There is some fairly compelling evidence that when cigarette prices go up, there is a slight decline in smoking, especially among teenagers. At the same time, though, if the price of cigarettes is raised because of an increase in the excise tax imposed on cigarettes, recorded sales of cigarettes drop off considerably. Sales decline much more than actual smoking declines. Here is what happens.
When one jurisdiction raises its excise tax on cigarettes, many people for whom arbitrage is inexpensive buy their cigarettes elsewhere --- in a neighbouring city or state. Failing that, if the price differential is sufficient to provide adequate rewards for transportation and risk, people will smuggle cigarettes from the low-tax jurisdictions to the higher-tax jurisdictions. Here is a graph of the effect, via the Tax Foundation:
To be honest, I expected the dots to fall closer to the line. The imprecision of the correlation should not, however, detract from the overall effect that "people respond to incentives." Higher excise taxes create an increased incentive for smuggling (and/or counterfeit tax stamps).
In Ontario we experience a variant of this relationship. When the provincial gubmnt raises the tax on cigarettes, more non-native smokers have an incentive to head to the reserves to buy their cigarettes, where cigarettes can often be found for sale at much lower prices because aboriginal Canadians are allowed to buy tobacco products tax free. [see this, for some details]
The result in all cases, though, is that the higher tax has less of an impact on smoking than would be indicated from legal sales, and the gubmnt policy has the effect of inducing more economic activity into black-market illegal activities.