Right, for comparison's sake I chopped off $51 billion bucks from the Northeast Corridor projection in the interest of balancing out the two.
Just because I felt like doing some more Google-fu, I found an article in the LA Times[0] that says a California HSR/bullet-train project is going to overshoot it's original budget (and deadline) of $68 billion. There's a lot of info out there about this project, and it's potential overruns, but let's forget all that and just stick to the original planned cost: $68 billion, so, about half of the cost of Amtrak's northeastern bullet. Let's use that number for our comparison.
If we are going to hold Elon to his "we can do it for 1/8th the cost" blurb, then we are giving him like $8.5 billion to use for his SF/LA Hyperloop. Still, that doesn't sound unreasonable, right? He'll get a good deal on tunnel boring with his other company, and fuselage manufacturing can be handled by SpaceX. When it comes to financing, I don't think it's a major issue compared to other infrastructure works out there.
Like I said, though, I'm just going off the top of my head. I don't know finance or economics or vacuums or magnets.
There's a new LIRR train being dug in NYC called East Side Access. This is a commuter rail line, and is going to cost ~$10 billion or so[1]. Logistically these aren't the same, obviously, but if adding to the LIRR is worth ~$10b then surely the Hyperloop experiment is as well, right?
EDIT: Also, just for disclosure, I don't live in California and I'd probably never end up using the Hyperloop myself so I'm neither for nor against it versus any HSR. I just want to entertain the idea that cost shouldn't be the main focus of discussion IMO.
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0. http://www.latimes.com/local/california/la-me-bullet-train-c...
1. http://web.mta.info/capital/esa_alt.html