Update: I added a comment on the post to clarify why I don’t think that having seniors stay at home is the correct Coasean solution. In short: social isolation has high costs!
Bryan Caplan has an interesting post on COVID and reciprocal externalities. Caplan starts off with the straightforward Coasean statement: “Yes, people who don’t wear masks impose negative externalities on others. But people who insist on masks impose negative externalities, too.”
For those not familiar with Coase’s 1960 article, one of his fundamental insights about property rights is that when property rights are not clearly defined, both parties can be imposing costs on one another. The externalities are reciprocal, not just in one direction. The efficient outcome, when bargaining is not possible, is to allocate the property right such that the “least cost avoider” is the one that adjusts their behavior. In other words, you allocate the property right to the party who would obtain the property right if bargaining were possible.
But Caplan uses this Coasean framework to come to the opposite conclusion that I would. Why?
Here is Caplan’s hypothetical example:
Is the cost of wearing masks ever actually lower than the cost of enduring COVID exposure? Definitely. Suppose ten healthy young people all work in an office from 9-5 on weekdays. Once a week, an immuno-compromised senior citizen stops by for five minutes. The unmasked workers definitely impose a tiny negative externality [on] one senior. But if you require everyone to wear masks all the time, you impose a large negative externality on all ten young workers. The efficient outcome would probably be to tell the senior to stay home if he’s nervous.
(Emphasis added)
My disagreement with Caplan comes down to his claim that the externality imposed on the senior is “tiny” and the externality imposed on the workers is “large.” Wearing a mask is a very small inconvenience. Perhaps we didn’t think so a year ago, but most of us now habitually do it without a second thought. It’s inconvenient, but not “large.” And an elevated risk of death hardly seems tiny to me.
But must we just quibble about “tiny” vs. “large”? Here’s a way to cut to the chase: use willingness to pay.
Let’s assume that the senior is not too senior: 60 years old. According to the CDC’s best estimate, this gives them a 0.5% infection fatality rate, and according to Viscusi’s estimates their VSL is about $8.5 million (these numbers are derived from WTP estimates, so we’re already playing in the right sandbox). Thus, if constantly being around unmasked young people gives you a 100% chance of being infected, the implicit cost to the senior is $42,500. If it gives you a 50% chance of being infected (probably the minimum required for herd immunity), then the cost is $21,250.
So here’s the question: would these 10 young people each be willing to chip in $2,000-$4,000 each for the right to not wear masks around this senior citizen? My guess: probably not!
What if our senior citizen is even more senior: 70 years old. Now the IFR climbs to 5.4%, according to the CDC, while the VSL is not much lower at $6.4 million. The implicit cost now is $345,600 at 100% risk of exposure, or $172,800 at 50% risk of exposure.
Would our 10 youngsters be willing to pay $17,000-$34,000 for the pleasure of not wearing masks? My guess: highly unlikely. My proof is that most of us are willing to under go a paltry misfortune to ourselves and voluntarily wear masks anyway. We do it for free! There are a few mask grumblers I have encountered on the internet, but I highly doubt that their grumbling would rise to the level of paying thousands or tens of thousands of dollars.
Furthermore, I don’t think his example is exactly right between the ratio of young, healthy people to old, infirm people is probably not 10:1. The percent of the population with potential COVID comorbidities is something like 45%, including about 20% of very young adults! Perhaps that definition of comorbidities is too expansive, but about 21% of the adult population in the US is over 65.
In Caplan’s terms, I would argue that the inconvenience of wearing masks is a $2 problem. For many, it seems to be a case where there is “a disconnect between how we feel and WTP.” You may feel like mask-wearing rules (either private or governmental) are a violation of your liberties, but you’d probably pay closer to $2 than $2,000 to avoid it.
Economist Writing Every Day 
One major problem with this analysis, at least given the framing from Caplan, is the assumption that the elderly person will contract Covid-19 with 100% certainty from a five minute exposure. In reality, the odds of them contracting it from that short of an exposure are likely in the single digits (again, depending on how close they were to an infected person – which is another thing not calculated – how likely is it that in an office of ten young people at least one of them has Covid-19? The odds are less than 1, and probably less than 50%).
