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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Ignored by the media, the Liberal Democrats are experiencing a revival

The crushed Liberals are doing particularly well in areas that voted Conservative in 2015 - and Remain in 2016. 

The Liberal Democrats had another good night last night, making big gains in by-elections. They won Adeyfield West, a seat they have never held in Dacorum, with a massive swing. They were up by close to the 20 points in the Derby seat of Allestree, beating Labour into second place. And they won a seat in the Cotswolds, which borders the vacant seat of Witney.

It’s worth noting that they also went backwards in a safe Labour ward in Blackpool and a safe Conservative seat in Northamptonshire.  But the overall pattern is clear, and it’s not merely confined to last night: the Liberal Democrats are enjoying a mini-revival, particularly in the south-east.

Of course, it doesn’t appear to be making itself felt in the Liberal Democrats’ poll share. “After Corbyn's election,” my colleague George tweeted recently, “Some predicted Lib Dems would rise like Lazarus. But poll ratings still stuck at 8 per cent.” Prior to the local elections, I was pessimistic that the so-called Liberal Democrat fightback could make itself felt at a national contest, when the party would have to fight on multiple fronts.

But the local elections – the first time since 1968 when every part of the mainland United Kingdom has had a vote on outside of a general election – proved that completely wrong. They  picked up 30 seats across England, though they had something of a nightmare in Stockport, and were reduced to just one seat in the Welsh Assembly. Their woes continued in Scotland, however, where they slipped to fifth place. They were even back to the third place had those votes been replicated on a national scale.

Polling has always been somewhat unkind to the Liberal Democrats outside of election campaigns, as the party has a low profile, particularly now it has just eight MPs. What appears to be happening at local by-elections and my expectation may be repeated at a general election is that when voters are presented with the option of a Liberal Democrat at the ballot box they find the idea surprisingly appealing.

Added to that, the Liberal Democrats’ happiest hunting grounds are clearly affluent, Conservative-leaning areas that voted for Remain in the referendum. All of which makes their hopes of a good second place in Witney – and a good night in the 2017 county councils – look rather less farfetched than you might expect. 

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