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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The New Statesman 2016 local and devolved elections liveblog

Results and analysis from elections across the United Kingdom. 

Welcome to the New Statesman's elections liveblog. Results will be coming in from the devolved legislatures in Scotland and Wales, local elections in England, and the mayoral contests in London, Salford, Bristol and Liverpool. Hit refresh for updates!

22:40: In case you're wondering, how would closing a seven point deficit to say, six, compare to previous Labour oppositions, I've done some number-crunching. In 1984, Neil Kinnock's Labour turned a Tory lead of 15 per cent at the general election to a Conservative lead of just one per cent. In 1988, one of 12 per cent went down to one per cent. (He did, of course, go on to lose in both the 1987 and 1992 elections). In 1993, John Smith's Labour party turned a deficit of eight points at the general to a Labour lead of eight points in the local elections. William Hague turned a Labour lead of 13 points to one of just six in 1998, while Iain Duncan Smith got a Tory lead of just one point - from a Labour lead of nine. 

22:35: John McDonnell is setting out what would be a good night as far as the party leadership is concerned - any improvement on the 2015 defeat, when the party trailed by close to seven points. Corbyn's critics say he needs to make around 400 gains.

I've written about what would be good at length before, but here's an extract:

"Instead of worrying overmuch about numbers, worry about places. Although winning seats and taking control of councils is not a guarantee of winning control of the parliamentary seat – look at Harlow, Nuneaton, and Ipswich, all of which have Labour representation at a local level but send a Conservative MP to Westminster – good performances, both in terms of increasing votes and seats, are a positive sign. So look at how Labour does in its own marginals and in places that are Conservative at a Westminster level, rather than worrying about an exact figure either way."

22:31: Oh god, the BBC's election night music is starting. Getting trauma flashbacks to the general election. 

22:22: A few of you have been in touch about our exit poll. Most of you have been wondering about that one vote for George Galloway but the rest are wondering what happens - under the rules of the London mayoral race (and indeed the contests in Salford, Bristol and Liverpool), 2 votes would not be enough for Sadiq. (He needs 2.5). However, all the other candidates are tied - which makes it through to the second round. What happens then is the second preferences are used as a tie-break. Of the tied candidates, Sian Berry has the most second preferences so she goes through to face Sadiq Khan in the final round. Final round is as follows:

Sadiq Khan: 3

Sian Berry: 2

3 votes is above the quota so he is duly elected. An early omen? 

22:19: Burnham latest. A spokesperson for Andy Burnham says:

"Approaches have been made to Andy Burnham to give consideration to this role. It is early days and no decision as been taken. Whatever the decision, he will continue to serve the leader of the party and stay in the shadow cabinet."

22:17: Anyway, exit poll of the office. We've got:

Sadiq Khan: 2

George Galloway: 1

Caroline Pidgeon: 1

Sian Berry: 1

22:15: Update on Andy Burnham. He has been asked to consider running. More as we get it. 

22:13: People are asking if there's an exit poll tonight. Afraid not (you can't really do an exit poll in elections without national swing). But there is a YouGov poll from Wales and I am conducting an exit poll of the four remaining members of staff in the NS building. 

22:11: It's true! Andy Burnham is considering running for Greater Manchester mayor. Right, that's it, I'm quitting the liveblog. Nothing I say tonight can top that. 

22:09: Rumours that professional Scouser Andy Burnham is considering a bid for Greater Manchester mayor according to Sky News. Not sure if this is a) a typo for Merseyside or b) a rumour or c) honestly I don't know. More as I find out. 

22:06: Conservatives are feeling good about Trafford, one of the few councils they run in the North West.

22:03: Polls have closed. Turnout looks to be low in London. What that means is anyone's guess to be honest. There isn't really a particular benefit to Labour if turnout is high although that is a well-worn myth. In the capital in particular, turnout isn't quite as simple a zero-sum game as all that. Labour are buoyant, but so are the Tories. In Scotland, well, the only questions are whether or not the SNP will win every single first past the post seat or just the overwhelming majority. Both Labour and Tory sources are downplaying their chances of prevailing in the battle for second place at Holyrood, so make of that what you will. And in Wales, Labour look certain to lose seats but remain in power in some kind of coalition deal. 

22:00: Good evening. I'm your host, Stephen Bush, and I'll be with you throughout the night as results come in from throughout the country. The TV screens are on, I've just eaten, and now it's time to get cracking. 

Stephen Bush is special correspondent at the New Statesman. He usually writes about politics.