Question

(a) If the government wants to maximize revenue from cigarette tax, should it simply set a very high tax rate on cigarettes? (b) If the government achieves its objective, what is the elasticity of demand for cigarettes at the price corresponding to this tax rate? You may assume that cigarettes are essentially free to produce and the entire price reflects the tax. (c) A research company measures elasticity and concludes that the demand for cigarettes is price- elastic. Should the government raise or lower the tax rate? (d) If the government wants to get some tax revenue but also wants to make people smoke less, should it set a tax rate above or below that which maximizes revenue from cigarette taxation?

Short answer

(a) No, a moderate rate maximizes revenue; (b) Elasticity is unitary; (c) Lower the tax; (d) Above revenue-maximizing rate.

Step-by-step solution

Understand Revenue Maximization

Revenue is maximized when the tax rate is set such that the elasticity of demand is unitary (i.e., elastic demand equals one). If the tax rate is too high, the tax revenue could decrease due to diminished consumption.

Calculate Elasticity at Revenue Maximization

At the tax level that maximizes revenue, the elasticity of demand is exactly unitary. This means that any increase in price due to higher taxes will lead to a proportional decrease in quantity demanded.

Decide Based on Research Findings

If a research company finds that the demand is price-elastic, it means that a percentage increase in price leads to a larger percentage decrease in quantity demanded. Therefore, the government should lower the tax rate because increasing it could reduce revenue rather than increase it.

Balancing Revenue and Health Objectives

If the government wants to discourage smoking while still collecting tax revenue, it should set a slightly higher tax rate than the revenue-maximizing rate. This will decrease consumption but could also result in lower total revenue because fewer cigarettes will be purchased.

Key concepts

Government Taxation

Government taxation can significantly influence consumer behavior, especially in markets like tobacco, where the price elasticity of demand is an important factor. When a government imposes a tax on goods, it directly affects the price consumers pay. In the case of cigarettes, which often have a high social cost, the government may impose taxes to achieve different objectives.

A primary aim might be to collect tax revenue. When setting a tax, the government should consider both the amount of revenue generated and the social impact, such as curbing smoking rates. The effectiveness of these taxes depends largely on the elasticity of demand for the product.

Thus, the government needs to balance between revenue generation and health goals. By carefully considering the elasticity of demand, which we will discuss later, governments can create tax policies that achieve public health objectives without severely hindering tax revenues.

Revenue Maximization

To maximize revenue from a tax, it's crucial to set the tax rate where the elasticity of demand is unitary. This means that the percentage change in quantity demanded matches the percentage change in price.

When demand is unitary elastic, total revenue from a tax peaks because the loss in sales volume is exactly offset by the increase in price from the tax. However, setting a tax too high can backfire. Consumers might reduce their consumption significantly if the tax pushes the price too high, leading to a drop in revenue.
If the demand for a product like cigarettes is inelastic, consumers are less sensitive to price changes, which might suggest setting a higher tax level. But if demand becomes elastic, revenue could decline with further tax hikes. Thus, understanding where demand is unitary elastic helps in identifying the optimal tax rate for revenue maximization.

Price Elasticity

Price elasticity of demand assesses the responsiveness of consumers to price changes. For cigarettes, price elasticity can influence how a government might structure its tax policy.

When demand is elastic, a rise in cigarette prices leads to a proportionally larger decrease in the quantity demanded. This scenario suggests that high taxes could lower revenues because consumers significantly cut back on purchases. Conversely, if demand is inelastic, a price increase does not drastically affect the quantity demanded, allowing for higher taxes without sacrificing revenue.

Understanding this elasticity is crucial, especially when a government aims to balance revenue goals with public health outcomes. For instance, if research determines that cigarette demand is becoming more elastic, lowering tax rates might prevent revenue drops while maintaining a reasonable decrease in smoking rates.
In conclusion, price elasticity provides key insights into consumer behavior, helping governments establish effective taxation levels that align with their fiscal and social objectives.