Monday, February 23, 2009

Buick or Toyota? You make the call.

If I am an energy-conservation-minded consumer who can't afford to buy a new car, should I rent a 10-year old Buick ($200/year, 20 miles per gallon) or a 10-year old Toyota ($600/year, 40 mpg)? What does my choice depend upon? Explain. (Hint: How many miles would you have to drive each year for the Toyota to become more cost effective than the Buick?)

Congratulations to Andrew Bolton for being the first to provide a correct answer. This question (with a few modifications) came from Robert Frank's Microeconomics and Behavior text. Frank writes that it depends on how many miles you expect to drive:

The impulse of many conservation-minded consumers is immediately to choose the Toyota because of its better gas mileage. But there are only so many used Toyotas to go around. Suppose there are a total of 1000 Buicks and 1000 Toyotas. If I rent a Toyota instead of a Buick, someone else will have to rent a Buick instead of a Toyota. If my goal is to save energy, I should take the Toyota only if the person who will end up with the extra Buick is someone who drives fewer miles each year than I do.

But how can anyone possibly know whether that would happen? If the rental rates of the two cars are determined in the open market-place, and people generally pick the kind of car that minimizes their total driving expenses, we can say this: My choosing the Toyota will reduce society's energy consumption if and only if the Toyota is cheaper for me than the Buick. To see why, first note that if gasoline costs $2 per gallon, the yearly cost of the Buick is given by Cb = $200 + 2M/20 where M is the number of miles I drive each year. The corresponding cost of the Toyota is Ct = $600 + 2M/40. These two costs will be exactly the same if I happen to drive 8000 miles (set Cb = Ct and solve for M). If I drive more than 8000 miles, the Toyota is cheaper for me; if I drive less, the Buick is cheaper.

But how do I know that the person who rents the Toyota I could have rented won't be someone who drives even less than I do? If everyone follows the rule "drive the cheapest car," this clearly cannot happen at the given rental rates. (If the Buick is cheaper for me, it will also be cheaper for someone who drives fewer miles per year than I do.) But what if half the drivers, including me, drive 4000 miles a year while everyone else drives only 3000? If that were the case, then everyone would find the Buick cheaper at the current rental rates. No one would want to rent a Toyota. Rental companies would then discover that they could boost the prices on their Buicks substantially and still manage to rent them all. By the same token, they would have an incentive to cut the rental rates on their Toyotas, rather than watch them gather dust in their parking lots. In the end, the rental rates of the two cars would adjust so that the Toyotas are cheaper overall for the heavy-mileage drivers, the Buicks cheaper for the light-mileage drivers.

1 comment:

Andrew Bolton said...

You would choose the buy the Toyota over the Buick only if you plan to drive it over 8,375 miles in the next year. This assumes that gas prices stay fixed at today's (2/23) regular average of $1.91 (taken from http://www.fuelgaugereport.com/). If you drive that many miles, then you will break even on the $400 rental cost difference between the two cars because of $400 saved on gas due to fuel efficiency. If you plan on driving under 8,375 miles, then you should rent the Buick because the Toyota would not be driven enough to achieve gas savings that cover the difference in the cost of renting the cars.