Ignoring the Keynesian Demand benefits for New Car makers, what is the payback period for the Cash for Clunkers payment of $4,500 measured solely in terms of reduced carbon emissions? My algebra suggests that it is 25 years or more and that's not too good.

UPDATE: Here is another set of calculations on this topic: Here is a Similar Exercise

UPDATE AGAIN: OK, I now realize that I am not the world's leading expert on C4C. This piece is also worth reading. Maybe, I should return to griping about my pay cut?

Let's make some assumptions:

1. Regardless of vehicle fuel economy, a household drives M miles

2. the interest rate equals zero

3. the marginal social cost of an extra ton of co2 equals $35

4. each gallon of gasoline consumed creates 23.5 pounds of carbon dioxide

5. The average household's vehicle that is scrapped achieves 15 MPG

6. This household buys a vehicle that achieves 30 MPG

The annual dollar value of the carbon externality when the household owned the "Clunker" = (M/15)*(23.5/2000)*35

The annual dollar value of the carbon externality when the household now owns

a "green car" = (M/30)*(23.5/2000)*35

The change in the household's annual externalty = -(M/30)*(23.5/2000)*35

Solve for N such that: $4500 - (M/30)*(23.5/2000)*35*N = 0

and N is the break even number of years. For any M that equals roughly 12,000 miles N is going to be a huge number. Note that if the interest rate is positive, N must be an even bigger number. N represents the number of years that the green 30 MPG vehicle must be driven.

Example: suppose M = 15,000 and N = 10 ; so the household drives the green vehicle for 10 years and then scraps it;

4500 - (500)*(23.5/2000)*350 = $2,443. In english this means that the cumulative carbon benefits from the "greening" of this vehicle and driving it for 10 years in an economy with a zero interest rate only gets you half way to the subsidy!

that is ugly.

If we value carbon at $75 a ton ,then these numbers will look better.

## 5 comments :

You're obviously going to great lengths to be favorable to C4C throughout, but that last calculation (M=15k, N=10) goes so far as to assume that the clunker would have stayed on the road for another 10 years without being replaced. These numbers start to look very bad indeed...

Here is another more simplistic estimation:

http://www.slate.com/id/2224306/

And here's a tool to do Matt's math (and to substitute your own assumptions as you see fit!)

Depending on the location, excessive HC and NOx emissions are quite expensive, at least based on the incentives offered by CARB and the SCAQMD. $1000-$1500 cash for vehicles that have failed smog or are smog exempt (diesels and vehicles manufactured before 1976) in CA, and as of 2010, another $2000-$2500 in dealer credits that can be used on a vehicles up to eight years old in the SCAQMD for vehicles that are smog exempt and specific vehicles that have high emitter profiles. This pollution depends widely on the region, so I doubt we could apply the same figures in the same manner to the rest of the U.S. but it implies that the reduction of other types of pollution have significant cost benefits.

That said, as usual I have more questions than info. Is $35/ton a good approximation of the weight average for carbon prices in the long run? This article states that in about a decade the price will be probably be $50-70/ton, possibly more in the long run as the impacts of GCC start to become more apparent. Is there any financial benefit to reducing the flow of cash from the U.S. to foreign countries that may not be very friendly and spending it on other things in the country?

some other numbers

Here’s some math from stories ballyhooing the fact that the average clunker got 15 mpg and the average replacement gets 25…

· A vehicle at 15 mpg and 12,000 miles per year uses 800 gallons a year of gasoline.

· A vehicle at 25 mpg and 12,000 miles per year uses 480 gallons a year.

· So, an average clunker transaction reduces U.S. gasoline consumption by 320 gallons per year.

· The total is about 700,000 vehicles – so that’s 224 million gallons/year.

· That equates to a bit over 5 million barrels of oil.

· 5 million barrels of oil is about ¼ of one day’s U.S. consumption.

· And, 5 million barrels of oil costs about $350 million dollars at $75/bbl.

· So, we all contributed to spending $3 billion to save $350 million.

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