Learning how to do “back of envelope” calculations is one of the most important tools you can master – it is a damn shame we don’t spend more time on them in school. The idea is you make some assumptions, round up and down often, so you can get a rough idea of what a range for possible answers are. This skill is especially important in an era of spreadsheets and other tools where a single error in data entry leads to GIGO (“garbage in, garbage out”).
My previous post was on how universal wearing of N95 masks for say a month could go so far in ending the pandemic. The next step is to do a back of envelope calculation on how much it would cost. So this blog will give you one for the upper bound on the cost. (Anyone who cares about lower bounds in these crazy times, well ….)
First off, you always need some real data to “anchor” a back of envelope calculation. I found, via a google search, that 3M said they added the capacity to produce 45 million additional mask per month to existing facilities for 80 million dollars. I’ll use that number as a starting point.
To make the masks reusable and easier to use correctly, I will want them to be designed more like a P100 mask. This means they have a full foam gasket and adjustable straps instead of the cheaper way N95 masks are produced.
These use to run about $3 each retail for quantity 100 but note that we don’t want a vent since that makes them useless to prevent the spread of Covid. So I am going to assume a production unit cost of $1.50 each, which is almost certainly too high for a ventless version – but that is what you want to do in a back of envelope calculation!
We need to send say 3 masks per person/week at most because high quality masks with a full foam gasket and adjustable straps are reusable if you put a used one away for a few days. So, say we need roughly 1 billion masks a week (900 million for the people over the age of say 13 and a lot of extras for health care workers and first responders). This gives us an upper bound on the costs of the masks themselves, using a unit cost of $1.50, of $6 billion a month to give us all 3 masks a week. Throw in another 1 billion a month for things like postage and Murphy’s law and we have the cost of supplying high quality masks to everyone is going to be less than 7 billion dollars a month.
The next step is figure out how many new factories we would need. Since we are building the factories from scratch, let’s double the cost that 3M announced, so each 45 million of new capacity will cost us 160 million for the factory. We need about 89 new factories (4 billion/45 million) but rounding up again say we need 100 new factories. That gives us 16 billion to make the factories. Throw in the costs of the masks and round up again and we see the cost to basically wipe out the pandemic in my fantasy land where people could be made to wear these masks for a month, seems certainly less than $25 billion.
Considering what the virus is costing us, this is peanuts. (And the factories could and should be mothballed for the next pandemic so counting them at full cost is really strange from an accounting point of view but heck forget that for the moment.)
When you compare the cost and complexity of building these factories to what we did to rapidly increase the production of planes, tanks, ships, guns ammo etc., in the early days of WW2, our lack of enough PPE for medical workers now, let alone for the general public, is simply criminal neglect.
And, yes I know it is a fantasy, because even if we made the masks, we don’t have the will to make people, via the threat of severe fines or even forced quarantining, to use them. But heck a mathematician can dream…