If you have a meeting scheduled at 2 and you are worried its going to drag on too long, what do you do? Here’s a confession: Sometimes I lie and say I have an appointment and I have to leave at 3. But it’s a double-edged sword.
Because warning my friend that I will have to leave at 3 implies that I anticipate that the hour will be a binding constraint. That would only be true if I expect the meeting to go that long. My friend will therefore infer that the topic of our meeting is important enough to me to potentially warrant an hour of face time.
As far as I know, had I never said anything he might have kept the meeting to 30 minutes, but now that I capped it at 3:00, its a sure thing we are going to meet for the full hour.
The problem is that there is no way I can know how long he was planning to meet. If i knew he was planning to leave at 2:30 I wouldn’t say anything. But if he is actually planning to stay until 4:30 and I don’t invent a 3:00 appointment I am hosed.
Of course some meetings really need to take more than 30 minutes and often you only discover that in the course of the meeting. The downside of the cap is that it commits you. Unless you want to lose all credibility you are going to have to keep to your fictional meeting and cut those meetings shorter than they should be.
So what is the optimal cap? The tradeoffs are reminiscent of textbook monopoly pricing. You have your marginal and infra-marginal meetings. If i raise the cap by a minute then the marginal meeting gets the extra minute that it really needs but the infra-marginal meeting gets needlessly extended.
Its a complicated calculation that comes down to hazard rates, incentive constraints, etc. but I will save you the effort; I have done the integration by parts. The optimal cap is exactly 37 minutes. You can’t say that of course because your friend will know that nobody schedules appointments at 2:37, so you will have to round up or down to the half hour.
Or schedule all your meetings to start at 23 minutes past the hour.