[Update June 10: There are two personal benefits from Cash for Clunkers. One is the voucher. That one's clear. But the other benefit is the dollar value of the gas savings that result from a trade in. That one is less obvious because gas savings are a not a one-to-one function of MPG increases.
In many cases--especially for very inefficient cars--the savings in gas costs will be larger than the rebate. In that sense, the gas savings can be thought of as a kind of "matching" program for the voucher. It doubles the value of the voucher.]
The table below shows how different levels of Miles per Gallon (MPG) translate to Gallons per Hundred Miles (GPHM).You can easily calculate the gas savings from a trade in by subtracting the new GPHM from the old one.For example, trading in a 17 MPG car for a 28 MPG car saves 5.9 minus 3.6 = 2.3 gallons per hundred miles.That saves more than 200 gallons of gas (and $500) over 10,000 miles of driving. It also saves 2 tons of CO2 emissions over that distance. The gas cost calculations below assume that gas costs $2.50 per gallon.
To see the gas savings from a Cash for Clunkers trade in use the table from this May 29 post or go to the gallons per mile calculator at http://www.gpmcalculator.com to explore savings over different distances and gas prices.
The Obama administration has proposed raising CAFE standards from an average of 25 MPG in 2009 to 35.5 MPG in 2016. We applaud this improvement because it accelerates gains that were planned for 2020. Detroit has signed on. However, we note that MPG has again caused confusion. Many prominent sources have interpreted the improvement from 25 to 35.5 as "40% cleaner" and as cutting "tailpipe emissions by almost 40 percent."
Before exploring the percentages, it is important to note that CAFE math is hard to interpret in general because it describes the average new vehicle sold in the fleet that year, and does not adjust either for an increase in total vehicles sold or for increases in the miles driven, both of which will diminish actual CO2 benefits. With that caveat, here's the right way to think about the increase of the average car's MPG from 25 to 35.5.
It is true that there is a 40% improvement, which can be seen by taking the difference between 35.5 and 25 (10.5), and dividing it by 25. However, this number does not tell you how much cleaner the average car is in terms of CO2 emissions. Instead, it tells you how much further you can now drive in a new vehicle on the same gallon of gas. One gallon will now take you 40% farther than it did before.
To see the percentage reduction in CO2 emissions, you need to calculate the percentage decrease in GPM. In this case, it is (1/25 - 1/35.5)/(1/25), which is 30%. Thus, for an average car driven a mile in 2009 and 2016, there will be a 30% reduction in gas consumption and CO2 emissions. (Many sources do get this right.)
More generally, you can calculate the percentage changes for MPG and GPM as follows, where MPGhigh is the MPG for the new, more efficient car and MPGlow is the MPG for the old, less efficient car:
Percentage improvement in MPG = (MPGhigh/MPGlow) - 1 Percentage reduction in GPM = 1 - (MPGlow/MPGhigh)
And you can calculate the relationship between percentage reduction in GPM and percentage increase in MPG as:
GPM% = MPG%/(1+MPG%)
For example, a 100% increase in MPG reduces GPM by 50%. A 50% improvement in MPG reduces GPM by 33%, and so on. CO2 is reduced as a linear function of changes in GPM, not MPG.
Note that CAFE calculations, which are based on the harmonic mean of all vehicles sold by a manufacturer, inherently involve GPM. The harmonic mean is simply a weighted average of GPM that is then flipped and expressed as MPG.
Carolyn Fischer at Resources for the Future has written a brief describing several benefits of switching from MPG to GPHM ("gallons per hundred miles"), including the ability to administer CAFE credits. The government routinely uses GPM for these calculations; why not make it a general practice?
Thanks to Frank Wang and Drew Carton for pointing out these misinterpretations of the CAFE increase.
Senators Feinstein, Snowe, and Schumer have proposed a Cash for Clunkers bill in response to the House compromise of May 5. Full details of the Senate bill are at the end of this post.
Here's a summary from a "GPHM" perspective:
This is a much stronger plan than the House compromise in terms of CO2reductions. It is stronger for two reasons.
Second, the system is more tiered than the House bill, encouraging drivers to seek higherlevels of gas savings, but giving them the option to choose any levelthey wish above a responsible minimum.
I think the new bill does a decent job of setting a minimum (closer between 1 and 2 GPHM) and providing tiered incentives for larger reductions in GPHM.Here's how the new trade ins compareon gphm (voucher value in parentheses):
Cars
17 to 24 saves 1.7 gphm ($2500)
17 to 27 saves 2.2 gphm ($3500)
17 to 30 saves 2.5 gphm ($4500)
Light trucks
17 to 20 saves .8 gphm ($2500)
17 to 23 saves 1.5 gphm ($3500)
17 to 26 saves 2 gphm ($4500)
Large light duty trucks *
(*This category has no maximum mpg for the old vehicle and simply requires that the new truck meet a minimum of 17 mpg. I picked a high starting mpg value for the old car, 16, to make this a more conservative test of gphm savings. A lower mpg value on the old vehicle would yield substantially greater gphm savings for the same mpg increments of 3, 5, and 7.)
16 to 19 saves 1.0 gphm ($2500)
16 to 21 saves 1.5 gphm ($3500)
16 to 23 saves 1.9 gphm ($4500)
The only increase that seems too small is the 17 to 20 mpg gain on lighttrucks, yielding less than 1 gallon saved per 100 miles.
