AI making units it does not have the resources to make?

Has anyone noticed that the AI is able to make units regardless of what resources it has? I've been trying to get a good game going with the sparse resource setting, but the AI(on hard) always seems to be able to produce troops, fast, a lot, and with weapons and armour they do not have the resources to make. I realize the difficulty level gives them a slight advantage, but its ruining the game for me since I can't get a game going where everyone has to rely on leather armour and wooden weapons a lot more. : /