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.