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.

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Is defeat in Stoke the beginning of the end for Paul Nuttall?

The Ukip leader was his party's unity candidate. But after his defeat in Stoke, the old divisions are beginning to show again

In a speech to Ukip’s spring conference in Bolton on February 17, the party’s once and probably future leader Nigel Farage laid down the gauntlet for his successor, Paul Nuttall. Stoke’s by-election was “fundamental” to the future of the party – and Nuttall had to win.
 
One week on, Nuttall has failed that test miserably and thrown the fundamental questions hanging over Ukip’s future into harsh relief. 

For all his bullish talk of supplanting Labour in its industrial heartlands, the Ukip leader only managed to increase the party’s vote share by 2.2 percentage points on 2015. This paltry increase came despite Stoke’s 70 per cent Brexit majority, and a media narrative that was, until the revelations around Nuttall and Hillsborough, talking the party’s chances up.
 
So what now for Nuttall? There is, for the time being, little chance of him resigning – and, in truth, few inside Ukip expected him to win. Nuttall was relying on two well-rehearsed lines as get-out-of-jail free cards very early on in the campaign. 

The first was that the seat was a lowly 72 on Ukip’s target list. The second was that he had been leader of party whose image had been tarnished by infighting both figurative and literal for all of 12 weeks – the real work of his project had yet to begin. 

The chances of that project ever succeeding were modest at the very best. After yesterday’s defeat, it looks even more unlikely. Nuttall had originally stated his intention to run in the likely by-election in Leigh, Greater Manchester, when Andy Burnham wins the Greater Manchester metro mayoralty as is expected in May (Wigan, the borough of which Leigh is part, voted 64 per cent for Brexit).

If he goes ahead and stands – which he may well do – he will have to overturn a Labour majority of over 14,000. That, even before the unedifying row over the veracity of his Hillsborough recollections, was always going to be a big challenge. If he goes for it and loses, his leadership – predicated as it is on his supposed ability to win votes in the north - will be dead in the water. 

Nuttall is not entirely to blame, but he is a big part of Ukip’s problem. I visited Stoke the day before The Guardian published its initial report on Nuttall’s Hillsborough claims, and even then Nuttall’s campaign manager admitted that he was unlikely to convince the “hard core” of Conservative voters to back him. 

There are manifold reasons for this, but chief among them is that Nuttall, despite his newfound love of tweed, is no Nigel Farage. Not only does he lack his name recognition and box office appeal, but the sad truth is that the Tory voters Ukip need to attract are much less likely to vote for a party led by a Scouser whose platform consists of reassuring working-class voters their NHS and benefits are safe.
 
It is Farage and his allies – most notably the party’s main donor Arron Banks – who hold the most power over Nuttall’s future. Banks, who Nuttall publicly disowned as a non-member after he said he was “sick to death” of people “milking” the Hillsborough disaster, said on the eve of the Stoke poll that Ukip had to “remain radical” if it wanted to keep receiving his money. Farage himself has said the party’s campaign ought to have been “clearer” on immigration. 

Senior party figures are already briefing against Nuttall and his team in the Telegraph, whose proprietors are chummy with the beer-swilling Farage-Banks axis. They deride him for his efforts to turn Ukip into “NiceKip” or “Nukip” in order to appeal to more women voters, and for the heavy-handedness of his pitch to Labour voters (“There were times when I wondered whether I’ve got a purple rosette or a red one on”, one told the paper). 

It is Nuttall’s policy advisers - the anti-Farage awkward squad of Suzanne Evans, MEP Patrick O’Flynn (who famously branded Farage "snarling, thin-skinned and aggressive") and former leadership candidate Lisa Duffy – come in for the harshest criticism. Herein lies the leader's almost impossible task. Despite having pitched to members as a unity candidate, the two sides’ visions for Ukip are irreconcilable – one urges him to emulate Trump (who Nuttall says he would not have voted for), and the other urges a more moderate tack. 

Endorsing his leader on Question Time last night, Ukip’s sole MP Douglas Carswell blamed the legacy of the party’s Tea Party-inspired 2015 general election campaign, which saw Farage complain about foreigners with HIV using the NHS in ITV’s leaders debate, for the party’s poor performance in Stoke. Others, such as MEP Bill Etheridge, say precisely the opposite – that Nuttall must be more like Farage. 

Neither side has yet called for Nuttall’s head. He insists he is “not going anywhere”. With his febrile party no stranger to abortive coup and counter-coup, he is unlikely to be the one who has the final say.