Sorry about the delay in answering this; I didn’t realize there was a pending question.
Let me clarify one thing about these types of examples, and tell me if this solves your problem. (I’m happy to continue discussing with you until you see it.) And of course, obviously I’m not trying to say, “I, Bob Murphy, endorse this plan of having the government own all the roads and achieving a social optimum via taxation.” Rather, I just want to make sure you see the logic of it, from the Pigovian perspective.
If any individual motorist takes the nice road and pays the toll, then total revenues go up by the toll amount. Let’s say it’s $10. Then, at the end of the period, the government sends everybody a lump-sum check that equally divides up the total revenue collected.
So if there are (say) 10 total people in the community, then the motorist would think, “If I pay this $10 toll, at the end of the month my check from the government will be $1 higher than it otherwise would have been, so effectively I’m only paying $9 to take this nice road right now.”
But of course there are more than 10 total people. Suppose there are (say) 1,000 people. Then in that case, the extra $10 in toll receipts gets divided up over 1,000 people, so everybody’s check that month goes up by one penny, if the motorist takes the nice road. So the motorist would think, “In reality, instead of costing me $10, this road is really only costing me $9.99.”
And then, if there are 10,000 total people in the community who get those checks, then the marginal cost to any motorist of taking the toll road is $9.999, etc.
So the idea is, people’s decisions about the toll road only have a very slight impact on how much they get in a lump-sum rebate check from the government. With a large enough community, the individuals can treat those lump-sum checks as “given,” even though in the aggregate the total amount rebated must equal the total amount collected in tolls.
Once you’ve digested this clarification, see if my discussion makes sense. If not, I’m happy to keep working with you, but it seemed the above clarification was the thing you needed?