Taxing sin goods and subsidizing health care

We consider a two-period model. In the first period, individuals consume two goods: one is sinful and the other is not. The sin good brings pleasure but has a detrimental effect on second period health and individuals tend to underestimate this effect. In the second period, individuals can devote part of their saving to improve their health status and thus compensate for the damage caused by their sinful consumption. We consider two alternative specifications concerning this second period health care decision: either individuals acknowledge that they have made a mistake in the first period out of myopia or ignorance, or they persist in ignoring the detrimental effect of their sinful consumption. We study the optimal linear taxes on sin good consumption, saving and health care expenditures for a paternalistic social planner. We compare those taxes in the two specifications. We show under which circumstances the first best outcome can be decentralized and we study the second best taxes when saving is unobservable.