How does Kandor maintain it's equilibrium while Superman searches for a way to restore the city back to it's original size? What does Superman have to do in order for Kandor to thrive? A city without commerce is a city in need of goods.
Evidently nothing. In Action Comics #866-868 we learn that Brainiac has been in possession of various "bottle cities" (including Kandor) for more than three centuries. In that time he seems to have had little or no input into their collective well-being other than storing them.
As to how they've managed to survive, it stands to reason that a highly advanced civilisation, such as that found on Krypton, would be able to achieve civilisational equilibrium with little or no effort when provided with an abundant supply of energy. Hydroponics would easily take care of basic food and clothing needs and the recycling of more complex goods would allow a basic standard of living to be maintained almost indefinitely.
Canonically, there has never been an explanation of how the Bottle City of Kandor maintained its needs. We have seen in the Silver Age images, a link to the bottle and the Fortress of Solitude, but we aren't ever informed how the ecosystem of the Kryptonians within was maintained.
- Given that the Kryptonians were a space-faring species for over 100,000 years, they likely had energy to matter conversion technology allowing them to have whatever goods they needed. They were likely to have to grow foods hydroponically.
- In the Silver Age, Brainiac captured dozens of alien cities and stored them, apparently without needing to tend to any particular needs of the citizens within. It is likely he was stealing civilizations whose technology would allow them to survive with little more than an energy contribution on his part.