Sin good consumption entails health damage, which is in general not fully perceived by individuals, what results in its overconsumption. One way to tackle this problem is to tax these unhealthy goods. However, not all the individual choices that affect health status can be easily observed and effectively taxed by the government. This paper considers a setting where individuals can consume two types of sin goods that differ in their observability (taxability) by the government. As a benchmark, the first-best taxes for the observable and non-observable sin good are derived, considering homogeneous individuals. In the second-best setting, where observability on sin good consumption is limited, the rule for the taxable sin good is shown to depend on the degree of complementarity or substitutability with the unobservable sin good. Finally, redistributional considerations are incorporated by extending the analysis to a setting where individuals differ in their wealth and in their degree of misperception of the health damage caused by sin good consumption. Policy implications are illustrated considering physical inactivity and illicit drugs as examples of non-taxable sin goods, while alcohol, tobacco, fat and sugar account for the taxable sin goodsillicit drugs, optimal taxation, physical inactivity, sin goods, taxability | INTRODUCTIONOne of the biggest health concerns today is that individuals engage in too much risky health behaviors. Sin good consumption and physical inactivity are the main reasons that account for the increasing risks of dying from a noncommunicable disease, which according to the World Health Organization (WHO) kill 41 million people every year. 1 Sin goods such as tobacco, alcohol, fat or sugar have been the target of different public policies aiming to discourage its consumption. These policies are justified by the fact that individuals fail to fully acknowledge the consequences caused by their sin good consumption, both to themselves and to the rest of the society through an increase in health care costs. One important measure to mitigate this overconsumption problem has been to increase their price through the so called sin taxes.While taxes have proven to be an effective tool to reduce tobacco, alcohol and sugary beverage consumption (Chaloupka et al., 2019), they are criticized for being regressive (e.g., Allais et al., 2010;Gruber & Kőszegi, 2004), as well as by the fact that they may induce consumers to substitute its consumption towards relative less taxed harmful goods. 2