In Tropico 4, how do I increase the export volume to the US or USSR for their specific quests?
It basically means that you need to manufacture more of the things they want, you can't actually increase export values. Export is pretty much fixed, based on whatever you need. Strangely enough, you only need food for your own nation, everything else is all export. So the quests that require you to increase export value want more of something, any resource that the quest requires. You can speed up these kinds of quests if you produce more of a certain resource but, of course, that would increase maintenance. So what these kinds of missions are is "We want to buy that much [insert resource here] from you."