The mayor shall be responsible for the preparation of a position classification and pay plan which shall be submitted to the city council for approval. Such plan may apply to all employees of the city and any of its agencies, departments, boards, commissions, or authorities. When a pay plan has been adopted, the city council shall not increase or decrease the salary range applicable to any position except by amendment of such pay plan. For purposes of this section, all elected and appointed city officials are not city employees.