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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Who will win the Copeland by-election?

Labour face a tricky task in holding onto the seat. 

What’s the Copeland by-election about? That’s the question that will decide who wins it.

The Conservatives want it to be about the nuclear industry, which is the seat’s biggest employer, and Jeremy Corbyn’s long history of opposition to nuclear power.

Labour want it to be about the difficulties of the NHS in Cumbria in general and the future of West Cumberland Hospital in particular.

Who’s winning? Neither party is confident of victory but both sides think it will be close. That Theresa May has visited is a sign of the confidence in Conservative headquarters that, win or lose, Labour will not increase its majority from the six-point lead it held over the Conservatives in May 2015. (It’s always more instructive to talk about vote share rather than raw numbers, in by-elections in particular.)

But her visit may have been counterproductive. Yes, she is the most popular politician in Britain according to all the polls, but in visiting she has added fuel to the fire of Labour’s message that the Conservatives are keeping an anxious eye on the outcome.

Labour strategists feared that “the oxygen” would come out of the campaign if May used her visit to offer a guarantee about West Cumberland Hospital. Instead, she refused to answer, merely hyping up the issue further.

The party is nervous that opposition to Corbyn is going to supress turnout among their voters, but on the Conservative side, there is considerable irritation that May’s visit has made their task harder, too.

Voters know the difference between a by-election and a general election and my hunch is that people will get they can have a free hit on the health question without risking the future of the nuclear factory. That Corbyn has U-Turned on nuclear power only helps.

I said last week that if I knew what the local paper would look like between now and then I would be able to call the outcome. Today the West Cumbria News & Star leads with Downing Street’s refusal to answer questions about West Cumberland Hospital. All the signs favour Labour. 

Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to British politics.