Market Urbanism has posted a fairly technical explanation why the congestion price that maximizes throughput also maximizes total revenue. I'm not sure his explanation is correct because he ignores drivers' sensitivity to price. If they are relatively insensitive, then the revenue-maximizing toll will be higher than the through-put maximizing toll. We have plenty of real-life examples. TxDOT charges tolls for SH45 even when traffic is light. Total revenue from these tolls exceeds the revenue that the optimal toll ($0) would generate.
That's a debate for a different day.
What I want to point out here is that Market Urbanism's argument does not affect my transit-subsidy hypothetical. (To be fair, I'm not sure that he's offering a rebuttal to my hypothetical.)
In my hypothetical, I assumed that both bridge users and transit riders are charged the optimal toll. I'm happy to assume these tolls also maximize revenue.
My hypothetical was about transit subsidies. The optimal transit fare might maximize revenue but still not cover the cost of the transit. But that's OK, libertarians, as long as the bridge users generate excess revenue -- i.e., more than the cost of the bridge. As long as everyone is charged the optimal fare, and the combined revenue covers the combined costs, the "network" -- bridge + transit -- is efficient, despite the transfer from drivers to riders.
That the optimal toll on one branch of the network maximizes revenue from that branch does not prove that the revenue will cover the cost of that branch. Nor does it show that the optimal toll should cover the cost of that branch when the system as a whole is revenue neutral.
