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.

Great post, but I'm beginning to wonder whether we are missing important pieces of information.

First, are we justified in assuming a $75M backfill --> 86M fewer cigarette packs sold? Remember, the $75M backfill estimate includes the effect of the tax increase on other tobacco products as well.Analyst Report pp. 15-16 (emphasis added)

But we don't know how that $75M gets distributed since we don't know the tax rates on non-cigarette tobacco products. The $75M could be made up of 86M cigarette packs lost or it could be made up of some number (less than 86M) of lost cigarette packs plus some number of lost snuff boxes, cigars, etc.

I guess if all tobacco products were perfect substitutes for each other, that might solve our problem...

Second, it seems like the analyst is projecting a decline in cigarette consumption between 2010-2011 and 2013-2014...But we don't know the basis for this projection.If the analyst anticipates a shift in the supply curve, that means that the equilibrium price will head farther above $5 right? Meaning that we cannot reasonably estimate the percentage increase in price represented by a ~ $1.07-$1.10 change in the cost of a pack of cigarettes.

Given these points, I think your -0.5 elasticity calculation may be too generous to the analyst.

P.S. My brain hurts. Glad I became a lawyer and not an economist.

P.P.S. I hope your daughter enjoys the land of smiles.

When Sweden raised tobacco taxes in the 90s by a huge percentage (don't remember, 40-50%?) it caused increased smuggling. They tried to fix it by lowering taxes somewhat but by that time it was too late, organized crime had already been established.

http://en.wikipedia.org/wiki/Serbian_mafia#Sweden