Child benefit withdrawal will make it better to work less for families with over seven children

And come 2076, that will be the case for every family in the nation.

The child tax credit withdrawal, taking effect on Monday, will lead to marginal tax rates of over 100 per cent on families with more than eight children earning between £50,000 and £60,000.

The IFS explains how the marginal rates are calculated:

Affected taxpayers will pay back one per cent of their family’s Child Benefit for every £100 by which taxable income exceeds £50,000. One per cent of Child Benefit is £10.56 per year for a 1-child family, and an additional £6.97 per child for larger families. Hence the marginal tax rate between £50,000 and £60,000 is increased by about 11 percentage points for the first child and by an additional 7 percentage points for each subsequent one. So, for example, while about 320,000 people will find that their marginal income tax rate increases to more than 50%, about 40,000 of them - those with three or more children - will find that it jumps to at least 65%.

They offer a chart with the rate calculated up to four children:

By seven children, the marginal rate rises to 99.35 per cent, and by eight, it breaks 100 per cent (106.32 per cent, to be exact). This means that any individual with a family of eight kids earning between £50,000 and £60,000 would be better off if they reduced their salary back down to £50,000. In fact, for that individual, they would have to earn £61,105 before their post-tax income was the same as it was at £50,000.

It's unclear whether any families actually exist matching that criterion - rather wonderfully, my back-of-the-envelope maths (which assumes that the exponential decrease in the number of families of each size continues: e.g., there are 1/8th the number of families with three or more kids as there are with two or more, so I'm assuming that there are correspondingly 1/8th the number of families with four or more as there are with three or more, and so on) suggests that there may be exactly one – but even if there are none at the moment, there's no reason why there won't be one in the future. Families with eight children do, after all, exist.

In fact, as time goes on, this problem will get worse. The IFS points out that child benefit is uprated with inflation, while tax bands aren't. Currently, each extra child after the first increases your "marginal tax rate" by around seven per cent, but suppose child benefit is uprated by two per cent a year. In that case, the marginal tax would exceed one hundred per cent for families with seven children next year; for six children in the year 2020; for five children in the year 2028; and, eventually, for families with just one child – i.e., every family – in the year 2076.

Hopefully the law will be changed before then, of course. But as a rule of thumb, laws which become ridiculously damaging unless you actively intervene ought not be signed in the first place. Oops.

Children. Photograph: Getty Images

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

Photo: Dan Kitwood/Getty Images
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Conservative disunity is not all good news for Labour

The Tory leadership election could squeeze Labour out of the conversation, just like Blair and Brown did to the Tories.

The first test of opposition politics is relevance. Other key yardsticks - political plausibility, economic credibility, setting the agenda and developing a governing vision - all matter greatly. But making yourself a central part of the relentless cycle of daily politics, the terms of which are generally set by the governing party, is the first hurdle. It matters not whether you sign up to new politics or old: be relevant or wither. 

The issue of relevance is becoming a pressing issue for Labour. Take George Osborne’s favoured issue of the so-called national living wage.  Leave to one side the rights, wrongs and nuances of the policy and just consider the basic political dynamic it creates.  Osborne has, quite deliberately, set up a rolling five year argument over a steadily rising wage floor. On one side, is the Chancellor arguing that his policy is the right thing for Britain’s ranks of low paid workers. Pitted against him are ranks of chief executives of low-paying big business. With each impending hike they will holler at Osborne to go no further and the media will happily amplify the row. In response the Chancellor will quietly smile.

Sure, on occasions this will be uncomfortable stance for Mr Osborne (and if the economy takes a downward turn then his pledge will become incredible; there are always big risks with bold strokes).  Yet the dominant argument between the Conservatives and big business leaves Labour largely voiceless on an issue which for generations it has viewed as its own.

We may well see a similar dynamic in relation to the new national infrastructure commission – another idea that Osborne has plundered form Labour’s 2015 manifesto. It’s far too early to say what will come of its work looking at proposals for major new transport and energy projects (though those asserting it will just be a talking shop would do well not to under-estimate Andrew Adonis, its first Chair). But there is one thing we can already be confident about: the waves of argument it will generate between Osborne’s activist commissioners and various voices of conservatism. Every big infrastructure proposal will have noisy opponents, many residing on the right of British politics. On the issue of the future of the nation’s infrastructure – another touchstone theme for Labour – the opposition may struggle to get heard amid the din.

Or take the different and, for the government, highly exposing issue of cuts to tax credits. Here the emerging shape of the debate is between Osborne on one side and the Sun, Boris Johnson, various independent minded Conservative voices and economic think-tanks on the other. Labour will, of course, repeatedly and passionately condemn these cuts. But so have plenty of others and, for now at least, they are more colourful or credible (or both).  

The risk for the opposition is that a new rhythm of politics is established. Where the ideological undercurrent of the government steers it too far right, other voices not least those within the Conservative family - moderates and free-spirits emboldened by Labour’s current weakness; those with an eye on the forthcoming Tory leadership contest – get reported.  Where Osborne consciously decides to tack to the centre, the resulting rows will be between him and the generally Conservative supporting interests he upsets. Meanwhile, Labour is left struggling for air.

None of which is to say there are no paths back to relevance. There are all sorts of charges against the current government that, on the right issues, could be deployed - incompetence, complacency, inequity – by an effective opposition.  Nor is the elixir of relevance for a new opposition hard to divine: a distinct but plausible critique, forensic and timely research, and a credible and clear voice to deliver the message. But as yet we haven’t heard much of it.

Even in the best of times being in opposition is an enervating existence. Those out of power rarely get to set the terms of trade, even if they often like to tell themselves they can. Under Ed Miliband Labour had to strain – sometimes taking big risks - to establish its relevance in a novel era defined by the shifting dynamics of coalition politics. This time around Jeremy Corbyn’s Labour is up against a Chancellor willing to take risks and pick big fights: often with traditional Tory foes such as welfare claimants; but sometimes with people on his own side.  It’s also a new and challenging context. And one which Labour urgently needs to come to terms with.   

Gavin Kelly is chief executive of the Resolution Foundation