The model you've presented doesn't account for a lot of other effects which we want as a collective want to account for. Let's break it down.

We can't assume perfect humans, so we must assume that sometimes, some of the people will act irrationally or make mistakes. Introducing this "error rate" into our actors means there's an un-removable noise floor of cases where we issue fines to our actors for breaking the law.

This noise-floor of mistakes leads to some very unfortunate side effects when we use constant fine pricing. Assuming an income distribution like what we have in reality, this means that a certain percentage of our population will have so little income that the fine will ruin their life, making them less effective and thus our population less effective. And there's no way we can remove this by adjusting the price of our constant fine. If we remove the fine, then everyone speeds. Even at the best sweet spot, we'll have a system where some people will always speed, and some people will never rationally choose to speed but will be economically "killed" by the fine anyway.

These two inefficiencies are what variable fine pricing are meant to address. By scaling price with actor income, we are able to maintain a similar relative (dis)incentive across income levels, and we remove the cases where we are sentencing a portion of the population to economic "death".

> Assuming an income distribution like what we have in reality, this means that a certain percentage of our population will have so little income that the fine will ruin their life, making them less effective and thus our population less effective. And there's no way we can remove this by adjusting the price of our constant fine. If we remove the fine, then everyone speeds. Even at the best sweet spot, we'll have a system where some people will always speed, and some people will never rationally choose to speed but will be economically "killed" by the fine anyway.

We already have a system for this, which is that the fine for speeding scales with speed. Then someone who can't afford the fine can drive more conservatively, so that if they make a mistake the degree to which they violate the rule is smaller, which reduces both the probability of enforcement and the amount of the fine.

Having at least that level of fine is inherently necessary, even for lower income people, because otherwise there is insufficient disincentive for them to speed and there is no compensation to society in the form of a proportionate fine when they do.

We can let a rich person get a thousand small speeding fines because taking their money and using it for lead abatement or cancer research saves more lives than they're risking. But we can't let anyone take that risk without "paying for it" or the net result is a very big social loss, multiplied by every person in that category who longer has any incentive not to do it.

Moreover, talking about "economic death" over a matter of something like a $250 fine is an exaggeration. Even for someone making the federal minimum wage, that's less than 2% of their income. That amount of money doesn't make the difference between whether anybody files for bankruptcy or not, it only makes the difference between whether it happens this month or next. And if you want to help those people, don't waive their traffic fines, just take all the money you would have waived in traffic fines and give it to lower income people regardless of whether or not they violated a traffic law or not -- so that you're helping them but not giving them incentive to misbehave.

>By scaling price with actor income, we are able to maintain a similar relative (dis)incentive across income levels

This is manifestly untrue, as I showed above.

If you're concerned over extremely poor people being unable to pay the cost, you can waive that or subsidize it. That's far from sufficient to justify scaling.

It's unnecessary to set a fine so high that the person doing it would "pay back" the harm to society on average if they did it. You merely have to set a fine so high that it deters people from doing it.

Let's say speeding causes a harm of 500 dollars, and there's a 10% chance of getting caught. Then you would put the fine at 5000 dollars. However, it might be the case that a 500 dollar fine (with an expected payment of 50 dollars) is already enough to stop everyone from doing it, since nobody likes speeding so much that they would pay 50 dollars for it on average. In that case, setting a 5000 dollar fine would just be overkill, and it could hardly be called efficient.

Moreover, your answer assumes that utility can always be measured solely in terms of money. If we measure the utility of society in terms of the number of people speeding (lower is better), then no amount of money can compensate for an increase in the number of people speeding. Then the answer would be to set the fine such that the number of people who choose to speed is the lowest, and does not involve the "expected harm" to society at all.

Even if you do assume that there is a conversion factor between "number of speeders" and "money", then it might still be sufficient to set the fine at a much lower number than you would get using your formula. You cannot just take into account the utility of the society, you also have to take into account the preferences of individuals (which guide their actions).

This can also be used to justify individual fines: if a 100 dollar fine is enough to stop you from speeding, and a 200 dollar fine is necessary to stop someone else from doing it, then why should I set the fine for both at 200 dollars? How can this be called efficient? You could argue it's more fair, but that's more a question of what's moral and has little to do with simple calculations, which you seem to be advocating for.

Yes, if for whatever reason nobody values an activity over the fine my formula produces, then any amount in between will be equally efficient: in your example any fine above $500 is equally efficient. But note that nobody ever pays the fine! In the real world, someone ends up paying the fine, it is not the case that fines deter everyone. So your example isn't reality.

>Moreover, your answer assumes that utility can always be measured solely in terms of money. If we measure the utility of society in terms of the number of people speeding (lower is better), then no amount of money can compensate for an increase in the number of people speeding. Then the answer would be to set the fine such that the number of people who choose to speed is the lowest, and does not involve the "expected harm" to society at all.

Sure, if your goal is prevent speeding at any cost then you should set the fine to be infinite. Or rather, set it at max wealth (since above that can't be collected) and pour all your policing resources into detection. Obviously, this also doesn't reflect reality.

>This can also be used to justify individual fines: if a 100 dollar fine is enough to stop you from speeding, and a 200 dollar fine is necessary to stop someone else from doing it, then why should I set the fine for both at 200 dollars? How can this be called efficient?

Again, it depends on the goals. In my framework the goal is to prevent people from doing something that harms society if and only if the benefit they get from it is less than the societal harm. Setting the fine equal to the harm (modulo probability) does that. If you charge some people more than this number, then they'll be deterred away from the action even when it would be efficient to do it. Conversely if some people are charged less.