Question

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?

Short answer

In the short run, consumers bear the entire tax burden, paying higher prices. In the long run, producers absorb the tax, leaving consumer prices unchanged.

Step-by-step solution

Understanding Elasticity Concepts

'Totally inelastic' in the short run means that consumers will buy the same quantity regardless of price changes. In the long run, 'perfectly elastic' means that consumers will react significantly to even small price changes, buying much less if prices rise.

Impact of Tax in Short Run

Since demand is totally inelastic, a tax will entirely be passed on to consumers. The full amount of the tax will be added to the price that consumers pay because changes in price do not affect the quantity demanded.

Impact of Tax in Long Run

With perfectly elastic demand in the long run, consumers will not tolerate any price increase. Hence, the producer must absorb the tax, keeping consumer prices unchanged. If producers raise prices, consumers will stop buying altogether.

Key concepts

Short Run vs Long Run

In economics, the concepts of "short run" and "long run" refer to different time frames in which consumers respond to changes in prices.
In the short run, demand is considered inelastic. This means that consumers do not significantly change the quantity they buy when prices change. A classic example is a necessity good like cigarettes. People may have a habit or addiction and will purchase roughly the same amount regardless of price increases.
Over the long run, demand can become more elastic. As time passes, consumers have more opportunities to adjust their behavior. They might find substitutes for goods or change their consumption habits. In the case of cigarettes, this might mean stopping smoking or switching to alternative products, leading to a high sensitivity to price changes.

Tax Impact

Taxation can have varying impacts on prices and consumer behavior based on the elasticity of demand.
In the short run, when demand is totally inelastic, any tax imposed on a product like cigarettes is typically fully passed on to consumers. Producers know that consumers will buy the same quantity regardless of higher prices, so they add the entire tax to the price.
In contrast, in the long run, if demand is perfectly elastic, even a slight increase in price due to a tax will lead to consumers stopping their purchases entirely. This forces producers to bear the tax burden to keep prices stable, ensuring that consumers continue buying the product.

Consumer Price Response

Understanding how consumers respond to price changes is crucial for predicting market outcomes.
In the short run, when consumers exhibit totally inelastic demand, they are unresponsive to price increases due to taxes, and willingly or unwillingly pay more. This can be explained by a lack of immediate alternatives.
However, in the long run, consumers become more price-sensitive. When demand is perfectly elastic, they respond promptly to any price hikes by reducing their purchases to zero. This reaction can pressure producers to find cost efficiencies or other means to absorb tax costs without passing them on.
The interplay between time, consumer habits, and the elasticity of demand deeply influences how prices evolve and affect market dynamics.