On and after January 1, 2001, whenever the employees in the classified service of the state merit system receive a cost-of-living increase or general performance based increase of a certain percentage or a certain amount, the compensation to which a member of a governing authority is entitled under general or local law shall be increased by the same percentage or same amount applicable to such state employees. If the cost-of-living increase or general performance based increase received by state employees is in different percentages or different amounts as to certain categories of employees, the amount to which a member of a county governing authority is entitled under general or local law shall be increased by a percentage or an amount not to exceed the average percentage or average amount of the general increase in salary granted to the state employees. The Office of Planning and Budget shall calculate the average percentage increase or average amount increase when necessary. The periodic changes in the amount to which a member of a county governing authority is entitled under general or local law shall become effective on the first day of January following the date that the cost-of-living increases or general performance based increases received by state employees become effective; provided, however, that if the cost-of-living increases received by state employees become effective on January 1, such periodic changes in the amount to which a member of a county governing authority is entitled under general or local law shall become effective on the same date that the cost-of-living increases or general performance based increases received by state employees become effective.