Fat Tax Burden

The truth is the Danes are some of the leanest folks on the planet, with less than a 10% rate of obesity, about a third of the United States’ obesity rate. The other truth is the new “fat tax” in Denmark has been quite successful in achieving the goal of limiting Danish citizens’ intake of unhealthy foods. That government would dare regulate food intake is what Fox News commentators will decry as social engineering. Denmark prefers the term, social responsibility.

Among the chief complaints registered by anti-taxivists is that a tax on food products, such as Denmark’s fat tax, creates dead-weight welfare losses and shifts the tax burden unduly onto the consumer.  Welfare (in economic terms) aside for the moment, we have to examine more closely the demand and supply elasticities of unhealthy food products to check if anti-tax rhetoric is fully supported by fundamental economics. To clarify, the Danish fat tax is an ad-valorem (“according to value”) tax, a percentage tax. Instead of shifting the supply curve directly upward, as a per unit excise tax does, the ad-valorem sales tax effectively rotates the producer’s supply curve counterclockwise from its axis point, such that the spread between the pre-tax and after-tax supply curves is proportional to the percentage tax rate at every output level. It turns out that demand elasticity for a sweet, fatty danish—we're talking food here—is rather elastic, meaning that demand for danishes and other fatty treats, unlike the demand for say gasoline, tends to be very responsive to changes in price.

Notice from the two graphs drawn in the figure below, that when demand for a product is more responsive to a change in price, the share of the tax burden on the buyer is reduced. This makes intuitive sense; another way of describing it is that the tax burden falls most heavily on the side of the market that can least escape it. If the buyers have greater alternative substitutes, and suppliers do not, then most of the burden will fall on suppliers. Hence, the share of a buyer’s tax burden is inversely related to the buyer’s demand elasticity. In other words, the greater the responsiveness of a buyer to the price of a product, the lesser will be the buyer's share of the tax burden—all else equal, of course.

The lower graph in the figure below reflects a greater share of tax burden to consumers who are less responsive to price changes. However, we expect there to be plenty of available substitutes to sweet, fatty danishes; thus the lower graph may well represent a tax on a more inelastic product, like gasoline (for American consumers). Notice also the higher new price (P1) associated with the less elastic demand curve in the lower graph. Danes, by the way, prefer bicycles over automobiles.

Greater demand elasticity, all else equal, also has the effect of reducing the quantity supplied. This also makes intuitive sense, and this can be seen in both graphs. If the demand curve is steeper (less elastic), as shown in the lower graph, the new quantity (Q1) supplied will be greater than if the demand curve is less steep (more elastic).

As far as economic welfare losses are concerned, I think it's safe to say that while the consequences of a fat tax result in higher prices to consumers, and lower quantities sold by producers, the switch to other food substitutes will likely result in lower prices and higher quantities sold of healthier alternatives, for a positive net gain to the health of society in general.

There’s an interesting opinion in the NY Times that describes the Danish rationale for taxing unhealthy products. When something is bad for its citizens, but not quite bad enough that it can be outlawed, it is TAXED! I can think of plenty of American products that would fall into this category. In Denmark the fat tax generates revenue to cover the some of the rising costs of universal healthcare. In the United States it seems excise taxes rarely garner much support unless the revenue generated is used to offset a reduction in another, more loathed, form of tax like the income tax. It’s a matter of social priorities, I suppose.