The Spirit of Divination

In Acts 16, there is a reference which, I must admit, puzzles me considerably. Perhaps someone else has seen something here that I haven’t, and can clear this up for me. It says that Paul and Silas came across a woman who was possessed by a spirit of divination, and her masters made use of her soothsaying to make a profit. I suppose it is possible that she merely told fortunes, but I get the distinct impression that she was able to predict shortages of certain materials or foodstuffs, and so her masters were able to stock up on such things before they became scarce, and then sell them at a higher price than the norm, thereby making considerable profit. It says that she followed them around for several days, announcing that these men were the servants of God, which show us the way to salvation. Finally Paul became grieved and commanded the spirit to leave her. After that, though, the men who owned this woman got angry at Paul and Silas, and had them arrested and thrown in prison.
What I am wondering, though, is the nature of the spirit. As far as I know, angels don’t go around possessing people, nor would an angel allow itself to be used by men to turn a profit, so that would suggest that this spirit was a demon. On the other hand, if it were a demon, why did not Paul cast it out immediately upon becoming aware of it? I’m also a little concerned at the thought of a demon, apparently of it’s own volition, following around men of God, and telling anyone who would listen that these were, in fact, men who were knowledgeable in the ways of God. I think that if I were a demon, the last thing I would want people to know is how to get saved, or who to talk to about how to get saved.
Of course, if you read through the Gospels, I don’t think that there were any demons cast out by Jesus that tried to deny who He was (some people today could learn from those demons) (see Luke 4:34). I can only assume that those demons were constrained by a mightier Spirit. Perhaps the same mechanism was at play in Acts 16. Don't misunderstand me, I'm not suggesting that demons can't lie about God, or about who is truly serving God, but I do think that demons are only as powerful as God allows them to be. If God does not allow them to lie, then they cannot lie.
That still leaves the question of why Paul waited so long to cast out the demon. Perhaps because it was God’s will to let this demon (known for clairvoyance) speak the truth for a time. There were men that were making a profit off of this demon, and God may have wanted them to have no excuse, because they would have had a chance if they had listened to her. In all honesty, it seems particularly strange that these men ignored what the demon said about Paul and Silas repeatedly for days. These men got angry at Paul and Silas, because she lost her ability to divine the future. If they had kept her away from Paul and Silas, they could have continued to make money off of her. If they had listened to what she said about Paul and Silas, they might have been considerably less concerned about material things. They were worried about making money, and missed the most important thing that ever came out of her mouth.