Caravan effects on cities?

What kind of effect, if any, will a caravan have on its starting town? Do caravans always return to their starting town, if so, will that affect its prosperity, food, etc.? Or do they just travel anywhere chasing the best profits?

The basis of my question comes from the fact I was just granted my first city, and it has a negative food stat. Some of the connected villages weren't doing great, so I'm making sure to patrol them and complete any missions they have, but they are improving almost none (I may just be impatient). I've also queued up food improvements in my city to be built. So while all that is happening, I've been manually buying food from other sources and selling it to my town to keep it afloat, and this got me wondering about my original questions.