The head of any family domestic unit or commercial unit shall have the right to make written application provided to the Common Council to be given a rate reduction below the minimum rates herein provided, and to make either a written or oral showing to the Common Council that the amount of garbage and rubbish which has been, or will be, hauled from the applicant’s unit is negligible and far below the average of the particular type of unit. If the applicant makes said showing to the satisfaction of the Common Council, the Common Council shall have the power to authorize a rate reduction to that applicant to any amount below the minimum being justified, depending upon the amount of garbage and rubbish to be hauled from that unit. The Common Council shall have the power, after due notice is given to a unit, to cancel at any time a rate reduction given to that unit under the provisions of this section. (Prior Code, § 50.23)