Taxation of unhealthy food consumption and the intensive versus extensive margin of obesity

If an individual's health costs are U-shaped in weight with a minimum at some healthy level and if the individual has both self-control problems and rational motives for over- or underweight, the optimal paternalistic tax on calorie intake mitigates the individual's weight problem (intensive margin), but does not induce the individual to choose healthy weight (extensive margin). Implementing healthy weight by a calorie tax is not only inferior to paternalistic taxation, but may even be worse than not taxing the individual at all. With heterogeneous individuals, the optimal uniform paternalistic tax may have the negative side effect of reducing calorie intake of the under- and normal weights. We confirm these theoretical insights by an empirical calibration to US adults.