Firstly, fat tax is relevant mostly to people who won't be affected by fat tax. Not to say their demand for fatty foods is perfectly inelastic, but they tend to have higher income and an increase in price won't decrease their quantity demanded that much. Secondly, fat tax is regressive since the tax rate in terms of income decreases as taxable income increases. Worse still, the poor usually spend more on food (esp. McDonald's food), so they are hit the hardest. Income inequality will no doubt be widened, and the burden on low-income consumers will be unbearably heavy. Thirdly, if the fat tax is the same for all food items above a certain number of calories, by Alchian's generalisation, people will eat more of the more expensive food, increasing their spending on fatty foods. Fourthly, it will drive small-scale competitors out of the market since the marginal cost of each unit of food increases. Fifthly, it will create a black market or, in the case of Denmark (the first country to impose and subsequently abolish the tax, force citizens to cross the border to Belgium to buy junk food.