This is where the MPG Illusion and the use of GPM is critical. Manypeople might think that the MPG increases on the Large Light Duty Trucks are unimpressive--starting at 14 and then moving to 17, 19, and 21. Butthose gas savings are greater than the savings produced by larger MPGincreases on the Light Trucks (from 17 to 20, 23, and 26).
The night and day difference between this Senate bill and the House bill is the requirements forLarge Light Duty Trucks. This bill is fairly responsible in thatcategory.
Here's a cut and paste of the May 19 fact sheet:
The revised “Cash for Clunkers” proposal introduced today would ensure that vehicles purchased under the program do not bring down the fleetwide averages that the Ten in Ten Fuel Economy Act intended to raise.
Feinstein-Collins-Schumer Counter Proposal
Passenger Cars
Light Duty Trucks
Large Light Duty Trucks (6000-8500 pounds)
Work Trucks (8500 to 10,000 pounds)
Minimum Fuel economy for purchased vehicle
24 mpg
20
17
n/a
$2,500 for new vehicle purchase, $1,000 for used vehicle purchase, 2004 model year or later
Mileage improvement of at least 7 mpg
Mileage improvement of at least 3 mpg
Mileage improvement of at least 3 mpg
Trade-in work truck must be pre-1999 model (used cars not included)
$3,500 voucher for new vehicle purchase
Mileage improvement of at least 10 mpg
Mileage improvement of at least 6 mpg
Mileage improvement of at least 5 mpg
n/a
$4,500 voucher for new vehicle purchase
Mileage improvement of at least 13 mpg
Mileage improvement of at least 9 mpg
Mileage improvement of at least 7 mpg
n/a
Trade-in vehicles must be 17 mpg or below. All fuel economy values are EPA combined city/highway fuel economy, as posted on the window sticker of new cars.
Details of Feinstein-Collins-Schumer Counter Proposal
Consumers may trade in their gas-guzzling vehicles to be scrapped – with a fuel economy of less than 17 miles per gallon – and receive vouchers worth up to $4,500 to help pay for the purchase of more fuel efficient cars and trucks. The program will be authorized for up to one year and provide for approximately one million new car or truck purchases. There are approximately 27 million vehicles on the road today that could qualify for trade-in under this program.
This proposal is consistent with the framework of the House compromise legislation, and divides the cars and trucks that would be purchased with the incentive voucher into four categories. Miles per gallon figures below refer to EPA “window sticker” values.
· Passenger Cars: The trade-in vehicle must get 17 miles per gallon (mpg) or less. New passenger cars with mileage of at least 24 mpg – the current average for this vehicle class – are eligible for vouchers.
o If the mileage of the new car is at least 7 mpg higher than the old vehicle, the voucher will be worth $2,500 for a new car purchase.
o If the mileage of the new car is at least 10 mpg higher than the old vehicle, the voucher will be worth $3,500.
o If the mileage of the new car is at least 13 mpg higher than the old vehicle, the voucher will be worth $4,500.
o The purchase of a used passenger car with a mileage of at least 24 mpg would qualify for a voucher of $1,000.
· Light-Duty Trucks: The trade-in vehicle must get 17 miles per gallon (mpg) or less. New light trucks, minivans or SUVs with mileage of at least 20 mpg – the current average for this vehicle class – are eligible for vouchers.
o If the mileage of the newly purchased truck or SUV is at least 3 mpg higher than the old truck, the voucher will be worth $2,500 for a new vehicle purchase.
o If the mileage of the newly purchased truck or SUV is at least 6 mpg higher than the old truck, the voucher will be worth $3,500.
o If the mileage of the newly purchased truck or SUV is at least 9 mpg higher than the old truck, the voucher will be worth $4,500.
o The purchase of a used light-duty truck or SUV with a mileage of at least 20 mpg would qualify for a voucher of $1,000.
· Large Light-Duty Trucks: Newly purchased large trucks (pick-up trucks and vans weighing between 6,000 and 8,500 pounds) with mileage of at least 17 mpg – the current size-adjusted Corporate Average Fuel Economy Standard for the largest pickup trucks – are eligible for vouchers.
o If the mileage of the newly purchased truck is at least 3 mpg higher than the old truck, the voucher will be worth $2,500.
o If the mileage of the newly purchased truck is at least 5 mpg higher than the old truck, the voucher will be worth $3,500.
o If the mileage of the newly purchased truck is at least 7 mpg higher than the old truck, the voucher will be worth $4,500.
o The purchase of a used large light-duty truck with a mileage of at least 17 mpg and 3 miles per gallon higher than the trade-in vehicle would qualify for a voucher of $1,000.
· Work Trucks: Under the proposal, consumers can trade in a pre-1999 work truck (defined as a pick-up truck or cargo van weighing from 8,500-10,000 pounds) and receive a voucher worth $2,500 for a new work truck in the same or smaller weight class. There will be a limit on these vouchers, based on this vehicle class’s market share. There are no EPA mileage measures for these trucks; however, because newer models are cleaner than older models, the age requirement ensures that the trade will improve air quality. Consumers can also “trade down,” receiving a $2,500 voucher for trading in an older work truck and purchasing a smaller light-duty truck weighing from 6,000 – 8,500 pounds.
