This document discusses using premium policies to efficiently assign Medicare beneficiaries to traditional Medicare or Medicare Advantage plans. It argues that a single premium cannot achieve efficiency and that an income-based premium is needed. The key points are: 1) A single premium for all beneficiaries cannot achieve an efficient assignment between traditional Medicare and Medicare Advantage plans. 2) An income-based premium, where higher-income beneficiaries pay more to join traditional Medicare, can implement any efficient allocation. 3) Allowing Medicare Advantage plans to set their own premiums interferes with using premiums to efficiently assign beneficiaries.