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
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