The poster (Symmetry) that said "the relevant basket of goods is the inputs in materials and labor that go into a bottle of Coke" is absolutely right, and that's exactly what Levy/Young point to in the academic paper. However, the puzzle that remains is that input costs still don't explain the [lack of] variation in the price of coke over the relevant 5 cent years.
Although the CPI/inflation answers seem to be the reasonable explanatory variables here, the most explanatory factor is pretty simple: menu costs + marketing contracts/agreements.
Menu costs, which are the costs associated with changing your prices, used to be a pretty popular topic in macroeconomics. However, as time has gone on and with the rise of the Internet, menu costs have lost a lot of their explanatory power since they are far less significant in a digital age. But of course, in the early 1900s changing your price, especially for a good which was widely distributed at the time, was a pretty costly matter. Tack that onto that the agreements over price (but not quantity) that were made when the early licensing deals were made and you have a completely reasonable explanation for the sticky price of Coke.
Prior to the introduction of the Euro, the price of a standard bar of chocolate has remained constant for around 50 years. The size of those chocolate bars was also fixed, unlike the Hershey's example somebody else mentioned.
The single most relevant factor explaining this is psychology: the price of chocolate was very much ingrained in people's minds, and people simply rejected the standard bar of chocolate above a price point of 0.99 DM.
Chocolate manufacturers had to squeeze the last bit of efficiency out of their production lines, and turn to larger chocolate bars with special gimmicks or other chocolate-related products for making a decent profit.