Friday, October 03, 2008

When Is More Expensive Gas Cheaper?

With the cost of gas going up so much there has been one benefit. I no longer worry about trying to go to out of my way to the station with the cheapest prices anymore. Figuring out how the cost plays mathematically makes it so that sometimes it's actually cheaper to pay a higher gas price.

Let's say your on your way home and you need to buy gas, and there's a gas station coming up, but you know they charge a little more than other stations. So initially you might think it's worth driving to one of those other stations to save some money, but that might not be the case.

First, figure out how far out of your way (total) you'll need to drive to get to the other gas station. Take that number and divide by the average number of miles per gallon you normally get. Then multiply that by the price of the gas at the current station. This gives you an estimate for how much money it would cost to simply drive to the other station. So take that value and divide by the number of gallons you foresee having to purchase, this will give you the approximate number of how much cheaper the gas needs to be at the other station just to break even (effectively this is the amount of cost savings on the price per gallon that would be consumed in the drive to get to the other station).

So let's walk through an example. The station on my way home from work sells gas for $3.54, but I know there's another station 2 and a half miles away from my house that sells it for $3.48. What should I do? Let's run the numbers.

The miles out of my way is actually 5 miles since it's in the opposite side of my house and I would have to drive there and back. And while my car gets about 28 or 29 miles to the gallon on the highway, it's terrible with stop and go driving and probably only gets about 20 mpg in my daily commute (if I'm lucky). And my car will take about 15 gallons if I wait until the refuel light comes on.

So that's:

(Miles Out Of Way You Have To Drive) / MPG * Price / Gallons

5 / 20 * 3.54 / 15 = 0.059 or about 6 cents.

So in this case I save basically no money whatsoever by driving to the other station even though it's 6 cents cheaper. And while I would break even, I would waste more of my time going out of my way to the other station. Once you start applying a threshold of pain for your time it suddenly becomes even easier and more cost effective to simply pay the higher price. If the cost at the other station is $3.45 then I'm saving 3 cents a gallon which for 15 gallons is 45 cents. Driving that extra five miles out of my way might take almost ten minutes, is it worth losing almost ten minutes you could be doing something else to save 45 cents?

Now, I'm not saying you should always just pay the higher price, but your circumstances will certainly dictate when it makes sense. Obviously if you can continue driving and there's a cheaper station on the way home it makes much more sense to go to the other station (since miles out of the way in this case would be 0 the whole equation goes to 0). The whole point of this is to see that with gas prices as high as they are driving anywhere out of your way wastes more money than you can hope to save. What this means is you happen to be driving in the area of the cheaper station you should fill up even if you're not at the point where you really need to, because if you have to drive out of your way once you need to, you won't get any benefit from it. And usually all gas stations are within about 10 cents of each other so there's very little potential benefit to be gained if you have to go out of your way at all.

I have no idea why I think of things this way.


Anonymous said...

math geek lol!

wtfree3 said...

Been there, done that...already know what my standards are. (People already know I'm a math ubergeek, working things out in my head.)

I usually just make sure that I have errands over in the area of cheaper gas when the need for a refill happens. Then, it all works out. Plus, I generally run about a week on a tank of gas, so it's easy for the weekly shopping to get filled up.

CAPT_Sawyer said...

Cost To Drive