Suppose there is a bill to increase the tax on cigarettes by $1 per pack coupled with an income tax cut of $500. Suppose a person smokes an average...

There is a problem in missing assumptions of the question, namely that the effect of changes in cigarette prices affects all demographics equally. That actually isn't the case. In general, cigarette taxes reduce smoking in the young and the economically disadvantaged, but have little effect on middle-aged smokers in higher economic brackets. Thus this answer needs to be parsed in terms of demographics.

For people with middle class incomes, the effect is likely to be negligible, with the decision of whether to continue smoking determined by other issues such as the availability of smoking cessation programs and personal choice. According to the CDC, people below the poverty level are twice as likely to be smokers as those living above the poverty line. Education is also a crucial factor, with only 3 percent of people with postgraduate degrees smoking but 24 percent of high school dropouts smoking. Thus, even though taxation is unlikely to change the smoking behavior of the well-educated and affluent, that population is already unlikely to smoke.

For people living in poverty, the income tax cut would be irrelevant, as over 80 percent of people with incomes under $50,000 have no tax liabilities. Since the income tax cut would have no effect on them, the increased cigarette prices would result either in reduced smoking or increased black market cigarette purchases.