Quick back of the envelope calculation…Is Covid present in the office? 25% (reasonable) assumption); likelihood of older person catching it if exposed for five minutes? 10% (generous) That means .25*.1*42,500+~$1000; Now would these young people be willing to chip in $100 to avoid wearing a mask? Maybe not – though anecdotal revealed preferences seem to suggest that a lot of people would rather not go to the office or to other social gatherings if they require facemasks…Depending on how much they would pay for those functions normally over the course of a week…and I don’t this this is nearly as clear cut at Horpedahl claims.
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Also, if the young people don’t wear masks, the senior has the option—besides spending the risky 5 minutes in the office—to stay away (maybe hiring someone to go in his place, maybe transacting remotely, maybe forgoing the whole interaction). How much would this cost him? That is unspecified.
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Correct– and that is the relevant comparison noted by Caplan: the cost to the senior of staying home. You can easily imagine that cost being less than that of the discomfort of many people wearing masks all day such that they would pay the senior to stay home.
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I think one thing missing from the mask discussion is “What kind of mask?” I have been wearing KN-95 masks for the 40 minutes I travel on public transportation every day since March 15 and I hate them. Walking rapidly up stairs with them on gives me a headache from what I assume is oxygen deprivation. Would I pay $10 a day to safely not wear them? Absolutely. Yet, from what I understand, wearing them tightly gives me almost perfect protection from the aerosols that transmit this disease and will protect others around me if I am infected. Now, I have tried on cotton masks, and they are much easier to breathe in, and even exercise in. Yet the aerosols are mostly in the 1 to 10 micron range and cotton masks have pores that are 100 to 150 microns wide. Sure, if the cotton mask is 2 ply, it might stop 20% of the aerosols (I have seen estimates of 50%, but that seems optimistic) but in an enclosed, poorly ventilated space, a contagious person wearing a cotton mask will sooner or later cause the concentration level of disease in the air to reach a level where everyone else wearing a cotton mask will get infected. Yes, I would pay $10 a day to only wear a cotton mask, and not pay very much to not have to wear any mask, but that is not the real choice.
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This argument assumes that the senior stopping by the office is nonnegotiable, or at least worth thousands of dollars. This seems unlikely. Assuming no masks, the most efficient outcome would likely be for the senior to stay home, as Caplan suggested.
The bigger issue is the way the young workers not wearing masks probabilistically contributes to community spread of the disease. Even if they never come into direct contact with elderly people, their actions help to keep the disease alive and increase the chances that it will spread to high-risk individuals.
If we had been able to globally coordinate mask-wearing and social distancing from the beginning, with near 100% cooperation, the disease would have died out several months ago. The costs of defecting early in the pandemic have been enormous and are far outweighed by the inconveniences of cooperation.
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I see that others have beaten me to the punch, but I came by to note that although I think your conclusion has a good chance of being correct, you’ve entirely missed Caplan’s point, which is that you can’t hold constant the amount of contact between people. If I spend every day in the presence of people who stop wearing masks, the cost to me is likely not to be an increased chance of death, but the forgone opportunity to spend time with those people. Your $21,250 is therefore not an estimate but an upper bound, and quite plausibly far in excess of the actual cost.
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In the canadian city where I spent 42 years before retiring a little bit more southerly, the winter temperature could go to -50 Celsius imposing on us the terrible burden of having to wear 3 or 4 layers of clothing,plusgloves (sometimes with a supplementary inner layer) plus scarves over the face and even sometimes a mask.
Plus having to plug the car into an electrical outlet to keepthe engine warm during the night.
Oh and having a entire fleet of snow removal vehicles including some small enough to clear the sidewalks.
Bizarrely, nobody in town ever died of that, though we survived the cold…
The incredible mask debates in the US seems to indicate an end of its natural life civilization
unwilling totake a single steptosave itself, the way late Romans preferred being overrunned by barbarians rather than serving in the Legions.
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Thanks everyone for your comments. But I would very strongly disagree with Caplan and everyone else’s assertion that the cost of a senior “just staying home” is very low. The primary argument against “lockdowns,” etc., throughout the pandemic is that social isolation has very high costs. And if we think about it in a WTP framework, it was seem that the WTP of someone to not wear a mask (or even 10 people) is much lower than the WTP of the senior to not be socially isolated.
