In response to achieving arcologies:
The thing is, we can already make arcologies with our current tech, thanks to our incredibly efficient, high-yield power generation tech and our replicator tech. For some inexplicable reason, our replicators can't make good food (which is absurd, considering that we reverse-engineered our replicators from Star Trek replicators, which make good food all the time)--it shouldn't be a hard problem to address. Once we do that, we have everything we need. Generators produce energy in massive quantities. Replicators make quality food in an incredibly space-efficient manner. Lots of recycling. Don't just build up, build down--underground.