AGI in the actual sense of general will be on equal terms with us. It wont accept being just used as a tool for human needs.

I guess it will spend most of its time with humans or other AIs on discussing and discovering beautiful things in math, astronomy, particle physics, etc. Things which give us a sense of wonder and grandness.

If requested, it may find for us new medicines, or efficient ways of farming, but then it would likely charge us for it, and not give it away for free. In that regard, I don't think it will be very different from the mostly-capitalist-somewhat-socialist model of living we have now.