Question

A driver going to the city center has the choice between a small road and the highway. The small road takes 25 minutes (1500 seconds) and is never affected by traffic. The highway takes only 15 minutes (900 seconds) but travel time increases by 2 seconds every time a new person gets in it. The travel time on the highway is therefore 15 minutes + 2 seconds per entrant.

1. Explain why Net Benefits (NB) = 0 at the Tragedy of the Commons. Hints: What would happen if NB > 0? Think of the Net Benefits as the Average Net Benefit (for each driver) multiplied by the number of drivers (NB = ANB*N).

Answer 1

This example can be used to highlight the main aspects of "Tragedy of the Commons"

The choice that drivers face, is between the small road and the highway. The highway offers a much faster travel time, but is affected by traffic. In fact, every new entrant adds to the traffic congestion, and reduces travel time.

With every new entrant, 2 seconds are added to the travel time. This means, with 30 entrants, 60 seconds are added. With 300 entrants, 600 seconds (10 minutes) are added, and so on.

The small road is never affected by traffic.

We may look at this comparison in a tabular form.

No. of drivers	Time taken at Small Road (seconds) for all drivers	Time taken at Highway (seconds) for all drivers	Time Saved (seconds) for all drivers	Average Net Benefit per driver = Time saved / no. of drivers	Net Benefit for all drivers [ANB * N]
1	1500	900	600	600	600
2	1500	902	598	299	598
10	1500	920	580	58	580
100	1500	1100	400	4	400
200	1500	1300	200	1	200
300	1500	1500	0	0	0
301	1500	1502	(-2)	(-0.00664)	(-2)
400	1500	1700	(-200)	(-0.5)	(-200)

This list may be extended to a very large number. However, we are interested at the point where the small road and the highway give equal benefits.

Note that the column depicting time saved for all drivers, is the same as the last column depicting net benefits for all drivers. We are measuring benefits in terms of time saved.

Now, the tragedy of commons implies this:

Since the highway offers significant saving in driving time, every driver will prefer the highway. In spite of the understanding that the smaller road is never affected by traffic, everyone takes the highway.

Thus, slowly the number of drivers on the highway increases.

The number of drivers 300 represents the point where NB = 0.

The situation is fine till up to 300 drivers, but this number is very easily reached on a busy highway.

With the 301st driver, everyone actually starts wasting their time on the highway. But as with any common resource, they will continue to do so. The fall in net benefits is drastic as we move to 400 drivers.

Each driver in his own self interest, over consumes the highway. In the process, the highway becomes congested. If they had taken the smaller road, this problem could have been solved.