A justification for taxing congestion: Multiple equilibria with a roading alternative?

Recent posts below (see “Taxing congestion: how I might justify it“) have sought reasons as to why toll-roads are so often touted as an economically efficient measure. For my part, I am quite sceptical that the are universally efficient, and struggle to find a compelling reason why they are even efficient most of the time. However there are some circumstances where it is quite conceivable that they can be efficient. Where there is a (slower) alternative to the road with a congestion charge, and different drivers place different values on congestion free travel, congestion charges/tolls can lead to an efficient sorting of road users between the (faster) toll road and the (slower) free road, resulting in socially optimal outcomes.

The intuition goes something like this:

The road that is a candidate for congestion charging has an alternative, but the alternative is slower. There are two types of travellers who use the candidate road, “high” and “low” types. “High” types value getting somewhere fast highly, with “low” types preferring quick journeys too, but only by a small amount. Without the congestion charge they both still use the candidate road because it is quicker than the alternative route, with the “low” types getting a small amount of utility compared to using the alternative route, and the “high” types getting a little bit more (but still not much since it is really congested and not much quicker than the alternative road).

If the “low” types didn’t use the candidate road the “high” types would get a very high amount of utility since there would be less congestion and they would get to where they want to go quicker. The low types would be a bit worse off for being excluded from the candidate road, but not by much since they didn’t value using it when it was congested by much more than the using the other road.

With appropriate paramater values, there exists a congestion charge that would exclude “low” types from using the candidate road (since the cost of the charge would be more than they value using the candidate road over the alternative road), but which would still have the “high” types using it. Without the “low” types clogging up the road the “high” types get where they want to go much quicker, and they experience much much higher utility, and with appropriate paramater values (such as the split in road users between high and low value types) this exceeds the drop in utility for the “low” types of now using the alternative route (due to the charge) and overall society is better off (the cost of the congestion charge is netted out because it is just a transfer between agents and not a cost on the economy overall).

Make sense? Of course note the qualifications, in particular “for appropriate paramater values”. Comments appreciated!

3 replies
  1. Matt Nolan
    Matt Nolan says:


    I’m not sure this is the multiple equilibrium argument – but it is an argument for congestion charging.

    Fundamentally you are saying that there are two types of agents those that place a high value on time and those that place a low value on time. In this case there are drivers that place a low value on time that are being held up for x minutes that are also holding up a bunch of agents with a high value of time for a cumulative x minutes – as a result even though the average externality cancels out, at the margin there are people who are placing a higher cost on society from driving than they face.

    In this case, a toll gets these people off the congested road leading to a net benefit (given our assumption of values).

  2. dant03
    dant03 says:

    True about it not being multiple equilibria – ’twas the term you used yesterday for it and I figured that you must know what you are talking about!

  3. Matt Nolan
    Matt Nolan says:

    True – however, I was actually talking about a multiple equilibrium model on Thursday which was in addition to this, two agent model 😛 .

    I agree with the argument you have used here for multiple agents – however the substitute road only influences the reservation value of those agents, so can be simplified out. On Thursday I was suggesting that the alternate road could be important if we had scope for “multiple equilibrium”.

    If we add search costs, and some type of bounded rational rule following, there is definite scope for a multiple pareto ranked equilibrium given the existence of difference types of roads. In the absence of rule following I’m not sure if government action (outside of education) can improve outcomes – but if we can define a rule that becomes suboptimal we may be able to justify it.

    However, this involves assumptions about the behaviour of agents I might not be comfortable with – and I’m wondering if there is a different way.

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