Tax the Big Mac?

Amazingly, today the British Government takes a look at Detroit Mayor Kwame Kilpatrick's potential plan to add a 2% sales tax to fast food, in addition to the 6% meals tax that already applies to Detroit restaurants.
Now, one quick thing about the report. It claims on first that

The move is expected to raise around $17 million a year, though this will not fill the city's $300 million budget deficit.

But also that

The Mayor has yet to define what constitutes a fast food restaurant. However, his spokesperson said that it is likely to include any outlet where food is purchased in advance.

It seems like those two statements could be mutually exclusive. How can a mayor estimate how much a tax will raise without knowing how broad the base will be, particularly if the rate is already defined?

But even so, the idea of placing a "sin tax" on fast food is thought provoking. Should a city (or state) treat unhealthy food the same way it treats cigarettes? According to some it can be sort of addictive. It has an enormously bad impact on people's health. Is the tax code a good means to try and improve people's health? I'm not sure. This tax will certainly fall onto relatively lower income citizens, so it is a regressive revenue source. It will also almost certainly diminish over time. People eat fast food because it is cheap. If the price goes up, some folks will swap their Whopper for a healthier lunch. So the tax base will shrink, and Detroit will still have a large deficit.

Is this even a good way of improving public health? There are lots of ways to get your hands on junk food. The quest for an unbalanced diet is, after all, a much more varied endeavor than the desire to smoke cigarettes.