How to Buy Gas, Part 1

Most people spend a sizeable amount of money on gasoline -- and several hours at the gas station over the course of a year.  Given that fuel economy is on people's minds, let's look at the economics of filling your gas tank.  In particular, how often should you go to the gas station, and how much gas should you buy when you go?

Let's say your time is worth $12 per hour after taxes (probably a serious understatment for most Applied Genius readers, but it makes the calculations work out nicely.)    Your gas tank holds 20 gallons (that's approximately 75.7 liters, for non-US readers.)   Your car gets 25 mpg average fuel economy; you drive 300 miles per week (using 12 gallons per week, even though Virginia Postrel thinks you're a gas hog.)  It takes 5 minutes to do your "gas errand", which includes pulling into the gas station, waiting your turn, pumping gas, flirting with the cashier, getting a cup of coffee (and, heaven forbid, a lottery ticket), etc. 

There is a downside to hauling too much gas around; a gallon of gas weighs 6.2-6.3 pounds, and the US Department of Transportation says that each 125 pounds of extra weight reduces gas mileage by 0.3 mpg.  (I won't translate that into kg and km/l, but you get the idea.)  In addition, let's assume that you expect that gas is going to be cheaper in a few weeks when you next fill up; let's be optimistic and assume that you think that the price-per-gallon will decline $0.01 per day for the next two weeks or so.

In operations management, the technique to solve this problem is called the Efficient Order Quantity (EOQ).  Originally developed in 1915, it came to many managers' attention in 1935(!) via an article in Harvard Business Review.  Economists William Baumol (1952) and (later, Nobel Laureate) James Tobin (1956) used it to estimate how much cash households needed for their day-to-day purchases (and Greg Mankiw once told me a very funny example about how seldom graduate students should use an ATM, in the same vein as this analysis.)  In EOQ terms, the mpg penalty of extra weight is a carrying cost, as is your expectation that gas will be cheaper next week.  Of course, the average driver fills up their tank waaay too often, just as the average student goes to the ATM about 10-15 times as often as is optimal.

Performing an EOQ analysis on this problem indicates that the cost of time spent at the gas station ($1 per stop) is waaaay bigger than the extra cost of a fuller tank, including both the effects of reduced mileage and buying at the high price.   In short, you should wait as long as you can, coast in on empty, and fill 'er up even though you know it'll be cheaper tomorrow.  (Of course, if you're coasting in on empty, you can hardly wait until tomorow unless you have a bus pass, too!)

I should note that you'd be much better off with a larger gas tank (my preliminary calculations indicate that you'd be willing to buy a little more than 74 gallons at a time if your tank could hold that much.)  Even when you buy only 20 gallons at a time, you're acting as if your precious time is worth only $0.85 per hour!  It puzzles me why smaller gas tanks are so popular in new car models; sure, they improve fuel economy, but they positively destroy overall filling-up economy by wasting time.

I should also point out that the 5% rebate on gasoline from a smart credit card is worth $93.60 per year to the consumer in this example, whereas having a magical ability to buy gasoline a little at a time, on an as-needed basis, without spending any time at the gas station (or suffering any fuel-economy penalty) is worth only about $32 per year.  If you haven't succumbed to my blandishments on smart credit cards yet, now would be the time!

Next week I'll be taking a look at how to find good prices for gas (without spending all your time, and gas, cruising around.)