The Costs the Umbrella Lobby Isn’t Telling You About

If it’s sunny in London, just wait a few minutes. The clouds were probably on a coffee break, but they’ll be back once they finish up. And pretty soon – maybe not right away – it’ll start raining.

A London rain isn’t like an American rain (Pacific Northwest excluded). Downpours are rare, but spotty showers are more common than double decker buses and Britons’ uneasy realization that their power in the world is diminishing. In fact, the rain is so persistent that the pavement outside my flat never fully dries. But that isn’t to say that it rains all the time. Some days it will rain a few different times, but only for about fifteen minutes each.

After spending some time in the British Isles, you become desensitized to the rain. I recently found myself leaving my umbrella in my backpack while walking through light rain; it just wasn’t worth taking it out. After all, using an umbrella comes with its own problems or, as we economists call them, “costs.”

Sometimes, even when it’s raining, the costs outweigh the benefits. We all know and think about the one obvious benefit of using an umbrella (the upper half of your body doesn’t get wet), but there are half a dozen or more annoyances that come along for the ride as well.

I have to hold one of my arms up then switch when it gets tired. I have to figure out what to do with a wet umbrella when I get to class. I have to play umbrella chicken with other Londoners: raising, lowering, and tilting umbrellas to avoid a collision with everybody’s massive golf umbrellas. Worst of all, my umbrella could be ravaged and mangled by an unruly gust of wind.

That’s all assuming that I didn’t lose my umbrella last time I took it out. For a lot of people, that’s a big assumption to make. A classmate is on his third umbrella in just over a month, and although that is unusually high, it’s not too farfetched.

Based on how strongly one feels about these considerations, it’s possible to be better off not using an umbrella. How could that be? Well, let’s take a look at a simple model of the Economics of Using Umbrellas. (I’m so excited to share it, because it’s the first model I’ve ever made – well, with the exception of the really horrible one I made about baseball teams in undergraduate econometrics, but that doesn’t really count, does it?).

Now I know I advertise my blog as economics without math, but bear with me. There’s no real math here (says the grad student who’s had dreams/nightmares about Lagrange multipliers); it’s just a few plus and minus signs, and some probabilities. If math isn’t your thing, then skip the equations and read the rest.

U(Carrying an Umbrella) = Pr(RAIN)*U<rain> + Pr(NO RAIN)*U<no rain> + R(RAIN | DIDN’T BRING UMBRELLA)

Where:

U<rain>= α(Staying Dry|How Hard It’s Raining) – β(Holding Up An Umbrella) – γ(Dealing With A Wet Umbrella When You’re Inside) – δ(Playing Umbrella Chicken) – θ(Wind Breaks Your Umbrella)

U<no rain> = -ε(Risk of Losing Umbrella) – η(Carrying An Umbrella)

α, β, γ, δ, ε, η are all constants based on personal preferences/aversions, assumed to be positive

I assume U and R are nice functions (i.e., continuous and meeting Inada conditions) and that the terms in the utility functions are real numbers which are discounted for personal preferences by their coefficients.

In words, the utility you get from carrying an umbrella is the average of two utilities (carrying an umbrella when it’s raining and carrying and umbrella when it’s not raining) weighted by the forecasted chances of rain. The utility also depends on R, which is the peace of mind of knowing that you won’t caught in the rain without an umbrella.

As I said above, the only real benefit from carrying an umbrella is that you stay dry (or that you have peace of mind that you will stay dry in the event of a sudden shower). This of course includes the value of things like your hair not getting ruined or you getting the chills from being wet. Notice that the value of having an umbrella when it is raining is conditional on how hard it is raining. When it rains extremely hard, the value of having an umbrella is high; when the rain is more of a mist, it is much lower.

But the costs are more numerous. Even if they seem like none of them on their own is more powerful than staying dry, they could overwhelm the benefits if the rain is light. That means there is a threshold amount of rain that makes it “worth it” to carry your umbrella, given a certain chance of rain during the day. This of course varies by person. A toughened Englishman or someone who doesn’t walk outside much would have a higher threshold than someone who walks everywhere or spends a lot of time on his or her hair.

So, sometimes a person might be better off not bringing an umbrella even if it might rain. What does that tell us? What good does it do? Really, not much – except to serve as a reminder that nearly every decision, no matter how minute, has a balance of benefits and costs. Usually economists will say that there’s no such thing as a free lunch, meaning that you are always foregoing something to get that lunch even if you pay zero dollars for it. The same is true of using an umbrella: You are staying dry if it rains, but you are also putting up with a whole slew of inconveniences along the way.