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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Donald Trump vs Barack Obama: How the inauguration speeches compared

We compared the two presidents on trade, foreign affairs and climate change – so you (really, really) don't have to.

After watching Donald Trump's inaugural address, what better way to get rid of the last few dregs of hope than by comparing what he said with Barack Obama's address from 2009? 

Both thanked the previous President, with Trump calling the Obamas "magnificent", and pledged to reform Washington, but the comparison ended there. 

Here is what each of them said: 

On American jobs

Obama:

The state of our economy calls for action, bold and swift.  And we will act, not only to create new jobs, but to lay a new foundation for growth.  We will build the roads and bridges, the electric grids and digital lines that feed our commerce and bind us together.  We'll restore science to its rightful place, and wield technology's wonders to raise health care's quality and lower its cost.  We will harness the sun and the winds and the soil to fuel our cars and run our factories.  And we will transform our schools and colleges and universities to meet the demands of a new age.

Trump:

For many decades we've enriched foreign industry at the expense of American industry, subsidized the armies of other countries while allowing for the very sad depletion of our military.

One by one, the factories shuttered and left our shores with not even a thought about the millions and millions of American workers that were left behind.

Obama had a plan for growth. Trump just blames the rest of the world...

On global warming

Obama:

With old friends and former foes, we'll work tirelessly to lessen the nuclear threat, and roll back the specter of a warming planet.

Trump:

On the Middle East:

Obama:

To the Muslim world, we seek a new way forward, based on mutual interest and mutual respect. To those leaders around the globe who seek to sow conflict, or blame their society's ills on the West, know that your people will judge you on what you can build, not what you destroy. 

Trump:

We will re-enforce old alliances and form new ones and unite the civilized world against radical Islamic terrorism, which we will eradicate completely from the face of the earth.

On “greatness”

Obama:

In reaffirming the greatness of our nation we understand that greatness is never a given. It must be earned.

Trump:

America will start winning again, winning like never before.

 

On trade

Obama:

This is the journey we continue today.  We remain the most prosperous, powerful nation on Earth.  Our workers are no less productive than when this crisis began.  Our minds are no less inventive, our goods and services no less needed than they were last week, or last month, or last year.  Our capacity remains undiminished.  

Trump:

We must protect our borders from the ravages of other countries making our product, stealing our companies and destroying our jobs.

Protection will lead to great prosperity and strength. I will fight for you with every breath in my body, and I will never ever let you down.

Stephanie Boland is digital assistant at the New Statesman. She tweets at @stephanieboland