This paper shows that if an individual’s health costs are U-shaped in weight with a minimum at some healthy weight level and if the individual has both self control problems and rational motives for over- or underweight, the optimal paternalistic tax on unhealthy food mitigates the individual’s weight problem (intensive margin), but does not induce the individual to choose healthy weight (extensive margin). Implementing healthy weight requires a further distortion (e.g. subsidy on other goods), which may render the tax on unhealthy food inferior to the option of not taxing the individual at all. In addition, with heterogeneous individuals the optimal uniform paternalistic tax may have the negative side effect of rendering otherwise healthy individuals underweight.
sin tax paternalism obesity extensive versus intensive margin