## Tuesday, September 9, 2014

### The rebound effect for a household that adds a car

Would the purchase of a Prius decrease fuel consumption if it is the second car in a household?    Let’s face it car pooling even with a person in your family can be inconvenient.   A second car makes separate trips convenient.   A second car that is a Prius makes second trips inexpensive.

Question:   A household with a Honda Pilot travels (21 mpg) travels 15,000 miles per year.   After the purchase of a second car the Toyota Prius (42 mpg) the amount traveled per year increases by 15%.   What percent of travel must occur in the Prius for this household to realize a decrease in gas consumption?

Data:

I need to do a better job documenting my fuel efficiency sources.

I relied on these fuel efficiency numbers in this post:

Fuel efficiency numbers for the Pilot:

Fuel Efficiency numbers for the Prius:

Answer:  Prior to the purchase of Prius the household uses 15000/21 or 714.3 gallons of gas.

Denote x amount traveled by pilot and 17250-x amount traveled by Prius.

714.3 = (x/21  + (17250-x)/42)

714.3 x 42 = 2x  +17250 –x

30000.6 = x +17250

x=12750.6

Plug 12750.6 into expression for fuel efficiency.

Note that

((12750.6/21) + (17250-12750.6)/42)  is equal to 714.3.

So if the Prius is driven over 26% of the time (17250-127750.6)/17250

fuel consumption will be lower in the Pilot/Prius household than in the Pilot household.