Notes on Traffic Congestion
Russell Degnan

There have been quite a few notewoethy blog posts on traffic congestion the past few days. In particular, Harry Clarke makes several forays into the area on his new blog. In one post he makes reference to several others worth reading: by Gary Becker; Richard Posner; and an older paper by Richard Arnott.

The latter is particularly broad, noting that political opposition to widespread congestion charging makes alternative methods worth considering, then works through them in some detail. It is worth reading in full, but I'll highlight a few points I thought were interesting. One aspect -- the bottle-neck approach to congestion, instead of the capacity approach -- I have covered before so won't again, except as it relates to some other parts.

First, a quote from the conclusion:

Let me start with an obvious point, but one that tends to get overlooked, even by economists and even by myself on occasion. The costs of congestion go hand-in-hand with the benefits of travel; zero congestion could be achieved if there were no travel. The optimal level of congestion has two characteristics. First, for a given level of benefits from travel, the costs of congestion are minimized. Second, when this efficiency condition is satisfied, the optimal level of congestion occurs when the benefits from increased travel are offset by the increase in travel costs induced by the increased travel. The optimal level of congestion could well be very high.

This can be seen easily by looking at a (not necessarily accurate) graph of the congestion costs versus the value (which needless to say looks like a demand-supply curve):

The red line represents the congestion costs as the number of commuters increase. It is well understood in engineering terms, and rises very quickly once a certain threshold is reached. The blue is the benefit each new commuter on the road makes from travelling. Because congestion costs aren't fixed -- they depend on traffic conditions -- the red line will move dramatically and unpredicatably from day to day. Similarly, the blue line refers to a specific time slice of a day; it will move as the time of day changes, and with changes in the weather (more people will benefit from driving on wet days), and from other intangibles. Thus, although it can be depicted prettily, it is not a stable cost, and difficult for individual commuters to optimise themselves to.

What a congestion charge does is shift the red line vertically, adding a fixed (or perhaps a shifting) monetary cost to the commute (without affecting the travel time cost) to reduce the number of commuters. What Arnott correctly notes is that on a highly congested road (which by nature must have a high benefit to the commuter), the benefits conferred by adding road capacity (by shifting the red line to the right) are very high, while a congestion charge needs to be quite high to shift many commuters off the roads.

Unless, as he explains, you can either shift demand onto a different time-slice without congestion problems, or (as was done in London) shift demand onto a different service (such as mass transport).

Two further quotes from this area got my attention:

It is remarkable that economists have such a well-articulated theory of congestion, but such a poorly-integrated body of theory related to the benefits of travel.


Remarkably, second-best transit policy with underpriced auto congestion has not, to my knowledge, been analyzed in the literature. Here is not the appropriate place to analyze it. But let me make a couple of comments. The first is that with constant long-run costs to auto travel and decreasing long-run costs to mass transit, a representative individual, and perfect substitutability between auto trips and mass transit trips, the unrealistic solution is obtained that either all trips should be by car or all trips should be by mass transit. Thus, to obtain a sensible solution, imperfect substitutability between car and mass transit trips should be assumed, which rules out simple geometric analysis. The second is that the problem is intrinsically complex. In the previous section, we analyzed how the plannerís choice of optimal road capacity is affected by the constraint that congestion is unpriced. That problem was complex enough. But now we have two imperfectly substitutable modes and three instruments -- road capacity, the transit fare, and transit capacity -- that the planner can adjust to mitigate the distortion associated with auto congestion being unpriced or underpriced. Thus, it is fair to say that, given the current state of the theory, little can be said about optimal transit policy in the presence of unpriced auto congestion.

This presents all sorts of problems. Even setting a congestion price becomes more difficult because the imperfect substitutability of different modes [1] and different times of travel, means that a price change, will not just shift the congestion curve upwards, but also cause some commuters to jump from the car-based commuting demand curve to the (differently shaped) rail-based curve, or the (differently shaped) car-based curve at another time of day.

In other words, although we can predict reasonably well that a change in the capacity of a road with a given demand will attract demand and justify (or not) the expenditure. The results of changing the inherent costs of existing roads, where alternative travel choices exist, is basically unpredictable.

Nevertheless, I thought the conclusion was excellent:

I have no panacea for traffic congestion; indeed, I think there is none. But there are so many distortions vis-ŗ-vis travel behavior which are so large that there is considerable scope for improvement. Traffic congestion will get worse. But as it does, the political opposition to ameliorative changes will diminish. As well, policy innovations will occur and those policy innovations that are successful will be widely adopted. Our politico-economic system is adaptive and we shall muddle through.

[1] And it should be noted here that none of the authors mentioned cycling or walking as alternative modes, despite their suitablity over short distances of up to 10km. For those wondering, just over one million people live within 10km of Melbourne's CBD, 300,000 of them within 5km walking distance. American cities are different in this respect, but to ignore those modes completely is a serious blind-spot.

Sterner Matters 16th February, 2006 23:40:59   [#]