Assume you use prevention efforts *P* to reduce a harm *H*, a harm which depends on those efforts via some function *H*(*P*). If you measure these in the same units, then at a prevention optimum you should minimize *P*+*H*(*P*) with respect to *P*, giving (for an interior optimum) d*H*/d*P* = -1. And since in general dlnX = dX/X, this implies:

-dln*H*/dln*P* = *P*/*H*.

That is, the elasticity of harm with respect to prevention equals the ratio of losses from prevention to losses from harm. (I previously showed that this applies when *H*(*P*) is a power law, but here I’ve shown it more generally.)

Yesterday I estimated that for Covid in the U.S., the ratio *P*/*H* seems to be around 5.3. So to be near an optimum of total prevention efforts, we’d need the elasticity -dln*H*/dln*P* to also be around 5.3. Yet when I’ve done polls asking for estimates of that elasticity, they have been far lower and falling. I got 0.23 on May 26, 0.18 on Aug. 1, and 0.10 on Oct. 22. That most recent estimate is a factor of 50 too small!

So you need to argue that these poll estimates are *far* too low, or admit that in the aggregate we have spent *far* too much on prevention. Yes, we might have spent too much in some categories even as we spent too little in others. But overall, we are spending *way* too much.

Note that if you define P to be a particular small sub-category of prevention efforts, instead of all prevention efforts, then you can put all the other prevention efforts into the H, and then you get a much smaller ratio P/H. And yes, this smaller ratio takes a smaller elasticity to justify. But beware of assuming a high enough elasticity out of mere wishful thinking.

## Optimum Prevention

What do you suppose P is as a function of lockdown duration? If it's not linear, then percentage change in duration doesn't give percentage change in P.

If, for example, much of cost P was incurred before mid-April (via multiplier effect of early job losses), then percentage change in lockdown duration overestimates dP/P in your polls.

I think there are in fact three local optima: (1) completely squashing the virus (2) just enough measures to avoid hospitals being overrun ("flattening the curve") and (3) not doing anything except for things like hand-washing, and accepting the death toll. It is intuitive for me that a small policy variation from each of them would result in a net loss. A lot of the debate comes down to which local optimum you believe to be the global one. Right now many western countries cannot agree internally on what to pick and compromise between (1) and (2), with obvious sub-optimal results. Your analysis shows that US are on the side of (2) with respect to the local maximum between (1) and (2), but does not resolve the underlying debate. "Pick one and implement it, it would be strictly better" of course is also a good position that we should hear more often. (2 is also really difficult to reach exactly)