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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Lord Geoffrey Howe dies, age 88

Howe was Margaret Thatcher's longest serving Cabinet minister – and the man credited with precipitating her downfall.

The former Conservative chancellor Lord Howe, a key figure in the Thatcher government, has died of a suspected heart attack, his family has said. He was 88.

Geoffrey Howe was the longest-serving member of Margaret Thatcher's Cabinet, playing a key role in both her government and her downfall. Born in Port Talbot in 1926, he began his career as a lawyer, and was first elected to parliament in 1964, but lost his seat just 18 months later.

Returning as MP for Reigate in the Conservative election victory of 1970, he served in the government of Edward Heath, first as Solicitor General for England & Wales, then as a Minister of State for Trade. When Margaret Thatcher became opposition leader in 1975, she named Howe as her shadow chancellor.

He retained this brief when the party returned to government in 1979. In the controversial budget of 1981, he outlined a radical monetarist programme, abandoning then-mainstream economic thinking by attempting to rapidly tackle the deficit at a time of recession and unemployment. Following the 1983 election, he was appointed as foreign secretary, in which post he negotiated the return of Hong Kong to China.

In 1989, Thatcher demoted Howe to the position of leader of the house and deputy prime minister. And on 1 November 1990, following disagreements over Britain's relationship with Europe, he resigned from the Cabinet altogether. 

Twelve days later, in a powerful speech explaining his resignation, he attacked the prime minister's attitude to Brussels, and called on his former colleagues to "consider their own response to the tragic conflict of loyalties with which I have myself wrestled for perhaps too long".

Labour Chancellor Denis Healey once described an attack from Howe as "like being savaged by a dead sheep" - but his resignation speech is widely credited for triggering the process that led to Thatcher's downfall. Nine days later, her premiership was over.

Howe retired from the Commons in 1992, and was made a life peer as Baron Howe of Aberavon. He later said that his resignation speech "was not intended as a challenge, it was intended as a way of summarising the importance of Europe". 

Nonetheless, he added: "I am sure that, without [Thatcher's] resignation, we would not have won the 1992 election... If there had been a Labour government from 1992 onwards, New Labour would never have been born."

Jonn Elledge is the editor of the New Statesman's sister site CityMetric. He is on Twitter, far too much, as @JonnElledge.