The Obama administration’s Cash for Clunkers program is supposed to run through 8 PM tonight, but as the Wall Street Journal reports, dealers across the country are ending their involvement early. The reason? “They worry that if a last-minute rush to enter applications jams the system, they will be on the hook for rebates already given to customers.” And dealers have every reason to worry. Last week the National Automobile Dealers Association reported that the nation’s car dealers have already submitted $3.3 billion in “Cash for Clunkers” claims despite the fact that the Obama administration has only secured $3 billion in deficit spending to cover the program.

It will be interesting to see what happens to those already-struggling auto dealers who are left holding millions of dollars in Cash for Clunkers claims when the Cash for Clunkers fund dries out. What we do know, however, is that the program has already caused an unprecedented government sponsored destruction of wealth. Associate Professor of Economics at the Naval Postgraduate School in Monterey, California, David Henderson explains:

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.