How do you price the death of the world?

Climate change is hard to account for.

Grist's David Roberts writes about the distinction between climate change and other environmental problems:

The first difference is that carbon dioxide is not like other pollutants… The typical climate-policy targets that get thrown around — reducing emission rates by 80 percent by 2050, for example — are relatively meaningless. They focus on the rate of flow from the faucet. But that’s not what matters. What matters is the amount in the tub. If the tub fills up enough, global average temperature will rise more than 2 degrees Celsius and we’ll be in trouble. Avoiding that — staying within our “carbon budget” — is the name of the game.

The second difference is that climate change is irreversible.

Roberts cites a 2009 paper from Nature, "among many others":

The climate change that takes place due to increases in carbon dioxide concentration is largely irreversible for 1,000 years after emissions stop. Following cessation of emissions, removal of atmospheric carbon dioxide decreases radiative forcing, but is largely compensated by slower loss of heat to the ocean, so that atmospheric temperatures do not drop significantly for at least 1,000 years.

Climate change is notoriously tricky to deal with in standard economic terms. Part of it is that, to any normal person, something which is irreversible for 1,000 years sounds at least ten times worse than something which is irreversible for 100 years, if not even worse still.

Economically, though, the two are essentially the same. "Present value" is an economic concept dealing with the fact that money in the future is worth less than money now – because you can always invest money now and have more money in the future. Of course, that assumes long-term growth, which, if we're talking about world-changing events like anthropogenic climate change, might not be a safe assumption.

But the end result of the calculations is that nearly any cost beyond a hundred years into the future isn't worth spending money today to avoid. The intuitive conclusion – that it's worth fighting climate change harder if it will last for a millennium than a century – isn't the case. Assuming growth.

But there are even bigger problems for climate change than that. The vast majority of economic responses to it require calculating a "likely cost", and then applying that to the measures proposed to combat it. So, for example, a properly implemented carbon tax requires a calculation of the damage one tonne of CO2 does to the environment, in order to accurately price in the negative externalities.

Unfortunately, conventional ways of pricing risk rather fall over when considering something like climate change, because it carries a non-zero risk of existential threat. That is, there are proposed mechanisms whereby "runaway climate change" could present a civilisation-ending threat.

How do you price the end of civilisation? One option is to look at the value of everything in the world. It would be quite an accounting task, and one faced by the UK government last year when they had to put a price on Stonehenge to fulfil new bookkeeping requirements. The American government puts the value of the entirety of the US at $110trn, so it seems likely that the value of all the world's civilisations is well into 16 figures.

That's high, but it's countable. The real issue comes when you look at an alternative way of measuring the cost of risk, which is the amount you would pay to prevent it. Presumably, there is no sum which would not be worth spending to prevent the end of civilisation. Any cost would be less than the destruction of everything.

By that measure, then, the damage caused by an existential threat is infinite. But the problem with infinite quantities is that they don't work very well in conventional mathematics. Back to the normal risk accounting: you typically multiply the damage you are risking with the chance it will happen. So we are happy to suffer high risk of low damage – like groping for a glass of water at midnight with the lights off – or low risk of high damage – like driving a car – but not high risk of high damage – like driving a car at midnight with the lights off.

But infinity multiplied by anything other than zero is still infinity. Conventional risk assessment simply falls apart when confronted with something the magnitude of the worst possibilities of climate change.

Note too that it doesn't require the risk to be large. I think the risks of climate change are greater than most, but I also think it's extraordinarily unlikely that it actually would result in the end of civilisation. But can we rule it out with certainty?

The best way to look at it is to compare it to our every day lives. Thousands of people are killed crossing the road every day. To do so carries a non-negligible personal existential threat – that is, you might die. Yet I see people dodging traffic to get to work 30 seconds earlier every day, which suggests that, instinctively, we don't treat the risk of death with as much weight as we perhaps should.

But I think theres a different motivator at work. We know death is bad, and that it's worth doing a lot to try and avoid it; but we also know death can come from any corner. And the same is true of fighting existential threats to civilisation. If we could spend ludicrous sums to eliminate them all, it might be worth it; but who's to say we won't prevent climate change, only to die from an asteroid hit? Or cap our future development by not experimenting with nanotech, only for an angry AI to kill us in our sleep?

Climate change could be very, very bad indeed. But making the important choices about the trade-offs we should make to fight it are hard because, not despite, its seriousness.

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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Q&A: What are tax credits and how do they work?

All you need to know about the government's plan to cut tax credits.

What are tax credits?

Tax credits are payments made regularly by the state into bank accounts to support families with children, or those who are in low-paid jobs. There are two types of tax credit: the working tax credit and the child tax credit.

What are they for?

To redistribute income to those less able to get by, or to provide for their children, on what they earn.

Are they similar to tax relief?

