Under the current so-called "Cash for Clunkers" program, people who have owned a car for at least a year that gets below 18 miles per gallon can turn in the car as trade for a new car and get a payment of up to $4,500 from the dealer. The dealer then destroys a certain amount of the car to take it out of circulation and then, at least in theory, gets reimbursed by the government.
The program destroys wealth. Here's how.
First, consider the baseline, a $4,500 subsidy that you get simply from buying a new car. The standard analysis of a subsidy to output applies here. The buyer and seller split the subsidy, with the split depending on the relative elasticities of supply and demand. But it's not a wash. There are two deadweight losses (DWL). One is from the incentive to buy a car that the buyer values below the cost. I have no idea how big this DWL is. Let's say it's minimal: $300 on the $4,500 subsidy. The other DWL is bigger, and comes about because the $4,500 in revenue to pay for the program is not a lump-sum tax. It's raised from future income taxes, sales taxes, etc. Each of these has DWL, sometimes called an excess burden. This excess burden is the loss to the economy from the distortion in behavior caused by the tax. A typical DWL number is 30% of the revenue raised. So the DWL from the $4,500 in tax revenue is $1,350.
So now we're up to $1,650 of DWL. But wait; there's more. There are two other factors, one of which could be a small gain and the other of which is a loss. The small gain is due to taking off the road a car that was imposing external costs with pollution and, if global warming is a problem, with more carbon dioxide. I have no idea how to estimate this. The other loss is more substantial and comes about because this is a cash-for-clunkers program, not a cash-just-for-buying-a-new-car program. It comes about, in short, because value is explicitly destroyed.
Imagine a car owner who takes advantage of the program. Ideally, for efficiency, the cars that get destroyed would be the lowest-valued ones. But the program gives the same subsidy to a person with a car worth $3,000 as it does to a person with a car worth only $1,000. So whoever gets there first is the one who gets the subsidy. (At least Congress had the "wisdom"--I use that word loosely--to limit the overall expenditure on the program to $1 billion, but then raised it to $3 billion. Otherwise, with no limit, the program would have caused every car worth under $4,500 to be destroyed and would have acted like a price support for wheat, driving up the price of cars to at least $4,500 just as price supports drive up the price of agricultural products.)
So let's imagine that the average car destroyed is worth $2,000. If you assume a lower number, you'll get a lower wealth loss, and if you assume a higher number, you'll get a higher wealth loss. Even if the $2,000 car is destroyed, maybe the spare parts that are "spared" are worth $200. So for that $4,500, $1,800 in wealth is explicitly destroyed. So, the net loss per $4,500 payment is $1,650 plus $1,800, or $3,450, minus the small environmental gain.