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Effects of increasing toll prices on traffic.

http://articles.nydailynews.com/2011-08-05/local/29873910_1_toll-hikes-hudson-river-crossings-path-train

Recently, in September, the prices for tolls of the bridges and tunnels that head into Manhattan have increased. The increase was a drastic one, rising from $8 to $12 for the Holland and Lincoln Tunnels, and the George Washington Bridge, and even higher for the Hudson River crossings, at a staggering $15.

It is interesting to see the effects of raising the prices of tolls on those who use them to commute to work. All of the examples below will use the assumption that 5000 people want to commute into Manhattan, and each of these people are greedy and want to spend less money than they have to. Therefore, the people use the bridge if it has the minimum price, and no one uses the bridge if it doesn’t. We’ll also say, for the sake of the argument, that each bridge has a rate of 1 car per second crossing into Manhattan, just to preserve the fact that each bridge is an equally viable option.

First, we will consider the scenario pre-September, where the prices were uniform. The network appears as such:

img_1

In such a scenario, the Nash Equilibrium will simply be 5000/4 = 1250 seconds per car. This is in accordance with our assumption above that the only thing motivating people is their desire to save some cash.

However, after the price raise, the network will change. In this scenario, under our assumptions that people only want to preserve their money, the Hudson River crossing would go unused. Therefore, the network effectively looks like this:

img_2

Obviously, this puts a lot more people through those bridges and tunnels that are still used. Nash equilibrium would be 5000/3 = 1666.66. What effect does this have? In between the two scenarios, there was an increase of 1666.66-1250 = 416 seconds per car. This means that in a scenario in which the price hike of tolls scares people away from using a certain bridge, the traffic will increase on other bridges and tunnels into Manhattan.
Clearly this is an exaggerated example, where the only thing motivating people is the paper in their pockets. In a real world scenario, people would take into account travel times (which will not be so uniform depending on various factors such as toll cost, distance from home, etc.) before choosing a bridge or tunnel. However, to some degree it does hold true that the prices would affect traffic in this way. Perhaps only the super-wealthy who can afford to throw away $3 and go faster into Manhattan would use the more expensive bridge. Since it is true that toll prices do motivate which roads people decide to take (many studies have shown this, including http://www.ops.fhwa.dot.gov/publications/congestionpricing/congestionpricing.pdf) this is a good way of seeing that a non-uniform increase in toll prices can lead to congestion on roads that were previously not as packed.

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