(a)   The board of mayor and aldermen may determine the salaries of aldermen and school committee members by ordinance provided that no ordinance shall take effect until the commencement of the next term of office of the board of mayor and aldermen.
   (b)   The salary of the mayor shall be set at sixty-eight thousand dollars ($68,000) after the election of a new mayor at the next municipal general election. The mayor's salary shall not be increased from the time of any election until the close of the term of the mayor then elected. The board of aldermen shall have the power to increase the mayor's salary as they deem necessary, but shall not lower said salary.