Why would a government tax on cigarettes be an ineffective method to decrease consumption of cigarettes if demand for cigarettes is inelastic?

Putting a tax on cigarettes would have the effect of increasing the price of cigarettes. If demand is inelastic, however, smokers will still buy the same amount of cigarettes, or show a very small decrease in consumption, regardless of the increase in price. The net result of the tax would be a large jump in price with a smaller-than-desired decrease in consumption.

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