# Clunky, Cliffy U.K. Soda Tax

My friend Don Marron reports on a new sugar tax in the U.K.:

“Beginning in 2018, the United Kingdom will charge the equivalent of 0.75 cents per ounce for drinks that contain more than 3 teaspoons of sugar in an 8-ounce serving and a full cent per ounce for drinks with more than 5 teaspoons per serving. These tax levels are similar to the penny per ounce that Berkeley, California levies on sugary drinks.”

So the tax (0.75 cents per ounce for drinks that contain more than 3 teaspoons of sugar in an 8-ounce serving and a full cent per ounce for drinks with more than 5 teaspoons per serving) yields these results; I take “more than” to mean “at least,” for simplicity:

If there are 3/8 tsp per ounce, the tax is 0.75 cents per ounce
If there are 4/8 tsp per ounce, the tax is 0.75 cents per ounce
If there are 5/8 tsp per ounce, the tax is 1.00 cents per ounce
If there are 6/8 tsp per ounce, the tax is 1.00 cents per ounce.

That leaves a lot of incentive to come in at 4.9 tsp per eight ounces (or 4.9/8 tsp per ounce).  There’s a tax cliff — take one incremental step from 4.99 to 5.01 and . . . OOPS.

To approximate the new tax’s result, a smooth function might be something like:

.75 cents for the first 3/8 tsp per ounce plus .125 cents for each additional 1/8 tsp per ounce.

That would yield:

If there are 3/8 tsp per ounce, the tax is 0.75 cents per ounce – as proposed
If there are 4/8 tsp per ounce, the tax is 0.875 cents per ounce
If there are 5/8 tsp per ounce, the tax is 1.00 cents per ounce – as proposed
If there are 6/8 tsp per ounce, the tax is 1.125 cents per ounce.

That creates a smooth function, but leaves me wondering why you tax additional teaspoons at a lower rate (.125 per 1/8 tsp/oz.) than the first three (.25 per 1/8 tsp/oz.). And it leaves aside the first discontinuity (from 2.99 oz. to 3.01 oz., with an enormous marginal rate) as a de minimis rule, with no tax unless the concentration reaches 3/8 tsp per ounce.

So this new tax is clunky and awkward. And spiky. A simple tsp per gram tax (with some de minimis threshold) seems more elegant: X cents per tsp of sugar in beverages. As Marron writes, “directly tax sugar content.” But the U.K. tax is a step in the right direction. At least it goes beyond a binary distinction – sweet and not sweet.