How much do we slow down traffic when we drive during rush hour?

I have recently been thinking about the question of how much an individual’s driving influences the commute time for other drivers. This negative externality is relevant, for example, in discussions around congestion fees in cities. I tried to look up estimates and couldn’t (easily) find them, so this weekend I did my own analysis (see below; please let me know if you identify errors!).

What I found is that the costs (in time) that you impose on others by driving is larger than the time that you yourself spend in traffic. For example, if you are stuck in traffic for half an hour (ie your drive without traffic is 20 min but as a result of traffic the trip takes 50 min) then you are slowing down others by more than half an hour. This time is obviously spread across a large number of drivers, but it represents a real increase in commuting time and hence a real negative externality. Indeed, depending upon the assumptions that are made, the time that you impose on other drivers is typically 2 – 3 times the time that you will spend in traffic.

From this perspective, driving during rush hour imposes significant costs on other drivers (of course, they are also driving during rush hour, so this is not a good-guy vs bad-guy scenario!). Given mean wages in the Boston area (and the fact that many cars and buses have more than one occupant in each vehicle), the negative externalities are ~$100 for each rush hour commute. This is a huge cost, and in my mind represents a strong argument for congestion fees. Even a $10 fee would likely have significant effects on behavior.

Analysis

Below are my calculations, where I analyze two models for how traffic speed v decreases as a function of the car density rho. The central insight from the mathematical analysis of traffic is that the flux of cars will have a maximum as a function of the density of traffic.

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