You're ignoring all the money spent by individuals on car and fuel. Roads are cheap. Cars are not.
Because individuals don't buy taxis. Have you ever bought a taxi? No, you pay for the fare. Why are you insisting on including the cost of somebody else buying a vehicle?
To... help you understand, sheb is bringing up the cost of somebody else buying a vehicle because you're using road costs -- of which only a tiny fraction is taxi-related -- vs. rail costs as a point of comparison. The road costs in question largely
don't include things like individual vehicle maintenance (including replacement) or gas costs, which is where sheb's problem is coming from. With those included, it would be a higher number. How
much higher, I couldn't say, especially considering vehicle purchase and maintenance patterns are very... suboptimal.
It's all kind of "back of napkin" calculations, though... the actual question you'd be looking for in terms of cost/benefit analysis would be dollar generated for the overall economic system per dollar spent, I think, which is a considerably more complicated question. In the case of the subsidies, ferex, if the tax money being spent in rail is overall generating more than is being sunk (by enabling people to get to work, or move product, or consume goods), then it's not really a loss even if the immediate transportation service is.
'Course, that said, given that vehicles largely
aren't subsidized, the fact that people have and use them kinda' imply they're managing an economic benefit somewhere in there, so unless the indirect effect of subways are rather impressive they're still going to be losing out pretty heavily in terms of cost efficiency.
Shouldn't the time wasted on the travel be included into the cost? Because subways are way faster than taxis.
They're only faster between very specific points, though, and time wasted on travel for rail involves transit time both to the subway, to the destination, and back again.
Assuming a typical small car like a Renault Clio, you're looking at 5l of gas/100 km, so 57 millions liter of gas. If a car run for 150000km before needing to be changed, you're going to get through 7600 cars. At 1.2 euros/l for gas and 12000 euros/car, you're still looking at something way cheaper than mass transit. Crap, look like I'm wrong here.
Do note that there's still maintenance costs involved to get those vehicles to run 150k-km. Probably still wrong with that included, but maybe not
as wrong

How can a public transportation system be more costly (per person) than an individual one???
Well, for one they tend to be underground. It's really bloody expensive to build underground. Also have a higher standard of maintenance they have to keep to to keep people from going splat. And then there's other stuff. Not exactly an expert on the economics of public transport, ha.