## Tuesday, October 7, 2014

### CAFE and alternative-fuel vehicles

Question One:  A manufacturer builds and sells 10,000 trucks that obtain 21 mpg.  In order to avoid a fine under the Corporate Average Fuel Economy Act the manufacturer must obtain a fleet average fuel efficiency of 23.5 mpg.    The EPA gives a fuel efficiency rating of 100 mpg to any truck that runs on alternative fuel.    How many alternative-fuel vehicles must the manufacturer sell in order to meet the 23.5mile standard and avoid the fine?

What are the policy implications of this finding?

Answer:   The manufacture must meet a harmonic average for his fleet.  He has two vehicles – one gets 21 mpg the other 100.    Sales for the 21 mpg truck are 10,000.   Denote sales of 100 mpg truck at X

FE = 23.5  = (10,000 + X) / (10,000/21  + X/100)

or

23.5 * (10,000/21)  + 23.5 * (X/100)   = 10,000 + X

23.5  * 10,000 /21  - 10,000  = X – (23.5/100) * X

or

X= 1557.

Part Two:  How many alternative fuel vehicles would the manufacturer have to sell if the conventional truck got 22 mpg?

At 22 mpg the company would need to build 892 alternative fuel vehicles.  (Just put 22 instead of 21 into the fuel efficiency equation for the fuel efficiency of the technical vehicle.)

Check the answer here:

 Things Check Cars Fuel Efficiency Car/Fuel Efficiency Check Truck 1 10000 21 476.1904762 Truck 2 1556.1 100 15.561 Total 11556.1 491.7514762 23.49987862 Cars Fuel Efficiency Car/Fuel Efficiency Truck 1 10000 22 454.5454545 Truck 2 891.3 100 8.913 Total 10891.3 463.4584545 23.50005679

Policy Implications:  Car companies that want to build gas guzzlers and not pay fuel efficiency fines might choose to build vehicles that run with alternative fuels.    Will a fuel efficiency regulation that provides generous credits for vehicles that run on alternative fuels help the environment?

Factors:

The gas guzzling trucks (which tend to be driven a lot of miles) will still be out there.)

Many of the alternative fuel vehicles (like pure ethanol vehicles) also run on conventional fuels.

Some of the electric vehicles cause downstream pollution.

Maybe yes or maybe no.  I don’t have a good sense of the answer to this final part.

Readers who want to learn more about how to calculate the harmonic average for a larger fleet should look at the post below.

Calculating fleet average fuel efficiency