Cigarettes and Elasticity---this time "Reservation Price" has a different meaning...

   A product that is always ripe to increase taxes on, with little resistance from interest groups, is cigarettes.  It is assumed that the demand for cigarettes is relatively inelastic, which means consumers of cigarettes will NOT DECREASE their quantity demanded (in percentage terms) by MORE than the percentage INCREASE in the price of cigarettes.  The formula is % change in Quantity Demanded divided by the % change in Price multiplied by 100.  If the result is LESS than 1, then the good is considered to be PRICE INELASTIC.  It is generally accepted that cigarettes have an elasticity of less than 1.  However, in this article, the numbers do not bear this out. Can you figure out why?  Key info here:

""New York state boosted the cigarette tax to $4.35 a pack from $2.75 on July 1 as one of a series of measures designed to help close a $9.2 billion deficit for fiscal 2011, giving it the highest cigarette tax rate in the country....(Hayward's note: Tax increased $1.60)

With the per-pack price rising to a range of $9 to $12, "aghast" smokers flocked to tribal stores, which are tax-free, the black market, and border states with lower cigarette taxes, said the New York Association of Convenience Stores. (Hayward's note: I will use $10.50 as the price)

Convenience stores that are located close to reservation competitors sold 45 percent fewer cigarettes; more distant stores experienced drops of 25 percent to 35 percent, the lobbying group said...."

     Assume the new per pack price of cigarettes is $10.50 (halfway between the $9 to $12 cited in the article).  Before the tax the price of a pack was $8.90 ($10.50 minus $1.60 increase in the tax). The percentage change in price is +18% ($10.50 minus $8.90=$1.60 divided by $8.90 times 100= 17.97%).  For the good to be price inelastic, the percentage change in quantity demanded would have to be LESS than 18%.  The article cites two statistics for change in quantity demanded. One for stores close to reservations/tribal stores (NOT subjected to State Taxes) and one for stores further away from reservations/tribal stores.  If you use the numbers quoted for change in quantity demanded and plug them into the formula to determine elasticity you yield a number LARGER than one, indicating the good is PRICE ELASTIC.  Remember 18% is in the denominator.  What is going on here? What caused the good to magically change from an inelastic good to an elastic one?  Was this a bad policy?