Saturday, March 09, 2013

Marginal Utility Theory of Daylight Saving Time

I just posted this on Facebook, and I thought I might as well post it here as well.

This is the marginal utility theory of Daylight Saving Time. If you could, you would allocate your daylight according to marginal utility -- starting with the most valuable hour to have daylight, then the second most valuable hour to have daylight, and so on. Suppose, as seems to true for many people, that your ordering (from most to least valuable) is something like this: The hours you want lit the most are from 7am-5pm. (Don't worry about the ordering of preferences within that period, because you'll get that much daylight even in the dead of winter, at least where I live.) Next, you'd like some daylight in the evening, after 5pm. And least important are the early morning hours, before 7am.

Under standard time, you've got your first period (7am-5pm) covered even in winter (at least where I live, Los Angeles). But as the daylight hours get longer, they are distributed approximately equally on both sides of that time period. This is inconsistent with your preference ordering, because you'd rather get the added daylight on the evening side. By mid-March, you've added a full hour in the morning (6am-7am) and full hour in the evening (5pm-6pm). But you'd much rather have had both hours in the evening (5pm-7pm). Switching to DST accomplishes this. And it does a similar thing the rest of the summer, although the specific hours swapped change.

But in that case, why not have DST year-round? Because if you did, then in the dead of winter you'd have daylight from 8am to 6pm. That means you'd be getting a less-valued hour of daylight, 5pm-6pm, instead of the more-valued hour from 7am-8am.

In other words, the order in which nature provides us with added hours of sun doesn't match our preferred ordering. Nature adds hours in a symmetric fashion, while our preferences order them asymmetrically, wanting to add more in the evening before we add more in the morning.

And in case you're wondering: yes, this scheme does imply that we might want to have Daylight SUPER Saving Time in mid-summer, so that we could trade an hour of daylight at 4am (useless!) for an hour at 9pm (awesome!). But given how much people bitch about changing over twice a year, the adjustment costs of four+ times a year would be too great.


Joel Bernstein said...

Now that so many of our timepieces are digital (and a decent proportion of those are internet-connected), wouldn't it be possible to have continuous DST?

i.e. define "6am" as sunrise, and add or subtract minutes from around 2am to compensate. The difference from day to day would be minimal, easing the transition and ensuring maximum use of all sunlight.

Glen Whitman said...

Yes, I suppose that would be possible. But it might create other problems. Among other things, it would be mean that you'd have hours that are not 60 minutes. This would create a problem for all kinds of scheduling, such as for TV shows.

Gil said...

We don't all have the same preference for evening over morning hours, you paternalist! :-)

And, you're not considering the relative costs and benefits involved in all of the clock changing, schedule adjusting, software adaptations to acts of congress...

You seem to be thinking like a bureaucrat rather than an economist.

Glen Whitman said...

Gil, I can see how it sounds that way. But I wasn't really trying to do a full cost-benefit analysis of DST. I was just putting the argument in favor in economic terms. Personally, I'm ambivalent.

With respect to not everyone sharing the same preferences... that's clearly true. But since we all have to share the same clock (so to speak), the same argument applies just as well to NOT having DST. When everyone has to share the same standard, you have to make a judgment as to what *most* people's preferences are.

Philip Whitman said...

I wish we could choose one or the other. I hate changing twice a year. It takes an hour each time to reset the clocks, and it takes my body a week to adjust to the change.

Unknown said...

Thanks for making this available to those of us who aren't in the Facebook loop. Good analysis. If we wanted to be really logical we could not only change time more often but do it by latitude, so Alaskans could enjoy their long sunlight evenings.