#1 Benefit = Survival of the human race.
I have long thought that a primary reason aliens do not visit us regularly is that a civilization would have to be incredibly lucky to get to the point of being capable of interstellar travel. Mo Nature is TOUGH — as recently as the last glacial period (an eyeblink in time), it is believed humans were down to a few hundred individuals, and that was just a “wiggle” in natural history. One cosmic burp of one sort or another, and we are done, if we don’t spread out.
Then include human ingenuity (a big nuclear war, biological warfare at its potential worst, etc).
The key is wealth. Just as it takes wealth to have a large population and a clean environment, it will take great wealth to save us (or at least some of us) from the otherwise inevitable.
Assuming technological advances on a par with the last 200 years, for the next 200, and assuming we could locate a planet within, say, 100 light years of Earth, that we’d be almost sure could support human life, what would be the cost to send 200 humans there? Assuming wealth creation increasing at 4% a year, what % of US GDP would be needed?
“#1 Benefit = Survival of the human race.”
Ah, but that is not an immediate benefit, just a speculative benefit that might arise at some indeterminate time in the future. So even if the benefit might be very great (in theory), it’s remoteness and uncertainty have to be taken into account when you weigh it against very immediate and concrete costs.
“Assuming technological advances on a par with the last 200 years, for the next 200, and assuming we could locate a planet within, say, 100 light years of Earth, that we’d be almost sure could support human life, what would be the cost to send 200 humans there?”
Well, I think your assumptions are too generous, since even with exponential technological advancement you cannot overcome obstacles like the laws of physics. We have not even conceived of any remotely plausible methods to travel faster than the speed of light, so I doubt anyone could ever reach another solar system in their lifetime unless we make some scientific discoveries that seem to be extremely unlikely.
We could possibly build slower than light speed ships (small unmanned ones for exploration necessarily) to see if there are any habitable planets, which would probably take us centuries to find (if they exist). Then we could build multi-generational colony ships that people would live, reproduce, and die on before they ever reached those planets. I wouldn’t even venture a guess as to the wealth required for such a project, but it would have to be (pardon the pun) astronomical.