Its true subways have lots of positive externalities not captured by the fares, that it would actually be better to have a deficit subway system than to not hav

Its true subways have lots of positive externalities not captured by the fares, that it would actually be better to have a deficit subway system than to not have it at all, both for economic reasons and plain welfare, but there's no need to abandon the profitability goal for that. IT is possible to devise a tax system that will capture some of that positive externality and make the subway better. It should be intuitive that the properties that got amazing value increases due to the subway should have an increased tax burden on them. A subway-proximity tax could be enough to turn subway profitable: and to easily fund expanding it!