Columbia University's Ray Fisman notices an interesting new study on milk pricing that suggests a small fat tax, increasing the relative cost of fattier foods by a quarter or two, could go a long way.

Economists Romana Khan, Kanishka Misra and Vishal Singh exploited a natural variation in milk pricing. In some supermarkets, full-fat milk and skim milk come with the same price-tag. In others, fat-free milk is priced cheaper to reflect the fact it actually has less value (since butterfat is an "expensive component," the authors explain, "the cost of milk increases with its fat content.")

The price difference is usually small. In supermarkets with non-uniform pricing, fat-free milk costs, on average, 14 cents less than 2-percent.

The impact of those differences can, however, be quite big. As variation in milk price increased, the study authors saw lower-income populations gravitate toward the less expensive milk product.

"This paper suggests a selective taxation mechanism by altering the relative prices of healthy and unhealthy products in a way that those changes are reflected in shelf prices at the point of purchase," they conclude. "Tax policies designed to alter the relative prices within narrowly defined food products can also mitigate regressive impacts by incentivizing consumers to switch to relatively cheaper and healthier options."

We might learn more on this front soon from Denmark: Last fall, it became the first country to tax all foods with a saturated fat content above 2.3 percent.