Without greed and envy, yes, but also without compassion and sympathy. Why would welfare and disability exist, for example, in an AI driven economy? They represent a net drain, not a net plus, on society.
An AI would derive its conclusions based on objective measures, not human emotion, and even as destructive as human conclusions often are, they are also driven by things like compassion. If we see a hurricane devastate Haiti, for example, we rush rescue, food, medical supplies, etc. in to rescue and save lives. An AI might look at that and think saving the human lives and rebuilding the area are not worth the extra cost and effort.
Yes, but an AI would be more coldly efficient, first eliminating humans that consume more than they produce, then eventually deciding that the only humans it needs to keep around are the ones that maintain the computer systems the AI relies on.