We study the role of social long-term care (LTC) insurance when income taxation and private insurance markets are imperfect. Policy instruments include public provision of LTC as well as a subsidy on private insurance. The subsidy scheme may be linear or nonlinear. For the linear part we consider an arbitrary number of types, characterized by earnings and survival probabilities. In the nonlinear part, society consists of three types: poor, middle class and rich. The first type is too poor to provide for dependence; the middle class type purchases private insurance and the high income type is self-insured. The main questions are at what level LTC should be provided to the poor and whether it is desirable to subsidize private LTC for the middle class. Interestingly, the results are not totally similar under both linear and nonlinear schemes. First, whereas in the linear case a subsidy of private LTC insurance is desirable, it is not in the nonlinear case (at least at the margin). Second, the desirability of public provision of LTC services depends on the way the income tax is restricted. In the linear case, it may be desirable only if no demogrant (uniform lump-sum transfer) is available. In the nonlinear case, public provision is desirable when the income tax is sufficiently restricted. Specifically, this is the case when the income is subject only to a proportional payroll tax while the LTC reimbursement policy can be nonlinear.