# Optimum Prevention

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.