If a city and the police department of such city adopt any program of incentives to authorize or encourage early retirements, whether for employees not yet eligible for regular retirement or for employees who are eligible but have not yet chosen to retire or for both, the retirement board shall be authorized to administer and pay such incentives for retirees who accept such incentives and are members of the retirement system under sections 86.1310 to 86.1640, in addition to such other benefits as such members or their beneficiaries are entitled to receive under sections 86.1310 to 86.1640, provided such city shall so request and shall agree to increase said city’s contribution under section 86.1390 sufficiently to provide the full actuarial cost of any such incentives in addition to the contribution required of such city necessary, in conjunction with members’ contributions under section 86.1400, to provide all other benefits provided under sections 86.1310 to 86.1640.