Everything more I learn about economics brings me back to this single problem. Instead of finding answers to how to solve this, the unsolvability of it is simply reinforced.
At the core, economies run on food. No other product, or economic production can really be substituted for it. You can trade with underpopulated countries, so long as someone out there has a food surplus, but world wide population growth coupled with world trade, causes those countries to become fewer every day and/or for their surplus to get smaller every day. Food growth requires real estate, and the quantity of real estate never increases. (It's quality does, but there are maximum practical limits on quality as well.)
Then there is energy. As more of the world industrializes, Oil gets more expensive. Uranium/nuclear power might start getting more popular, but it also has the potential to run out. Solar and Wind require real estate, and.... then we're facing the same problem as food.
World trade enthusiasts often point out that countries can extend their access to resources by trading with each other, but I think sometimes they forget that Planet Earth itself is still a closed system. If all the countries become overpopulated, we're not going to start trading with aliens to solve our problem.