Congestion, carbon, and bus lanes

Following yesterdays suggestion to lower the speed limit in order to reduce carbon emissions I’ve got to thinking about congestion and carbon.

Firstly, I’ll put down the obvious problems with this scheme. Lowering the speed limit will make congestion problems worse – as in the short run cars will be on the road for longer. In order to solve these congestion problems the government wants to introduce “congestion charging” in urban centres. This will, over time, lead to more urban sprawl, which will increase the distance people drive, canceling out some of the carbon savings.

However, I doubt the scheme is serious – the social cost associated is likely to exceed the paltry reduction in carbon emissions.

Anyway, this scheme is not even the focus of this post. Instead I wish to discuss congestion and why bus lanes could be a useful mechanism in the case of congestion (even though the guys from Top Gear don’t like them).

When you put your car into traffic, you cause a negative externality insofar as you slow other people down. However, it is commonly stated that this externality is fully internalised, as on average you are slowing down the traffic as much as it is slowing down you – so on average you are paying the full social cost of taking your car for a spin.

However, there are a couple of other ways to think about this that indicate there is a problem.

Firstly, the marginal driver coming onto the road is not the average driver. As there is often a “tipping point” for congestion where a few additional cars will add significantly to the total amount of congestion time associated with driving. If we are close to the tipping point, then getting a few cars off the road can make a huge difference to the amount of congestion time other people face – implying that the “social cost” of the drivers who come in on the tipping point is a lot higher than the cost they face.

(Note: Think of it this way. If there are 99 cars on the road and no congestion, but the 100th car causes 20mins of congestion, then the cost independent of the 100th cars own cost is 1980 minutes while the time cost they face compared to the no congestion case is 20 minutes).

In this case, a small lift in the cost associated with joining in traffic may prevent these guys entering at the margin greatly reducing congestion.

Secondly, we may have a “prisoners dilemma” (our favourite!).

How does this work?  Well to start with, we know that people like to drive there cars above other substitutes in the “no-congestion” state.  However, we have also observed that they currently driver their cars in the “congestion” state – implying that driving your car is a “dominant strategy” between these states of the world.

The congestion state is caused by everyone else driving their car – so if everyone has driving a car as their dominant strategy we will end up in a case where we are in the “congestion” state.  However, the payoff from driving your car in the congestion state is lower than the payoff from driving in the non-congested state.

Now lets think about why this is a dominant strategy.  Assume that the only realistic alternative is a bus.  In the non-congested state driving the car provides the payoff Cnc, while in the congested state is gives Cc<Cnc.  In the non-congested state, the bus gives the payoff Bnc, while in the congested state is gives Bc<Bnc as congestion also legthens how long a bus ride will take!!!

Now since driving the car has been observed to be the dominant strategy we also know that Cnc>Bnc and Cc>Bc.  However, now assume that the most important attribute to a person using a form of transport is the time it takes (assume say lexicographic preferences for simplicity).  In this case, the bus in non-congestion will be more highly valued than the car in congestion, such that Cc<Bnc.  It is this assumption that creates the possibility of a prisoners dilemma.

Everyone would be better off if we were all in buses driving around (note this is a simplistic example – I am not saying that in reality everyone should be on buses) as we would all receive Bnc.  However, in that state people would want to switch to a car to receive Cnc, but if everyone switches to Cnc we only get Cc, which is less than Bnc – dang!

Here is where bus lanes come into effect.  Bus lanes ensure that Bnc=Bc>Cc, because buses are no longer in the congested traffic.  As a result we no longer have a prisoners dilemma as in the congested state there is a movement against cars and in the non-congested state there is a movement for cars.  In the end we would settle down to some mid-point between them.

As long as the creation of the bus lanes does not increase congestion (which it often does by taking up road space), and given the “tipping point” argument, bus lanes could be an extremely effective strategy for lowering congestion.  Furthermore, we could appeal to rule of thumb, infrastructural positive externalities, or experience good arguments to support a bus lane – however I find the prisoners dilemma + tipping point argument the cleanest and most satisfying .