You don't seem to understand that as long as enforcement isn't 100%, the cost of punishment must exceed the cost of compliance if it's going to deter violation.
If the only cost of overrunning a meter were paying the amount of the overrun, any economically rational actor would simply never pay meters. If he doesn't get caught, he's parked for free; if he does get caught, he pays only what he otherwise would have.
The civil penalty for laws like unpaid parking meters and illegal downloading of copyright works should be slightly greater than the original cost times the inverse enforcement rate. If we catch 1% of parking meter cheaters, they should pay at least a hundred times their overrun to ensure that it's economically rational to pay meters. Since we need only deter humans, not "economically rational actors", we can take risk aversion and incomplete knowledge into account and probably decrease that fine somewhat.
The same principle that applies to parking meters applies to copyright infringement.
I'm more concerned about does the cost of the punishment fit the crime. Using your formula if the original media costs $1 and only 1:20000 people are caught it makes the case that a $20,000 fine is perfectly reasonable. This I disagree with.
Your assuming you need to deter violation. Many organisations like the red cross operate just fine despite the free rider problem. Personalty, I don't support copyright for Music performances period end of story, and I doubt the vast majority of musicians would notice a difference.
However, more generally the final penalty needs to be adjusted by the penalty associated with being prosecuted. If the penalty is 1,000$ / song, but you need to go to court to defend yourself then the effort associated with that court case is also part of the penalty of enforcement. Also, because your fine can't drive you past bankruptcy ridiculous penalties have little meaning (this plays into the last banking bubble. I can sell a trillion dollars worth of insurance far below costs if I don't have a trillion dollars because my downside is limited to the value of my assets.)
The "economically rational actor" thing has been debunked long ago (see Kahneman and Tversky). There are much better ways to get people to behave the way you want then appealing to their statistical skills.
If people are more annoyed by parking tickets than by people parked in the places where they prevent traffic and provoke accidents, then we should consider toning those down and/or making rules less strict.
But I guess that if the problem really exists, people would be pro big parking ticket fines, because a minority who get those also annoys the whole population.
The trouble is that the parking tickets may have caused the decline of the number of people parked in places where they prevent traffic or provoke accidents. In that case, the major annoyance is gone and the parking tickets is only the new minor annoyance, but now the biggest, that took it's place. Reversing the amount or height of parking tickets will not cause a decline in annoyance then.
