Post #560: Real backpackers don’t use toilet paper: The arithmetic of panic shopping

Posted on March 19, 2020


First, a brief public service announcement, prompted by my visit to the Pan Am Safeway two days ago.  The T.P. aisle was bare.  For those of us with standard American T.P. anxiety, note that a) 70% of the world’s population doesn’t use toilet paper, b) neither do hard-core backpackers, these days, and c) you can buy (or for that matter, easily improvise) a “handheld bidet“.

And that’s more than enough said about that.

But what about panic shopping in general?  When will it end, has it already ended, will it end?  Really, the underlying question is, when will we stop seeing empty store shelves?

I was asked this question yesterday, and I’m not quite sure what to say about it.  But that won’t stop me from writing.

First stop:  The arithmetic of bare shelves.

Rule 1:  They only bring stuff into stores at the rate we normally use it.  Otherwise stuff would pile up in the aisles.  (I know that’s obvious, when you think about it, but who in their right mind thinks about it.)

Rule 2:  More-or-less the entire supply chain is set up to accommodate Rule 1.

So let’s do a quick-and-dirty (hah!) calculation for TP use by the Town of Vienna.  In a typical day, the Town of Vienna uses enough toilet paper to fill …

Details:  We have about 16,500 a … ah, my wife won’t let me say that.  We have 16,500 citizens.  I’m not even going to go near the topic of gender-related differences in use.  I simply appoint myself Toilet Czar, and hereby ration each person to three visits per day, with a not-over-generous 18 sheets per visit.  Ignoring business-related use and rounding up, the Town of Vienna uses about a million sheets of toilet paper a day.  Next, a quick trip to the john reveals that what I’m currently using has 450 sheets per roll, apparently well within industry norms, so let me round up to 500.  That yields a total use of just 2,000 rolls of toilet paper per day.  Returning briefly, tape measure in hand, I find that such a roll, packed, amounts to a right rectangular solid about 5x5x4, or a nice round 100 cubic inches.  Thus we consume about 116 cubic feet of toilet paper in a day, so let me round up to 128, which is the size of a standard cord of firewood.  Grocery store shelves vary in size, but 24″ is a good guess and a round number, and with 7′ tall being, I think, just about as high as they’ll pile it in the grocery store.  Thus I arrive at:

about 9 linear feet of shelf space at the grocery store.  Roughly as much volume as you’d get in a standard cord of firewood.

Or I could have just looked up somebody else’s estimate.  In this case, Wikipedia cites 24 rolls/person/year for average USA consumption, which would amount to just over 1000 rolls/day for Town of Vienna use.  So, if anything, my from-scratch estimate was far too generous.  If the Wikipedia estimate is accurate, we only use enough TP to fill five-ish linear feet of shelf space, per day.  No matter how you roll it, it ain’t much.

So that’s about the rate at which the supply chain is set up to deliver TP to Vienna.  That’s for all the stores in town.  (And, of course, that assumes Vienna is a closed system, which it is not, but this is good enough to make the point.)

Here’s where it gets ugly.  That’s roughly the rate at which they deliver it, so that’s roughly the rate at which it would be replenished, if the normal rate of delivery continued and people quit buying it.  You’d restock the Town at somewhere around 9 linear feet of shelf space, (2′ deep, 7′ tall) per day.

But note that I didn’t say quit panic-buying it.  Just buying it, period.  If normal deliveries continue, and people merely go back to buying it at their usual rate … those shelves remain empty.

Why?  See Rule 1.

Why don’t the shelves stand empty for a long period after (say) a snowstorm?  With a normal (i.e., localized) disaster, suppliers can divert supply to a specific geographic area where panic shopping has cleared the shelves.  But this is, more-or-less, a nation-wide phenomenon.  They can take what’s already in the supply chain and deliver it a little faster, nationwide.  But short of that — short of moving it more quickly from their warehouses to the stores, there’s not much slack in the system.  In this case, you have to expect the shelves to be empty for a while, because they can’t supply more of everything, to everybody.

Why?  See Rule 2.

The upshot of this is that even if we quit panic-shopping, I believe we should expect those shelves to stand skimpy-to-empty for a long time.  So, to explain an unusually long period of bare shelves, you don’t need to assume bad behavior, or price-gouging or anything like that.  It doesn’t even mean that people are continuing to panic-shop TP.  They might be, or they might not be.  Arithmetic, in and of itself, provides an adequate explanation of the facts.

What I’m saying is, don’t freak out if the shelves remain skimpy.  It doesn’t mean that the supply chain has broken down.  (Yet.) It doesn’t even necessarily mean that people are continuing to hoard things.


The madness of crowds.

If you read this blog, you realize that I am totally unsurprised by panic-shopping.  That’s because it’s a completely normal phenomenon.  It’s more-or-less unstoppable, except by threat of force.  The only thing unusual about the current situation is the nation-wide character of it in this case.  That means (best guess) the shelves are going to look skimpy for what will appear to us to be an unusually long time, because nation-wide hoarding behavior puts an unusually large strain on the supply system.

I have more to say on this topic, but for now, I’m just going to suggest a little light reading.

Economists, in particular, delight in identifying situations where individuals, each acting rationally in their own self-interest, create mass action that is absolutely irrational.  We have a whole popular and scholarly literature on this topic.

If you you have time on your hands, check out the classic description of this phenomenon:  “Extraordinary Popular Delusions and the Madness of Crowds“.  That was published in 1841. And it’s still in print, which tells you something.

Hey, it’s currently free for download to Kindle.

For a modern economist’s take on the same phenomenon, mostly in the context of financial panics, I think the one that every economist would recognize is “Manias, Panics, and Crashes“.  I see that’s now in its 7th edition.  Which again tells you something.

It’s just the way the world works sometimes.  Stuff happens.