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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The deafening killer - why noise will be the next great pollution scandal

A growing body of evidence shows that noise can have serious health impacts too. 

Our cities are being poisoned by a toxin that surrounds us day and night. It eats away at our brains, hurts our hearts, clutches at our sleep, and gnaws at the quality of our daily lives.

Hardly a silent killer, it gets short shrift compared to the well-publicised terrors of air pollution and sugars food. It is the dull, thumping, stultifying drum-beat of perpetual noise.

The score that accompanies city life is brutal and constant. It disrupts the everyday: The coffee break ruined by the screech of a line of double decker buses braking at the lights. The lawyer’s conference call broken by drilling as she makes her way to the office. The writer’s struggle to find a quiet corner to pen his latest article.

For city-dwellers, it’s all-consuming and impossible to avoid. Construction, traffic, the whirring of machinery, the neighbour’s stereo. Even at home, the beeps and buzzes made by washing machines, fridges, and phones all serve to distract and unsettle.

But the never-ending noisiness of city life is far more than a problem of aesthetics. A growing body of evidence shows that noise can have serious health impacts too. Recent studies have linked noise pollution to hearing loss, sleep deprivation, hypertension, heart disease, brain development, and even increased risk of dementia.

One research team compared families living on different stories of the same building in Manhattan to isolate the impact of noise on health and education. They found children in lower, noisier floors were worse at reading than their higher-up peers, an effect that was most pronounced for children who had lived in the building for longest.

Those studies have been replicated for the impact of aircraft noise with similar results. Not only does noise cause higher blood pressure and worsens quality of sleep, it also stymies pupils trying to concentrate in class.

As with many forms of pollution, the poorest are typically the hardest hit. The worst-off in any city often live by busy roads in poorly-insulated houses or flats, cheek by jowl with packed-in neighbours.

The US Department of Transport recently mapped road and aircraft noise across the United States. Predictably, the loudest areas overlapped with some of the country’s most deprived. Those included the south side of Atlanta and the lowest-income areas of LA and Seattle.

Yet as noise pollution grows in line with road and air traffic and rising urban density, public policy has turned a blind eye.

Council noise response services, formally a 24-hour defence against neighbourly disputes, have fallen victim to local government cuts. Decisions on airport expansion and road development pay scant regard to their audible impact. Political platforms remain silent on the loudest poison.

This is odd at a time when we have never had more tools at our disposal to deal with the issue. Electric Vehicles are practically noise-less, yet noise rarely features in the arguments for their adoption. Just replacing today’s bus fleet would transform city centres; doing the same for taxis and trucks would amount to a revolution.

Vehicles are just the start. Millions were spent on a programme of “Warm Homes”; what about “Quiet Homes”? How did we value the noise impact in the decision to build a third runway at Heathrow, and how do we compensate people now that it’s going ahead?

Construction is a major driver of decibels. Should builders compensate “noise victims” for over-drilling? Or could regulation push equipment manufacturers to find new ways to dampen the sound of their kit?

Of course, none of this addresses the noise pollution we impose on ourselves. The bars and clubs we choose to visit or the music we stick in our ears. Whether pumping dance tracks in spin classes or indie rock in trendy coffee shops, people’s desire to compensate for bad noise out there by playing louder noise in here is hard to control for.

The Clean Air Act of 1956 heralded a new era of city life, one where smog and grime gave way to clear skies and clearer lungs. That fight still goes on today.

But some day, we will turn our attention to our clogged-up airwaves. The decibels will fall. #Twitter will give way to twitter. And every now and again, as we step from our homes into city life, we may just hear the sweetest sound of all. Silence.

Adam Swersky is a councillor in Harrow and is cabinet member for finance. He writes in a personal capacity.