Copenhagen is dead. Hurrah! And I say that as someone convinced that climate change is happening, we're causing it, and we need to do something about it. However, what we don't need to do is the ghastly mess that was being cooked up in Denmark.

They've essentially agreed to, um, well, try - and they'll think a little bit more about what they're going to try sometime later. And that's the best result we could have hoped for. We already know what needs to be done, as the economists have worked it out. It is true that economists are not exactly the flavour of the month right now, but they are still the experts here.

We are trying to change people's behaviour, and long experience tells us that the way to do that is to change the incentives people face. We might make it illegal to burn coal, for example - as we largely have done in British cities - and the motivation people would have for doing so would be an incentive not to.

Yet observation of humans over the past couple of centuries has shown that the carrot tends to provide a better incentive than the stick. Being shot for failing the Five Year Plan should concentrate minds more than the alternatives of bankruptcy or hot and cold running lingerie models which our own system provides for failure or success, but which has been better at producing economic growth? Quite.

So economists have thought long and hard about how we might alter incentives to change behaviour and avoid boiling Flipper. There are essentially two options. The first reaches back to Arthur Cecil Pigou and his publication in 1912 on welfare economics. He note that markets are very good things indeed, but they are not perfect. They have periods when they do not act as advertised. The most obvious of these is when there are externalities: things which affect others but which are not included in prices and thus are not in the calculations that market participants make when deciding how to act.

Externalities can be positive or negative: if they're positive then this means that markets unadorned will not provide enough of these nice things. The fact that knowledge is a public good and has positive externalities is the reason that the taxman asks us to pay for basic research in universities and the like. The correct thing to do with positive externalities is to subsidise them.

Pollution is a classic example of a negative externality. My factory polluting the river has costs for those downstream. If I'm not forced to pay those costs then they're not included in my prices, so I'll be making a profit while harming others. We should tax negative externalities, and with climate change, this leads us simply to taxing emissions. Alternatively, we could tax fossil fuels when they're dug up: a suggestion recently made by James Hansen which might be his most intelligent contribution to the debate so far.

So, solution 1) from the economists: slap on a carbon tax and we're done. The tax should be at whatever the damage done costs and we should reduce other taxes to make it revenue neutral. We might want to study what the actual cost of that damage is: current estimates range from around $5 a tonne CO2 from William Nordhaus to $80 a tonne from Lord Stern - the differences stem from technical points such as the length of the technological cycle and discount rates, which is not stuff we have room to explain here.

However, the economists agree that we should slap on the tax and then let everyone get on with it. But when this simple idea meets the world of politics and Copenhagen, one subtlety gets missed which makes a mess of the entire theory.

The economists insist that the tax should be what the cost of the pollution is. Not a high enough tax to stop people polluting at all, but rather just the cost of the pollution. This is an offshoot of welfare economics and what we're trying to do is maximise the welfare of everyone, current and future. We only want to stop people doing things where the cost is greater than the benefit. We don't want to stop people doing something where the benefit is greater than the cost.

A ban on petrol?

Think, for a moment, of petrol. Every use of it brings that moment when Bangladesh sinks below the waves that tiniest amount closer. So, should we immediately ban all use of petrol? What, even for the ambulance taking the woman in labour to hospital? Maybe I should walk rather than drive to the shops though? And this is exactly what that carbon tax is supposed to do. We should only be producing emissions if our emissions are worth more than the damage. So if the damage is as Lord Stern says, then $80 a tonne it is.

But this is where the subtlety gets missed: a Stern tax on petrol would be 11p a litre. We've already used the fuel duty escalator to raise duty by 23p since we agreed to “meet our Rio commitments” in Ken Clarke's words. So we don't want to raise the carbon tax further. We're already done. We're already balancing the benefits of our using petrol with the costs we impose upon others.

Air Passenger Duty likewise already covers the costs of aviation pollution. Indeed, total green taxes are around and about the level of total costs imposed by UK emissions, but you never hear a politician saying this, do you? APD must rise further to stop people from flying, fuel duty to stop them from driving. Which is to entirely miss the point that Pigou was making about such taxation as above.

Of course it is not the first time that politics and campaigners have made a mockery of well crafted economics, and it won't be the last, as the alternative, economists' second solution - cap and trade - will show.

Cap and trade starts from the other end: what are the maximum emissions that can be allowed before disaster strikes? Fine, make that the cap and give (better to sell to but that's something that will be phased in over time) everyone permits. If an organisation wants to emit more than they have permits for, then they've got to go and buy them.

Some people will reduce emissions to sell permits and so we've got a market. As markets tend to do, we'll get a price set on carbon and only those activities which are worth more than that price will happen. We've again done what we all want, which is for people to internalise the costs they impose upon others. Once again, we can go away, having solved the problem.

But again there's a subtlety here. We want just one cap and trade system for everything. We want it to be global and we want it to be across all sectors. Imagine, just as an example, that we have to reduce emissions by 80% by 2050. So, which 20% of our current emissions do we still want to be doing? I dunno, nor do you and nor does anyone else. OK, so how do we find out? Well, markets are not just distribution systems. They're also information systems. Those emissions that people value most will be the ones they're willing to pay most for.

It might be that we're all happiest using cement (currently, cement production is about 6% of global emissions) plus a bit of driving. It might be that we don't care about cement and that fuel cells really work so we want to spend that 20% allowance on the methane inevitable in steak production. Could be we'll care not a whit for Charolais and Cheddar and we'd really rather spend that allowance on flying to Malaga.

So what we want from our cap and trade system is one cap and then trade so that we can a) find out which emissions people value the most and b) allow them to make the emissions they value most. We want trade across sectors that is, we absolutely do not want to try and have different caps and different targets for each sector on its own: that obviates the very point of what we're trying to do.

So what are the politicians and the campaigners trying to set up? Yes, separate caps and targets for different sectors and no trading of permits across sectors. There are a number of people running around (yes, Plane Stupid, I'm looking at you) telling us that if we don't restrain aviation emissions then it'll be 50 per cent, 70 per cent, umptybignumber per cent of all allowable emissions by Thursday week. This entirely fails to understand that this is the whole damn point of what we're trying to do: discover which emissions we value most so that we get the greatest value from the amount allowed under our cap.

This is why I'm cheering that Copenhagen has failed: what economists have been shouting we should be doing for this past decade will work, but what the politicians and activists have been hearing is very different from what has been said.

What has been said is that we can use either method: carbon tax or cap and trade. Make people pay the cost of their pollution and they'll pollute less. The tax should be the cost the pollution imposes, or the cap should allow trade amongst all nations and all activities. What we absolutely should not be doing is taxing more than the cost of the pollution nor should we be trying to to exempt, favour, punish, or ban any particular activities by selective use of caps and permits.

In short, set the system up and then leave well alone: no politics please, no special interest groups and no “civil society organisations” trying to ram their prejudices down other peoples' throats. And what was Copenhagen other than that politics, those special interest groups (it was especially pleasing to see the Third World Dictator's Pension Fund come up short) and prejudices being forced down peoples' throats?

We're well shot of it. There's even the vague possibility that the adults will take over at some point and we'll end up with something that actually works: a simple carbon tax or a simple cap and trade scheme. ®