I will try to give an answer, without citing sources and by reading the question in ways that may make my answer to be a bit off-topic. But that's me!
At the current population numbers we should be all able to live like kings - literally speaking. The only reason we don't, is that we have no leaders that are capable of cooperating and making strong friendships with other nations instead of going to war with them, being able to understand the planet's ecosystem and work with it instead of against it, being able to put order into mega-corporate and banking chaos, and also our population is raised with pretty nasty principles (cultivated by our ill-minded leaders again).
So, what's the max number of people our planet can hold without us starving to death?
I would say it is about 100 times the current population and without your futuristic assumptions, provided that we fix our attitude.
Most people count the land available for producing food, but they tend to forget that most of the planet's surface is oceans which too produce food, while they are brutally harvested and polluted and destroyed for no reason. If there were regulations in place that made it possible for the fish populations to grow in numbers and preserve the oceans clean from pollutants, GMO that eliminate well functioning organisms and other threats, the food coming from the oceans could make a huge difference (I will provide a link to a paper here, although I have not read it yet, but I imagine it shares some of my views: http://bioscience.oxfordjournals.org/content/59/11/967.full). The amount of material, food and energy waste today is unthinkable. The U.S. seems to be the king of wasting resources, but I can assure you, all countries do it in an extreme manner. In summary, our house building ways are terrible, our power production, storage and distribution ways are terrible, our way of life is organized in a terrible and inefficient manner. We live like we have unlimited and free energy already! Surely, future technology could help, but (1) the issue is that we currently don't need that and (2) history teaches that technology rarely do that, especially in our case, since the problem is not technological.
But I think I should divert your question to another path.
It's surely in our nature to dream and hope. But I think we should all dream and hope about different things than we currently do. The enemy of humanity is not the supposed lack of resources, energy, living space or food. The enemy always lies within us. It's our choices, our desires, our ideologies, our way of life, our habits, our desire to enjoy ourselves and our very dreams which are corrupt. Those are that always destroy us throughout history and they will destroy us in the future.
But if you desperately need some other threat to humanity that does not emanate from humanity itself, that would be our decaying genome. Contrary to what Dawkings wants you to believe, humanity and the animal/plant kingdom are fading fast genetically. Despite the fact that a vast percentage of this problem is again attributed to ourselves and our choices (one can say so much on this topic...), avoiding this is not possible. And if one dreams of us understating and fixing our genome, good luck with that... Even the simplest things in the inner workings of bacteria baffles scientists for decades. And if understanding those systems in their entirety seems impossible, fixing them is simply not doable. Our best bet for living some extra years as a species is keeping our population big enough and divergent enough and procreate before our 20-ies with one and only mate.
Earth is our home. Our only home. Resource-hungry NASA may manage to plant some toxic GMO plant on another planet making humanity believe that we may soon get a new, fresh, clean and unpolluted home. But that will never become our home and if it does it would only be a misfortune for us. Our home is one and our future is limited. Come to terms with that and let's make the time we have matter.