In the cost/benefit analysis course i teach, one of the actual cost/benefit analyses we work our way through–and one that I present as a reasonably good CBA–is a study done by two St. Louis Federal Reserve economists on adding another runway at St. Louis’s airport. The authors are Jeffrey P. Cohen and Cletus C. Coughlin.

When I taught it this quarter, I was unable to convince one of the students that congestion is an externality. We had discussed earlier in the course the fact that when you have private property, there is not an externality because the owner takes into account the gains and losses to various people. But I pointed out that the airport is government-owned.

This was not his objection, though. His objection was as follows:

When I show up at the airport, that’s a choice on my part. I know that if I show up at a busy time, I will have to wait longer, but I take that into account. So does everyone else who shows up.

My answer was, and is, that, yes, you take into account the amount of time by which you are slowed down, and everyone else takes into account the amount of time by which he or she is slowed down, but no one takes into account the amount of time by which he or she slows others.

That still didn’t fly (pun not intended.)

So I gave a numerical example. Let’s say there are two people: A and B who arrive at the airport. (It’s hard to imagine that two people would create congestion, but if we complicated it with way more people, the essence wouldn’t change.) A will lose $10 worth of time by arriving at the airport at a congested time but he values being there at that time, versus the uncongested time, at an additional $15. He also causes B to lose $10 worth of time. Vice versa for B. So A looks at the extra cost he will bear–$10 due to B slowing him down–versus the extra benefit–$15–and decides to arrive at the congested time. B likewise.

Now let’s tote up the costs and benefits. The benefits to A and B add up to $30. The costs are $20 each, or $40 total. Why $20 each? Take A. A’s cost that he bears is $10–it’s imposed on him by B. A’s cost that he imposes is $10–it’s imposed on B and he doesn’t take it into account. They total $20.

This is the first time I’ve written this down rather than just said it and now I’m feeling implausible. Am I double-counting the $10 that each imposes on the other? I’m getting the uncomfortable feeling that I am. It’s funny how writing things down can expose flaws in thinking.

So here’s the help I want. First, is my numerical example good or flawed, and why? Second, what’s a good way of showing the student that there really is a congestion externality?