Are you including just the fare you pay in a nationalized system or also including the subsidies to keep it running?
Because it is nearly certain that costs will rise when the government takes over. They will raise salaries, increase the number of jobs "needed" to run it, bloat the administration with political cronies, and all the other things government does when they try to run a business.
I'm talking about government infrastructure payments, and subsidies that count as "profits" which ultimately come from the tax-payer for a service that is supposedly "privatized". In reality it is not.
It also appears that privatization has resulted in the closure of manufacturers of rolling stock.
I will fully admit that I really do not know how much a nationalized rail service will cost (particularly the cost of re-nationalizing, which may be considerable), but it seems to me that privatization has not lived up to its promises and has not resulted in a more efficient service, has reduced accountability and meant that government is not in control to improve things.
I wonder what would happen if government subsidies were to suddenly halt. Would the rail services simply go bust? It seems like it.
When were the military and police nationalized? And since when were those considered businesses anyway?
Well, armies and navies used to often be made up of privateers, militias and pirates - standing armies are relatively modern, as I am sure you will know from your history lessons.
As for the police, I believe that nationalized police services began with the Bow Street Runners.
Of course there are still private security firms, mercenaries and bounty hunters that governments could turn to instead of national organizations, and there are some "libertarians" who favour such ideas. Not me, though.