To me, that's the beauty of having a detailed budget that is approved by the membership at the start of the year -- you DON'T have to vote on every little expenditure, as long as they are within budget. In my opinion, there's no need to detail that in the bylaws, it's implied by the fact that your budget is approved.

We have an approved budget detailing how much money is paid for specific items. We give teachers a stipend each year and give cash prizes for halloween costume winners. Can the treasurer act on the authority of the president to pay those items out? Or does the board have to re-approve the payout. Should this be specifically outlined in the by-laws?