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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Owen Smith apologises for pledge to "smash" Theresa May "back on her heels"

The Labour leader challenger has retracted his comments. 

Labour leader challenger Owen Smith has apologised for pledging to "smash" Theresa May "back on her heels", a day after vigorously defending his comments.

During a speech at a campaign event on Wednesday, Smith had declared of the prime minister, known for wearing kitten heels:

"I'll be honest with you, it pained me that we didn’t have the strength and the power and the vitality to smash her back on her heels and argue that these our values, these are our people, this is our language that they are seeking to steal.”

When pressed about his use of language, Smith told journalists he was using "robust rhetoric" and added: "I absolutely stand by those comments."

But on Thursday, a spokesman for the campaign said Smith regretted his choice of words: "It was off script and on reflection it was an inappropriate choice of phrase and he apologises for using it."

Since the murder of the MP Jo Cox in June, there has been attempt by some in politics to tone down the use of violent metaphors and imagery. 

Others though, have stuck with it - despite Jeremy Corbyn's call for a "kinder, gentler politics" his shadow Chancellor, John McDonnell, described rebel MPs as a "lynch mob without the rope"

Smith's language has come under scrutiny before. In 2010, when writing about the Tory/Lib-Dem coalition, he asked: "Surely, the Liberal will file for divorce as soon as the bruises start to show through the make-up?"

After an outcry over the domestic violence metaphor, Smith edited the piece.