The optimal gas needle

I learned yesterday that my gas needle is broken. It moves rather quickly to three-quarters of a tank, but is very sticky once it gets to half a tank. It used to be very sticky when it started on full. I could drive for two hours and it would remain on full the entire time.

I started wondering (actually I’ve been wondering this for years now) how an optimal gas needle should be structured. Assume that if a buyer has a bad experience with a car, such as running out of gas, he blames the car manufacturer with some probability. You might then expect that a car needle will stand on “Empty” long before the tank is empty. The needle makes you prematurely fearful and you are less likely to run out of gas.

You also might expect that the needle will be sticky at the top end of the register. Why?

When you fill your tank with gas, you have the clearest idea of exactly how much is in the tank. You are most likely to use observations from that point to gauge the fuel efficiency of the car. All other observations will be noisier. So the automaker wants to make a good impression about fuel efficiency right off the bat. This doesn’t require driver irrationality, only that you measure fuel efficiency with some imperfection. You’re never sure if the car gets great mileage or if the needle is just biased. But you attach some probability to the former. Economists call this a “signal extraction” problem. You suspect the needle is biased but you never know quite how much. (The technically-minded will note that once you introduce these information asymmetries, the assumption of rational expectations no longer rules out all kinds of errors; I first learned this from reading Joe Stiglitz.)

Furthermore some people refill their gas tank well before it gets to the bottom; they are just nervous nellies. These people will rarely observe the needle when it is on its path of swiftest descent. They observe how much they pay at the pump, but of course gas prices change all the time. They too will face a signal extraction problem and may overestimate the fuel efficiency of their car.

Some people will see through this entire business. But for them it doesn’t matter how the needle is structured. So a “sticky at the top” needle is most likely to induce a repeat purchase of the same kind of car.

Is this good? It may slightly limit competition in the car market. People stick with a brand because they think it offers better gas efficiency, when in fact it doesn’t. On the other hand, the practice makes the buyer feel good about his purchase. People think they bought a car with good mileage. The nervous nellies can rest easy. And the more irresponsible types are less likely to run out of gas.

So don’t forget the subtitle of this blog: Small ideas for a much better world.

Addendum: Of course as in most game theory you can spin alternate stories. Does this tempt you to switch disciplines? Just read Thomas Nagel’s recent essay on why there is something rather than nothing. Nagel is extraordinarily bright, but this is enough to bring you back into the fold.