Unemployment on a 1 trillion pop world (EEK!)

So I began to take a closer look at the population of Kobra World and realized I had a problem, the neighboring worlds and sectors in the Collapse Zone couldn't possibly sustain its level of economic growth, or even a low level of stagnation. Early on, I had imagined that the various worlds of the Kobra Alliance were helping the 1 trillion people survive, but looking at it now, the numbers just fall too short. For one, there are just a handful of agricultural worlds nearby, no where near enough to support a city-planet the size of Kobra: starvation issue!!! Also, I would guess that the governor of the planets' primary job would to try and get work for the unemployed on the planet, which I guessed was between 200-300 billion people! With that many citizens just sloshing around the planet and not producing anything and sucking down resources, I think I have a serious problem. I mean 1 trillion people on a planet would consume a VAST amount of products, food, medicine, etc. and the local Kobra Sector in its entirety still cannot support this number of people. In addition, with so many unemployed, there is a very bad secondary problem: idle hands are the devils workshop. People tend to get into mischief when they are bored and have nothing to do. I think I am missing out on how bad it could really be on Kobra World, that it most likely could be more of a "crime world", with billions and billions of pick pockets, thieves, et al. I guess I will have to rethink this but only a few options present themselves. First, Kobra World itself is at TL18-20, and therefor could use advanced 3D food printing technology. That alone could solve most of my problems. Second, at TL18 antimatter plants are available, so that covers energy. Third, Kobra World could use automated mining ships across the sector (or even manned ones) to support the vast influx of resources needed to sustain the city-states' technological civilization. Or, several jump conduits are still open at Kobra World and bring goods and services from other nearby sectors? I will ponder more. Any feedback is welcome.