David Alpert seems unhappy with Virginia’s HOT lane plan. It’s certainly not perfect, but in my view any step toward educating drivers that they should pay to use roads, and that paying to use roads can lead to improved traffic flow, is probably a good one. But let’s address this:

Right now, traffic generally moves swiftly in the HOV lanes, giving sluggers and bus riders a quick ride to the Pentagon, downtown, and other major job centers.

Once Transurban takes over control of the lanes, they will understandably want to maximize their profit. The more people pay a toll, the more money they make. The more cars enter the lanes, of course, the slower traffic will move. However, as long as the lanes are moving even moderately faster than the often very crowded free lanes, enough people will pay tolls.

Therefore, Transurban’s natural profit motive will be to fill up the lanes as much as possible, but only until traffic slows down to the point where people stop paying for the extra benefit. If that means that the carpools and buses are driving 10 miles per hour slower than they do today, well, those carpools and buses aren’t their customers. They’re not paying tolls. So who cares?

The thing is, the mechanism used to increase or decrease the flow of cars into the HOT lanes is the level of the toll. So if Transurban is allowing more cars in, then it’s doing so by reducing the toll rate. One hundred cars paying a $3 toll is better for Transurban than 250 cars paying a $1 toll, so it’s far from clear that it’s in Transurban’s interest to drop the toll rate, let more cars in, and slow traffic.

The key factor here is the elasticity of demand for a congestion-free commute. Highly elastic demand means that drivers respond a lot to a small change in price. In this case, there’s little room for Transurban to increase the toll, because a small rise in the toll leads to a big drop in use of the toll lanes, which hurts profits. BUT, a small drop in the toll leads to a big increase in use of the toll lanes, which causes them to rapidly bog down. Remember how congestion works — as more cars enter a road traffic slows, which reduces the carrying capacity of the road, which causes traffic to slow. When a tipping point is reached, the road flips from free-flowing to congested. Given elastic demand, Transurban will price the lanes just above that tipping point, plus a safety margin so that roads generally flow well. In this case, the company just doesn’t have a lot of room to move the toll around.

But note that in this case, there aren’t many drivers who place a large value on the congestion-free commute relative to the congested commute. And if that were actually true, it would undermine the idea that there’s much value in the HOV lanes themselves. The reason HOV lanes work, remember, is because a large number of commuters value a congestion-free trip enough to switch to carpooling and bus riding. This switch clearly isn’t cheap or easy, or many more people would do it. And so the same economics that support travel in the HOV lane imply a relatively inelastic demand for congestion-free travel.

Inelastic demand means that drivers don’t respond very much to big price changes. People really want a congestion-free commute, and so one has to raise the toll quite high to deter enough drivers from coming into the HOT lanes to keep traffic flowing smoothly. In this case, one might conclude that Transurban does have lots of room to play with speed levels and disadvantage bus riders. But highly inelastic demand suggests that good substitutes are lacking, which means that Transurban enjoys monopoly power. In this case, the profit maximizing entity will raise tolls to a higher level than the social planner. Traffic moves faster in the private case.

Put a different way: given Transurban control over a limited amount of road space, the company clearly wants to use as much of that space as possible on paying customers. And doing that means crowding up the HOT lanes until carpoolers and bus riders figure that if they’re going to sit in slower traffic, they may as well be in their own car. But were Transurban to do that, it would give up the piles of money it could make sticking it to the truly desperate commuters with really high tolls. That’s where the big money is. (One way to think about this is that Transurban will capture a lot of surplus from people who, for various reasons, now find themselves cheating on the HOV lanes and risking a big fine.)

This is how a private company runs a HOT lane — only allowing in a relatively small number of desperate drivers, whose surplus can then be extracted through very high tolls. And that, of course, leaves a lot of lane space open for carpoolers and bus riders. An optimal social planner would opt to take less of the big, profit-padding surplus among desperate drivers in order to let more people have a faster commute.

The big risk of HOT lanes to those carpooling and taking buses is a political one — that the government won’t tolerate what some will call gouging and will then mandate a toll ceiling that’s below the social optimum. In my experience, this is where most public tolls are set: at a level too low to maintain the free flow of traffic. Very nearly everyone would benefit from higher toll rates, but it’s politically difficult to increase them.

As a supporter of congestion tolling, I recognize how big a problem this is; it’s hard for public authorities to charge a toll high enough to cut congestion, and it’s hard for public authorities to allow private companies to charge the toll they want to charge, and if public authorities do allow private authorities to charge the toll they want to charge, well, that toll will often be above the socially optimal level. It is worth pointing out that good transit options reduce the monopoly status of the tolled road and therefore reduce the difference between the profit-maximizing toll and the socially-optimal toll. One of the reasons the pricing options on I-95 aren’t that attractive is because existing transit alternatives, which include the HOV options, are pretty lousy. But this is a big public policy problem — how to enable governments to price scarce publicly-owned resources appropriately.

And that’s one reason I think the HOT lanes are a good idea, even if the Virginia plan isn’t the best. With more models in place, we get a better sense of what works and how it works, so we can design later tolling and transit plans more effectively.