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pereh: So one might think that the output of a farm is not important, as long as it has water under it and the needed amount of workers. But a game that simulates an economy should not work that way; or if it does, it is not worth playing.

What am I missing here?
The game simulates an economic system, not the minutiae of real farming, real import/export, ceramic making or any other industry. It probably applies an average to each industry sector since it is a city building game.
I found a fantasic website, and this page shos which months exactly are certaing crops being tended and harvested. So you can optimize your farms: emperor. heavengames. com /gameinfo/tables/s1