The two-type model of non-linear income taxation with asymmetric information on individual ability levels is extended to discuss welfare effects of two policy instruments: a pure public good and a publicly provided private good. This latter is interpreted as health care. Three different cases are analysed:\ when each policy instrument is used in turn and when they are jointly used. The publicly provided private good is proved to be welfare enhancing when it is used as the only policy instrument. By contrast, in the mixed case, the publicly provided private good acts as a lump-sum transfer to all individuals.