Are these useful comparisons? How can you possibly compare a train running the length of Manhattan to anything in Copenhagen? I want to know how much a new train line costs in Tokyo.
A quick glance at this [2] engineering book indicates Copenhagen is limestone. Apparently the same is true for Paris. Any engineers here who want to chime in about how that affects cost?
[1] http://mobile.nytimes.com/2012/08/05/magazine/tunneling-belo...
[2] https://books.google.com/books?id=6UAqS62NJDMC&pg=PA2616&lpg...
https://pedestrianobservations.wordpress.com/2011/05/16/us-r...
Also note that Tokyo is much less dense than Manhattan. A better comparison would be Hong Kong, except that labor and other costs there will be dramatically less.
https://en.wikipedia.org/wiki/Special_wards_of_Tokyo
Note that the entirety of the Fukutoshin Line was within the 23 wards.
https://en.wikipedia.org/wiki/Tokyo_Metro_Fukutoshin_Line
However, it's only a single stop on the line; the other 15 stops are in Central Tokyo.
https://en.wikipedia.org/wiki/Manhattan
and therefore still significantly larger than Central Tokyo's 15,146/km². The 10,194/km² figure you quote is for all of New York City (all 5 boroughs)
https://en.wikipedia.org/wiki/New_York_City
which is to be compared with 6,225/km² for Tokyo Metropolis (i.e., the city proper, not the greater metro area, which is 2,662/km²).
Not exactly Tokyo, but in Seoul between $43m/km and $87m/km, Hong Kong $586m/km, Singapore $600m/km.