Congestion Pain Is Hyperbolic

When dealing with overloaded capacity, small causes have enormous effects

If you Google “congestion is hyperbolic,” the results you get are a bunch of pages full of very dense mathematical jargon and equations. They show various studies that are likely to go over most people’s heads. They sure go over mine! But while the methodology and details are incredibly complicated, the finding isn’t, and it’s important to understand: the pain of an overloaded system exhibits hyperbolic growth.

Think back to high school math for a moment. A hyperbola is a graph with a sharp “hockey stick” bend in it. It transitions very abruptly between mostly-flat horizontal and mostly-flat vertical. And researchers have found that a graph of the performance of an overloaded system looks like a hyperbola.

What do you mean, “an overloaded system?”

Imagine you’re at home and you have to get to another city. It’s about half an hour away, if you’re able to take the freeway and go the speed limit. And if you’ve spent any amount of time behind the wheel, you know what this looks like. If traffic is light, you have no trouble going the limit. You’re probably even familiar with “medium traffic,” where the road feels like it’s full of vehicles, but you’re not getting slowed down. But then sometimes you get into traffic jams that slow everything to a crawl, and it doesn’t really feel like traffic is all that much denser than in medium traffic, but suddenly you’re doing 15 instead of 60 or 70 and your half-hour trip takes two hours.

Well, it turns out that when you feel like the traffic isn’t that much heavier than medium traffic, this isn’t an illusion or a cognitive trick or any of those errors smart people love to talk about. Traffic really isn’t that much heavier. That’s the problem: it doesn’t need to be.

Let’s imagine that a road has a property we’ll call “easy capacity,” and the stretch of road between your starting point and your destination has an easy capacity of 1000 cars. As long as there are less than 1000 cars along that stretch of road, you’re in the blade of the hockey stick, and everything’s good. But once you hit 1000, you’re at the inflection point. Add another 50 cars to the road, and things don’t get 5% worse; they get much, much worse and suddenly your drive time is 2-3x longer. The road has become overloaded. Studies have found that hyperbolic congestion doesn’t just apply to cars on roads; you see similar phenomena anywhere you have a hard limit on the capacity of some resource.

Why are you writing about this?

Because we have a lot of resources with hard limits on capacity, and people are making a political issue of them without understanding this point.

You’ve probably heard about sky-high prices for Taylor Swift tickets lately. It’s been hard to miss, even if you’re not a fan of Taylor Swift. People claim that TicketMaster’s monopoly power is to blame for prices going well into five figures, to the point where some politicians, ever eager to be seen Doing Something, have announced investigations into their business practices.

Out of curiosity, I looked up her current tour. It looks like she’s got two shows in Seattle this weekend, at a venue called Lumen Field. According to Google, Lumen Field has a capacity of 68,740 seats. There are over 4.1 million people in the Seattle metropolitan area, so Lumen Field has the capacity to hold approximately 1.67% of that population.

There are two shows. Just for simplicity’s sake, let’s say nobody goes to see her twice, and nobody from outside the Seattle metropolitan area comes to see her. We still have a hard limit on capacity: only about 3.36% of the population will be able to get a seat because that’s all that’s available, and she’s popular enough that it’s a safe bet that there’s more than 3% of people who’d love to see her in concert. If there are more Taylor Swift fans than that in the Seattle area… well, I’m no fan of TicketMaster or of monopolies in general, but in this particular case, the principle of hyperbolic congestion graphs tells us that ticket prices are going to shoot to the moon anyway, no corporate malfeasance necessary.

So this is about concert tickets?

Concert tickets aren’t the only “how many people do we have space for?” question. Let’s talk about something a lot more fundamental: housing. Everyone needs a roof over their heads, but there are only so many roofs available. A capacity limit exists to the number of people we can house in any given area. And you hear a lot of complaints recently about how much housing costs, both for renters and for homebuyers.

I’ve mentioned on here before about the way Obama Administration policies reinflated the housing bubble by throwing easy money at the perceived problem, but that’s not the only factor contributing to high prices. There are three other political problems that are making everything significantly worse: natural supply reduction, artificial supply reduction, and The Big One: illicit demand.

1. Natural supply reduction. A lot of places have laws and policies that reduce the amount of housing that can be built. Virtually everywhere has zoning laws these days, and that’s not necessarily a bad thing, but that’s not all there is to housing policy and some policies are significantly worse than others. (Oh hi, California!)

