I am interested in getting some answers for
- Why a new bounty system for SO questions?
- Is it to increase answer rate to unanswered question?
- What is the purpose of opening bounty to other user's questions?
I'm assuming you already read the related blog post?
Becausethe old system was very imperfect and caused a lot of complaints and feature requests.
I like to view it as the fixing of a system that was partly broken, with beneficial consequences all round.
The main purpose is probably avoiding duplicates: If you had a question you urgently need answered, and it had been asked already, under the old system, you were forced to try and open a duplicate and hope it survives until the 24 hour waiting period was over. Now, you can simply add a bounty to the already existing question.