In the short run the demand for cigarettes is totally...

In the short run the demand for cigarettes is totally inelastic. In the long run, suppose that it is perfectly elastic. What is the impact of a cigarette $\operatorname{tax}$ on the price that consumers pay in the short run and in the long run?

Key Concepts

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to changes in its price. When demand is inelastic, a change in price leads to a relatively smaller change in quantity demanded; in contrast, when demand is elastic, a small change in price leads to a large change in quantity demanded. This concept is key to understanding how consumers adjust their purchasing behavior in response to tax-induced price changes in different time horizons.

Tax Incidence

Tax incidence refers to the distribution of a tax burden between buyers and sellers, which is determined by the relative elasticities of demand and supply. When demand is relatively inelastic, consumers end up bearing a larger portion of the tax burden, whereas when demand is elastic, producers tend to bear a greater share of the tax. Analyzing tax incidence helps explain who ultimately pays the tax under different market conditions.

Short-run Demand Inelasticity

In the short run, the demand for a product can be inelastic if consumers find it difficult to change their consumption habits immediately, often due to lack of close substitutes or habit persistence. This inelasticity means that a tax imposed on the product is likely to translate into a higher price for consumers since their quantity demanded does not drop significantly in response to the tax increase.

Long-run Demand Elasticity

Over the long run, consumers have more time to adjust their behavior and find substitutes, making the demand for a product more elastic. In situations where demand becomes perfectly elastic, any tax imposed is fully absorbed by the producers as consumers will only purchase the product at its equilibrium price. This shift in elasticity alters the tax incidence, transferring the entire burden of the tax to sellers in the long run.

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