Monday, June 22, 2009


Economists love models. They luuuuurve models. In fact, models are to economists the way mudkipz are to anonymous. Some of the models are simple, straightforward affairs, such as ye olde law of demand, while others can be massive, multivariable monstrosities replete with scary-looking matrices and bone-chilling equations that, in other circumstances, might explain the origins of the Universe. Whatever the interesting phenomenon however, as long as it involves the interaction of people, you can slumber in comfort knowing that somewhere, there is some economist ready to man the trenches and provide the world with a mathematical interpretation of the goings-on.

In contrast to the luuuurve economists have for models, most drivers have an abiding hatred for traffic. It's a loathsome irritant, a delay, a fly in the ointment, a nettlesome, needling, noisome bother that all motorists have to put up with at one time or another.

I won't bother to catalog the differences in driving styles here. I'm sure anyone reading this has read a Dave Barry column or something similar in the past, and can well imagine how to caricature doddering grannies, gun-rack libertarians, NORP commuters, and enraged mall punks. The point is, we have a heterogenous blend of drivers on our roads, each with their own preferences, patterns, and peccadilloes.

I feel I should pause here for a moment to explain one of the foundations of economic thinking: margins. If you've been through an econ course or two, you've likely been browbeaten into thinking on the margin. If not, you should have been. Margins are simply what happen at the cusp of indifference. That should clarify things. Let's move along.

Just joshing. Oh, what a splendid jape. Let me be more clear. Any time when large groups of people interact, the interaction produces changes. The interesting thing is that these changes happen with a relatively few number of actions. For example, imagine a busy restaurant. Say, 50 covers for dinner. Naturally, there will be some level of background noise, from diners eating to kitchen noise to music to what-have-you. If but one table begins a conversation, there is an increase in overall noise experienced by everyone in the restaurant. Interesting, eh? We see this phenomenon everywhere. The standard classroom usage is with prices. If you raise the price of apples by a penny, there will be some people on the margin who will stop buying apples. This is a marginal change and the people who stop buying apples are marginal consumers. It is they who define the environment and they who determine prices (and I use a very broad definition of "prices" here). In the context of traffic decisions, we have a few types of marginal drivers: those who change lanes, hoping for faster travel; those who exit and enter the system; and those who create noise. I'll explain the latter later. The lane-changers are the interesting folks, so I'll spend a bit more time illustrating how they affect the dynamics of a traffic jam.

Let's start the way all economists start: we'll build a road (don't let the title and the tenure fool you; economists are actually well-dressed construction workers). We'll start with a simple 2-lane road with no exits, no blind curves, and nothing blocking the smooth flow of automobiles. Got that built? Well done. Crap. I just splattered ice cream on my shirt. Okay, ice cream notwithstanding, let's put some drivers on this sucker. No sense in having empty roads, right Ted Stevens? We'll say in our model that one lane holds 50 cars per minute. That is to say that at the average driving speed, any given point along the road will see 50 cars pass in one minute. No problems so far, but what happens when we double the number of drivers that want to use the road? We have to increase the traffic density, say, by double. Now, at a given speed, this means less following distance. Invariably, with an upper limit on speed (which there will be for any number of reasons), this leads to congestion, slowdowns, and short tempers.

Enter the next lane. With two lanes to choose from, we are back to a situation where each lane once again holds 50 cars per minute. No sweat. We can keep adding cars and lanes until we've got, say 4 lanes of 50 car per minute traffic, all zipping along, happy as clams on the road to nowhere. This is kind of boring. Let's add a little chaos. Let's add some exists, and maybe a David Byrne concert at the fairgrounds. The concert lets out and a monsoon of middle aged tax accountants and barbers hits the road in their Pontiacs and Mitsubishis. As they merge into the right lane, they greatly increase the density in this lane, creating an incentive for motorists there to switch to a relatively sparsely populated lane. These shifts propagate as the density information gets transmitted throughout the system. Well, at first, it's easy to see that it makes sense to move over a lane. There is clearly no sense in traveling in a lane moving at 20 mph when there's one going 60 a mere flick of the wrist away. The cost of switching lanes is small (though it does exist), and the benefit is quite noticable. However, a half mile down the road, things have started to even out, and the lane differentials are lower. Yet, we still see the North American Weaverbird, switching lanes madly, edging for that small advantage, hoping to make good time, despite only moderately discernible differences in average lane speed.

This driver is what we call an arbitrageur. We see this same sort of behavior in financial markets. These are the people who look for small differences in price in order to make profits from sytemic irregularities. In the stock market, they are the marginal actors, and prices swirl around their skirts as they drive inefficiency out with the ruthlessness of a rat exterminator or a Britsh Schoolmaster. On the roads, they provide much the same function. By exploiting small differences in the density of traffic in each lane, they help to provide uniformity across every lane. They are why if there's an accident in the right lane, the traffic in the left lane slows down.

The typical economic explanation stops there. Often glossed over are the hidden cost of traffic arbitrage. I can tell you from my own driving experiences that these drivers put the rage back in arbitrage. They are the buttholes who cut you off just when you manage to get a confortable driving distance, or who leapfrog across three lanes just to pass one car, then swerve back over, tracing a pattern that would dizzy a professional seamstress. To use more economic jargon, these are externalities, costs imposed on others. Sometimes, they occur as actual threats to safety and can produce collisions (though distracted and drunk driving probably poses more of a threat), or as irritants, as we fume at the aggressivve jerk who just tore ahead of us, zipping back and forth. The former is pretty clearly illegal under reckless driving statutes and the tort of negligence, while the latter, though annoying, is well within the purview of the law (which is probably why we find it so infuriating).

Well, take heart, for even though that aggressive jerk can get on our nerves individually, by exploiting arbitrage opportunities for his own gain, he is providing a valuable service for the rest of us by eliminating lane speed differentials and allowing the rest of us non-marginal drivers to coast along in our own lane, fairly well confident that, on average, we won't be much better or worse off than in any other lane. Those guys do all the adjusting, so that we can enjoy one price. The only thing we have to worry about is whether or not we choose to drive or take the train, or bus, or camel, or teleporter. My advice is to just relax, listen to some Vivaldi (or Slayer [or both]) and realize that even if that douche in the Toyota just cut you off, you'll still get where you're going at pretty much the same time anyway and that you spend more time at red lights than you can reasonably expect to make up by going 5 mph faster on the freeway. Or something. Try the math yourself.

Also, this whole lane change thing makes for a rather interesting mathematical model. You can assign probabilities to gains made from lane changes, quantify costs, add in the noise term, and do all sorts of cool shit with the numbers. I might keep this in mind for a term paper later on.

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