Medicare was designed to guarantee medical care to the vulnerable elderly. However, it is precisely this vulnerable population that tends to die younger and receive fewer Medicare benefits. Motivated by this fact, we propose to answer three questions. (1) Is Medicare actuarially fair to individuals at high risk for mortality? (2) What is the effect of Medicare on the welfare of groups with different mortality risks? (3) Can different payment schemes, such as means testing or more progressive tax payments, improve the welfare effects of Medicare? We focus specifically on three identifiers of high-risk individuals: having low educational attainment, being a racial minority, and being a smoker. To conduct the calculations of actuarial fairness, we propose to use the Health and Retirement Survey (FIRS) Earnings and Benefits supplement to calculate total Medicare taxes paid by groups with different mortality risks. Expected tax payments are then compared to expected Medicare benefits, calculated from Medicare Current Beneficiary Survey (MCBS) data. To calculate the welfare effects of Medicare, we rely on the theoretical insight that Medicare functions as a mandatory annuity for medical care. Young taxpayers are required to purchase this annuity, which pays out medical care when the taxpayer reaches age 65. Requiring everyone to purchase this annuity raises the annuity price paid b individuals with high mortality risks and lowers it for those with low mortality risks. This analysis provides us with formulae for calculating the welfare lost by high-risk people and gained by low-risk people, using life table data and MCBS data. Finally, we will use our results to simulate the impacts on actuarial fairness and on welfare of making Medicare taxes and co-payment rates more progressive.