2. Artificial supply reduction. In an ideal world, every house would either have people living in it or be available for people to buy and live in. Sadly, that’s not our world, because we have speculators. Between house flippers buying up houses in a bubble and hoping to resell them to a greater fool, investment firms buying up real estate left and right, and foreign nationals parking money in American housing to try to get around capital controls, there are a lot of people making a lot of homes impossible to buy because they’re treating these houses as investments rather than homes.
   Have a look at this speech by Ron DeSantis. When he talks about his various policy achievements as Governor of Florida, you could probably guess beforehand that his work to protect children from the various harms targeted at them by Leftist institutions would get the most applause and cheers from the audience, and it does. But would you have ever suspected that the enthusiasm would be just as strong when he mentioned banning “land purchases by entities controlled [by] or related to the CCP”? Some of that’s just that we know the CCP is evil and we don’t want them having any more influence here at home, but I think at least some of it is that people recognize that the scarcity is being made worse by people taking housing off the market for purposes other than living there.

3. Illicit demand. Remember when I said that on an overloaded highway, adding an extra 5% worth of cars will make the drive times worse by far more than just 5%? The population of the USA is currently about 332 million. 5% of that is 16.6 million. And well… anyone want to guess how many illegal immigrants are currently in the USA, taking up housing just like anyone else?
   Even Leftists are finally starting to wake up to the problem here. Look at the way New York City and Chicago have been screaming about the problems of trying to pack a few small busloads of illegals into their millions-upon-millions of capacity. NYC is now paying for signs at the border trying to discourage illegals from coming to their “sanctuary,” specifically because they don’t have room and housing is too expensive. At this point Democrats are out of excuses. Any politician who tells you they care about housing prices, but refuses to secure the border and take aggressive action to deport illegal immigrants, is lying through their teeth.

So this is all about housing?

It’s about bad policies causing severe pain where there are hard capacity limits. To come full circle, let’s talk about traffic in the greater Seattle area.

If you visit Seattle today, or have done so basically any time in the last 20 years, you’ll probably come away with the impression that the local highway system is one big perpetual traffic jam. (It’s not quite as bad as, say, LA or Washington DC, but that’s not saying much!) But it wasn’t always like that.

Back in the 90s, traffic in western Washington was pretty decent. But then a libertarian demagogue named Tim Eyman started making trouble. He started pushing a citizens’ ballot initiative that would cap car tab fees at $30/year, no matter how expensive a car you were driving. People who were actually paying attention were almost unanimously horrified by this idea, because what he was looking to reduce wasn’t your typical “government waste” at all; that revenue was being used specifically for state highway funds. They warned that, since you can’t not pay for basic tasks like road maintenance, the revenue shortfall would have to come out of mass transit funding, which would lead to horrible traffic congestion. Eyman and his supporters laughed, calling these predictions slippery slopes and telling everyone to just think of how much money they’d save. And sadly, it worked.

The $30 car tabs initiative passed in 1999, and a whole lot of buses got taken off the road, forcing a lot of people who would have ridden the buses into cars. There weren’t all that many people on those buses, relatively speaking, but it only takes a small percentage increase to push a busy highway from medium traffic to overloaded. Congestion and commute times skyrocketed, exactly as predicted.

And here’s the truly crazy part. Let’s do a little bit of math. A car’s engine burns close to a gallon of gas per hour just for being on, even if it’s just idling. If the additional traffic adds just 15 minutes to the length of your commute, you’re idling for an extra half hour every day. Approximately 260 working days per year, that’s at least 130 gallons of gas going up in smoke. At an average gas price of $1.17/gallon in 1999, commuters were losing $152 of their car tab savings on extra traffic alone. (And most people had far more than just 15 minutes added to their commute!) But how much were they saving? Well, the excise tax was 2.2% of the value of the car. The average price of a car in 1999 was $20,710 for a new car, $8,828 for a used car, so the car tab tax was under $500 for people who could afford to buy a brand new car, and under $200 for most everyone else. If your bill went from $200 to $30, you think you’re saving $170, but then you lose 90% more of that in additional costs of gasoline… it’s not such a big savings afterall. (And is the time wasted in traffic really worth the money?)

Also, if you’re paying attention, you might have noticed something in the paragraph above. Gas at $1.17?!? Well, yeah. This was before 9/11. This was right before 9/11, in fact. Tim Eyman’s initiative had been around less than two years before gas prices shot through the roof and never recovered. And traffic in Seattle remains miserable to this day.