In other words, if you think that “lockdowns” (I put this in scare quotes because the US has never actually had lockdowns in the sense that China did) have a high soical cost, then the Coasean solution is for everyone to wear masks outside of their home.
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The point isn’t that the cost of social isolation is “very low”, it’s that it’s potentially of a different order of magnitude to your (entirely arbitrary) VSL number.
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N95 masks, both with and without vents, are available from reputable manufacturers for less than $2. Why not advocate for their voluntary use to protect the wearer instead of ruminating on the externalities of a mandatory policy based on protecting others?
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I have long advocated wearing masks! I was telling people 8 months ago to buy surgical masks, and pointing them to places to find them:
And as I started to find places to purchase N95 masks, I alerted people too:
These things are not mutually exclusive.
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I still think you are missing the actual Coasian point from “The Problem of Social Cost.” A huge part of why Pigou was wrong in his analysis of externalities was because he calculated the total value of crops/land damaged by sparks from a train, not the marginal value. That seems to be exactly what you do here in calculating the total loss to a senior of contracting and dying from Covid.
But this situation is so contrived anyway – why require constant mask-wearing when what matters is the interaction with the senior? This could be the case if they wore a mask when the senior came to the office or if the senior was interacting with someone they hired to go for them or if the senior wants to interact with people in their own homes.
As a matter of policy I agree that requiring masks instead of shutting down businesses (not a Chinese-style lockdown, but a lockdown in any normal world) is superior, but the question is how necessary and how far mask requirements should go and to whom they should apply.
The lags behind the costs of shutting off economic activity, or severely limiting human interaction, including interaction while wearing masks should be concerning as well.
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I still think you are missing the actual Coasian point from “The Problem of Social Cost.” A huge part of why Pigou was wrong in his analysis of externalities was because he calculated the total value of crops/land damaged by sparks from a train, not the marginal value. That seems to be exactly what you do here in calculating the total loss to a senior of contracting and dying from Covid.
But this situation is so contrived anyway – why require constant mask-wearing when what matters is the interaction with the senior? This could be the case if they wore a mask when the senior came to the office or if the senior was interacting with someone they hired to go for them or if the senior wants to interact with people in their own homes.
As a matter of policy I agree that requiring masks instead of shutting down businesses (not a Chinese-style lockdown, but a lockdown in any normal world) is superior, but the question is how necessary and how far mask requirements should go and to whom they should apply.
The lags behind the costs of shutting off economic activity, or severely limiting human interaction, including interaction while wearing masks should be concerning as well.
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Constant mask-wearing is for two reasons:
1. You don’t know if you are interacting with a vulnerable person. Age is only one factor. The contrived example comes directly from Caplan, I am just responding to it.
2. Community transmission is as important as directly infecting others. The worse community transmission is, the more likely governments (as we have seen in practice) are to impose even harsher measures.
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As a data point, I’d pay $4k to not wear a mask anywhere, but I’m older and I have some money.
One objection I have is your assumption that “wearing a mask is a very small inconvenience.” Is it a very small inconvenience to women in Iran when they are forced to wear the hijab? The purpose does not matter – whether fighting covid or fighting the kafir – the convenience is independent of the purpose.
As far as WTP, no one should be willing to pay – or expected to pay – anything to obtain his own natural rights. This clause, “young people… willing to chip in $2,000-$4,000 each for the right to not wear masks” is wrong on the morals. You can pay to acquire land rights, or IP rights, but not the rights to your own body. You’re born with those.
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I like how Horpedahl begins his essay by point out the reciprocal nature of externalities–or what Coase himself refers to as “harmful effects.” Alas, Horpedahl draws the wrong lesson here (putting aside the total artificiality of his numbers). As Stigler points out in his short essay “Two Notes on the Coase Theorem” (Yale Law Journal, 1989), available here: https://digitalcommons.law.yale.edu/ylj/vol99/iss3/4/, Coase’s main point is that no efficient bargains will occur when the costs of bargaining exceed the gains to be made by such a potential bargain. The problem with Horpedahl’s analysis (and Caplan’s, for the matter) is that there is more than just one senior citizen who may have to visit the office in his example, so any bargaining between the ten office workers and all the seniors who want to potentially visit the office is going to be too costly relative to the potential benefits that could be obtained by both groups if such a bargain were made.
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