The magic numbers spin before our eyes. No one can grasp the scale of the handouts, or understand how public money that didn't exist - could never exist - for hospitals or schools or public toilets begins to flow as soon as bankers fall to their knees. We are punch drunk, reeling, uniquely vulnerable - because none of it makes sense any more - to demands from every species of scrounger.

So prepare yourselves, ladies and gentlemen, for the worst scam of all. It's another reward for failure, but this one offers no prospect of rescuing the economy. Thanks to its cunning disguise as an environmental measure, we seem willing to be conned. I want to show you why we should resist it.

I'm talking about the scrappage payments being proposed by almost everyone linked to the motor industry: the Society of Motor Manufacturers and Traders, most of the big car firms, the AA, and the unions. Lord Mandelson is said to be a fan. They argue that drivers should be paid around £2,000 a head to scrap their old cars and buy new ones. As well as saving the jobs of hundreds of thousands of workers, this, they say, will catalyse a low-carbon transport revolution. It's bunkum.

Let's start by getting a misconception out of the way. The media are reporting the proposal as a subsidy for switching to smaller, more efficient cars. But the manufacturers have called for no such thing. The model they keep referring to is Germany's. Here drivers are being offered €2,500 to trade in cars at least nine years old for new models. The only requirement is that the new cars meet the Euro 4 standard on exhaust emissions. This is another way of saying all cars: since 2005 every new car on sale in the EU has to meet this standard, which has nothing to do with CO2. So £2,000 from the government could help you trade in your old Citroen C1 for a new Porsche Cayenne.

There is a simple way of working out whether a green subsidy is worthwhile: how much does it cost to save a tonne of carbon dioxide? No one appears to have done this yet so, if you'll bear with me, I'll attempt it here. I've had to make a few assumptions where data don't exist, but it gives us a rough idea of what we are exposing ourselves to (all the sources, as usual, are on my website).

Let's imagine that the average age of the scrapped cars is 12 years. In 1997 new cars in the UK produced an average of 189.8 grams of CO2 per km. If they've since become 10% less efficient, their average output will be 208g/km today.

Cars manufactured this year will put out an average of around 160g/km, which means a saving of 48g/km. This translates - with a mean annual driving distance of 16,500km - into a cut of 792kg/car/year. Assuming that drivers are each paid £2,000, that's a cost of £2,525 for every tonne of CO2 avoided, divided by the average age of the cars on the road - 4.9 years. You'd get almost as much value for money by reclassifying £10 notes as biomass and burning them in power stations.

The management consultancy McKinsey has calculated the costs of saving CO2 by other means. We could do it for £3.50 a tonne by investing in geothermal energy, or £9 if we put our money into nuclear power plants. Mini hydroelectric schemes would save money as well as carbon against normal electricity prices. So would energy efficiency: switching from incandescent lightbulbs to light-emitting diodes, for example, saves £80 for every tonne of CO2 you cut.

I would have liked to give you some transport comparisons, but McKinsey doesn't publish figures for public transport or for promoting walking or cycling (a McKinsey consultant wouldn't be seen dead on a bus). Nor, as far as I can discover, does the government. The carbon payback for other projects - creating better cycle lanes in towns and coach lanes on motorways, helping children to walk to school, better enforcement of speed limits, better timetabling for buses - is likely to be hundreds or thousands of times higher than any returns from the scrappage scam.

In fact I have grossly overstated the scheme's value for money. My rough figures take no account of the rebound effect: when driving costs you less (after buying a more efficient car), you are likely to travel further. Nor have I considered the fact that many people would have bought new cars anyway, which means they'll be given the money for nothing. Without this subsidy, others might have stopped driving altogether and started cycling or using public transport instead: in this case the scrappage scheme will have raised their emissions. Nor did I calculate the carbon costs of manufacturing the new cars.

A paper published in 2000 by the journal Transportation Research comes to even grimmer conclusions: that replacing old cars with new ones increases carbon pollution. Because between 15% and 20% of a car's emissions are produced during its manufacture, the optimal age for a car, the paper says, is 19 years. (The average age of the UK's fleet is 4.9 years). If the paper's assumptions hold (they may be out of date now), it would make more sense for the government to pay us to keep our old bangers on the road.

Low-carbon transport? Pull the other one. Scrappage schemes are nothing but handouts for car firms, resprayed green to fool the incautious buyer. The motor trade wants the money because it's collapsing. Some companies - notably Vauxhall and the rest of the General Motors group - are in imminent danger of insolvency. So the question changes: should we support them regardless of their impact on the environment?

No. State aid rules forbid scrappage schemes from discriminating between cars made here and cars made abroad. So, given that British car plants assemble only around 15% of the vehicles sold in this country, and given that the motor industry is highly automated and has vast capital costs, this subsidy is likely to be just as bad at saving jobs as it is at saving carbon. Every pound we spend on driving is a pound withheld from the alternatives, many of which (such as buses and trains) employ far more people for the same amount of money.

This leaves only the value of preserving the industry for its own sake. It is hard to think of a less deserving cause. The motor companies have repeatedly failed to anticipate trends in demand. They have carried on producing thunderous gas guzzlers long after the market collapsed. Every so often the bosses wring their hands about jobs, put out the begging bowl, get the money, then shaft their workers anyway. Like the bankers, they have wrecked their own industry. And like the bankers, they want the rest of us to pay.

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