The mayor shall have the power to investigate and to examine or inquire into the affairs or operation of any city department, division, bureau or office; and when so authorized by the council, the mayor shall have power to employ consultants and professional counsel to aid in such investigations, examinations or inquiries if money has been budgeted therefor in the year in which they are employed or if an emergency ordinance has appropriated the necessary funds for such personnel. (1957 code § 1.03.090.)