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.

How Jim Murphy's mistake cost Labour - and helped make Ruth Davidson

Scottish Labour's former leader's great mistake was to run away from Labour's Scottish referendum, not on it.

The strange revival of Conservative Scotland? Another poll from north of the border, this time from the Times and YouGov, shows the Tories experiencing a revival in Scotland, up to 28 per cent of the vote, enough to net seven extra seats from the SNP.

Adding to the Nationalists’ misery, according to the same poll, they would lose East Dunbartonshire to the Liberal Democrats, reducing their strength in the Commons to a still-formidable 47 seats.

It could be worse than the polls suggest, however. In the elections to the Scottish Parliament last year, parties which backed a No vote in the referendum did better in the first-past-the-post seats than the polls would have suggested – thanks to tactical voting by No voters, who backed whichever party had the best chance of beating the SNP.

The strategic insight of Ruth Davidson, the Conservative leader in Scotland, was to to recast her party as the loudest defender of the Union between Scotland and the rest of the United Kingdom. She has absorbed large chunks of that vote from the Liberal Democrats and Labour, but, paradoxically, at the Holyrood elections at least, the “Unionist coalition” she assembled helped those parties even though it cost the vote share.

The big thing to watch is not just where the parties of the Union make gains, but where they successfully form strong second-places against whoever the strongest pro-Union party is.

Davidson’s popularity and eye for a good photo opportunity – which came first is an interesting question – mean that the natural benefactor in most places will likely be the Tories.

But it could have been very different. The first politician to hit successfully upon the “last defender of the Union” routine was Ian Murray, the last Labour MP in Scotland, who squeezed both the  Liberal Democrat and Conservative vote in his seat of Edinburgh South.

His then-leader in Scotland, Jim Murphy, had a different idea. He fought the election in 2015 to the SNP’s left, with the slogan of “Whether you’re Yes, or No, the Tories have got to go”.  There were a couple of problems with that approach, as one  former staffer put it: “Firstly, the SNP weren’t going to put the Tories in, and everyone knew it. Secondly, no-one but us wanted to move on [from the referendum]”.

Then again under different leadership, this time under Kezia Dugdale, Scottish Labour once again fought a campaign explicitly to the left of the SNP, promising to increase taxation to blunt cuts devolved from Westminster, and an agnostic position on the referendum. Dugdale said she’d be open to voting to leave the United Kingdom if Britain left the European Union. Senior Scottish Labour figures flirted with the idea that the party might be neutral in a forthcoming election. Once again, the party tried to move on – but no-one else wanted to move on.

How different things might be if instead of running away from their referendum campaign, Jim Murphy had run towards it in 2015. 

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

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