In a comment on my post yesterday, BLM4L had another way of calculating the implied elasticity of demand for cigarettes. His looked right; mine looked right too. But they didn't give the same result. The problem, it turns out, is that he and I were both wrong. I did the analysis in too much of a hurry because I wanted to get it done quickly and deal with all my emotions about my daughter leaving for Thailand yesterday after a short visit.
We should have both forgotten about the earlier year baseline and simply worked with the data on (1) the estimated tax revenues gross of backfill and (2) the backfill. Those two numbers, combined with the price before the tax increase, are all we need.
So here goes.
The gross revenues from the tax are estimated to be $810 million. That means that the analyst must be assuming 810 million packs sold in the first full year after the tax is implemented. So that part of what I did was right.
But then we can use the "backfill" number to estimate what the analyst estimated to be the reduction in the number of packs bought because of the tax. The loss in tax revenues that the state government collects with the old 87-cent tax is $75 million. That means that he's estimating $75 million divided by 87 cents, or 86 million fewer cigarettes sold because of the $1 tax increase. This is a reduction of 86 million divided by 896 million (810 million + 86 million) or 9.6%.
So a 20% price increase leads to a 10% cut in quantity. Bottom line: elasticity of demand = -0.5.