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: Getty
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PMQs review: Jeremy Corbyn prompts Tory outrage as he blames Grenfell Tower fire on austerity

To Conservative cries of "shame on you!", the Labour leader warned that "we all pay a price in public safety" for spending cuts.

A fortnight after the Grenfell Tower fire erupted, the tragedy continues to cast a shadow over British politics. Rather than probing Theresa May on the DUP deal, Jeremy Corbyn asked a series of forensic questions on the incident, in which at least 79 people are confirmed to have died.

In the first PMQs of the new parliament, May revealed that the number of buildings that had failed fire safety tests had risen to 120 (a 100 per cent failure rate) and that the cladding used on Grenfell Tower was "non-compliant" with building regulations (Corbyn had asked whether it was "legal").

After several factual questions, the Labour leader rose to his political argument. To cries of "shame on you!" from Tory MPs, he warned that local authority cuts of 40 per cent meant "we all pay a price in public safety". Corbyn added: “What the tragedy of Grenfell Tower has exposed is the disastrous effects of austerity. The disregard for working-class communities, the terrible consequences of deregulation and cutting corners." Corbyn noted that 11,000 firefighters had been cut and that the public sector pay cap (which Labour has tabled a Queen's Speech amendment against) was hindering recruitment. "This disaster must be a wake-up call," he concluded.

But May, who fared better than many expected, had a ready retort. "The cladding of tower blocks did not start under this government, it did not start under the previous coalition governments, the cladding of tower blocks began under the Blair government," she said. “In 2005 it was a Labour government that introduced the regulatory reform fire safety order which changed the requirements to inspect a building on fire safety from the local fire authority to a 'responsible person'." In this regard, however, Corbyn's lack of frontbench experience is a virtue – no action by the last Labour government can be pinned on him. 

Whether or not the Conservatives accept the link between Grenfell and austerity, their reluctance to defend continued cuts shows an awareness of how politically vulnerable they have become (No10 has announced that the public sector pay cap is under review).

Though Tory MP Philip Davies accused May of having an "aversion" to policies "that might be popular with the public" (he demanded the abolition of the 0.7 per cent foreign aid target), there was little dissent from the backbenches – reflecting the new consensus that the Prime Minister is safe (in the absence of an attractive alternative).

And May, whose jokes sometimes fall painfully flat, was able to accuse Corbyn of saying "one thing to the many and another thing to the few" in reference to his alleged Trident comments to Glastonbury festival founder Michael Eavis. But the Labour leader, no longer looking fearfully over his shoulder, displayed his increased authority today. Though the Conservatives may jeer him, the lingering fear in Tory minds is that they and the country are on divergent paths. 

George Eaton is political editor of the New Statesman.

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