No. They don’t have much to do with tax. They’re more of a welfare thing. You don’t need to be a taxpayer to receive tax credits. It’s just that, unlike other benefits, they are based on the tax year and paid via the tax office.

Who is eligible?

Anyone aged over 16 (for child tax credits) and over 25 (for working tax credits) who normally lives in the UK can apply for them, depending on their income, the hours they work, whether they have a disability, and whether they pay for childcare.

What are their circumstances?

The more you earn, the less you are likely to receive. Single claimants must work at least 16 hours a week. Let’s take a full-time worker: if you work at least 30 hours a week, you are generally eligible for working tax credits if you earn less than £13,253 a year (if you’re single and don’t have children), or less than £18,023 (jointly as part of a couple without children but working at least 30 hours a week).

And for families?

A family with children and an income below about £32,200 can claim child tax credit. It used to be that the more children you have, the more you are eligible to receive – but George Osborne in his most recent Budget has limited child tax credit to two children.

How much money do you receive?

Again, this depends on your circumstances. The basic payment for a single claimant, or a joint claim by a couple, of working tax credits is £1,940 for the tax year. You can then receive extra, depending on your circumstances. For example, single parents can receive up to an additional £2,010, on top of the basic £1,940 payment; people who work more than 30 hours a week can receive up to an extra £810; and disabled workers up to £2,970. The average award of tax credit is £6,340 per year. Child tax credit claimants get £545 per year as a flat payment, plus £2,780 per child.

How many people claim tax credits?

About 4.5m people – the vast majority of these people (around 4m) have children.

How much does it cost the taxpayer?

The estimation is that they will cost the government £30bn in April 2015/16. That’s around 14 per cent of the £220bn welfare budget, which the Tories have pledged to cut by £12bn.

Who introduced this system?

New Labour. Gordon Brown, when he was Chancellor, developed tax credits in his first term. The system as we know it was established in April 2003.

Why did they do this?

To lift working people out of poverty, and to remove the disincentives to work believed to have been inculcated by welfare. The tax credit system made it more attractive for people depending on benefits to work, and gave those in low-paid jobs a helping hand.

Did it work?

Yes. Tax credits’ biggest achievement was lifting a record number of children out of poverty since the war. The proportion of children living below the poverty line fell from 35 per cent in 1998/9 to 19 per cent in 2012/13.

So what’s the problem?

Well, it’s a bit of a weird system in that it lets companies pay wages that are too low to live on without the state supplementing them. Many also criticise tax credits for allowing the minimum wage – also brought in by New Labour – to stagnate (ie. not keep up with the rate of inflation). David Cameron has called the system of taxing low earners and then handing them some money back via tax credits a “ridiculous merry-go-round”.

Then it’s a good thing to scrap them?

It would be fine if all those low earners and families struggling to get by would be given support in place of tax credits – a living wage, for example.

And that’s why the Tories are introducing a living wage...

That’s what they call it. But it’s not. The Chancellor announced in his most recent Budget a new minimum wage of £7.20 an hour for over-25s, rising to £9 by 2020. He called this the “national living wage” – it’s not, because the current living wage (which is calculated by the Living Wage Foundation, and currently non-compulsory) is already £9.15 in London and £7.85 in the rest of the country.

Will people be better off?

No. Quite the reverse. The IFS has said this slightly higher national minimum wage will not compensate working families who will be subjected to tax credit cuts; it is arithmetically impossible. The IFS director, Paul Johnson, commented: “Unequivocally, tax credit recipients in work will be made worse off by the measures in the Budget on average.” It has been calculated that 3.2m low-paid workers will have their pay packets cut by an average of £1,350 a year.

Could the government change its policy to avoid this?

The Prime Minister and his frontbenchers have been pretty stubborn about pushing on with the plan. In spite of criticism from all angles – the IFS, campaigners, Labour, The Sun – Cameron has ruled out a review of the policy in the Autumn Statement, which is on 25 November. But there is an alternative. The chair of parliament’s Work & Pensions Select Committee and Labour MP Frank Field has proposed what he calls a “cost neutral” tweak to the tax credit cuts.

How would this alternative work?

Currently, if your income is less than £6,420, you will receive the maximum amount of tax credits. That threshold is called the gross income threshold. Field wants to introduce a second gross income threshold of £13,100 (what you earn if you work 35 hours a week on minimum wage). Those earning a salary between those two thresholds would have their tax credits reduced at a slower rate on whatever they earn above £6,420 up to £13,100. The percentage of what you earn above the basic threshold that is deducted from your tax credits is called the taper rate, and it is currently at 41 per cent. In contrast to this plan, the Tories want to halve the income threshold to £3,850 a year and increase the taper rate to 48 per cent once you hit that threshold, which basically means you lose more tax credits, faster, the more you earn.

When will the tax credit cuts come in?

They will be imposed from April next year, barring a u-turn.

Anoosh Chakelian is deputy web editor at the New Statesman.