(b) Each license issued pursuant to section fifty-five-a of this article shall be effective for a license year expiring on the thirty-first day of March following the date of its issuance and the license fee prescribed therefor shall be the license fee due and payable therefor and shall be paid in advance of the time of the application as provided for in this article. 2. When application for any license under this article is made after the commencement of the license year hereinbefore provided the license fee therefor shall, for the balance of the license year, be in proportion as the remainder of such year shall bear to the whole year, except that it shall in no case be for less than one-half of such year.