Each member who has retired under the tier II plan and who is receiving benefits, each spouse or contingent annuitant receiving income under an option specified in section 5-192q, and each spouse or contingent annuitant receiving benefits under section 5-192r, shall be eligible for an annual three per cent cost-of-living allowance increase commencing on the first anniversary date following the completion of nine months of retirement. Such cost-of-living allowance increase shall be computed on the basis of the retirement allowance to which such employee was entitled on the day preceding his latest anniversary date. The anniversary date of such employee shall be the first day of January or the first day of July following completion of nine months after the effective date of retirement. If the member was not covered by Social Security, for at least half of the period of his vesting service and the member, spouse, or contingent annuitant receiving benefits has attained age sixty-two, the cost-of-living allowance increase shall be six per cent. If on any applicable anniversary date, the Retirement Commission determines that the National Consumer Price Index for urban wage earners and clerical workers for the previous twelve-month period has increased less than the cost-of-living allowance increase provided by this section, the cost-of-living allowance increase shall be equal to the percentage change in such index, provided such cost-of-living allowance increase shall not be less than three per cent. In addition, a member’s benefit may be increased by the Retirement Commission as provided in subsection (b) of section 5-162h. If a member’s benefit under section 5-192p is changed under subsection (f) of said section, the new benefit will be increased by all the cost-of-living allowances that had applied to the member’s previous benefit.