the breadth of support to beat Jeremy and then to go on to win in 2020.

It's interesting that Andy has not been willing to make it clear that second preferences should go to Yvette or Liz. Yvette has been very clear that she would encourage second preferences to be for Andy or Liz.

Having watched Andy on Sky's Murnaghan show this morning, he categorically states that Labour will not get beyond first base with the electorate at a general election if we are not economically credible and that fundamentally Jeremy's economic plans do not add up. So, I am unsure why Andy is so unwilling to be clear on second preferences.

All the recent polling suggests Andy is losing more votes than anyone else to Jeremy. He trails fourth in London – where a huge proportion of our electorate is based.

So I would urge Tom to reflect more widely on who is best placed to provide the strongest opposition to the Tories, appeal to the widest group of voters and reach out to the communities we need to win back. I believe that this has to be Yvette.

The Newsnight focus group a few days ago showed that Yvette is best placed to win back those former Labour voters we will need in 2020.

Labour will pay a massive price if we ignore this.

Diana Johnson is the Labour MP for Hull North.