Question

Economists' estimates of price elasticities can differ somewhat, depending on the time period and on the markets in which the price and quantity data used in the estimates were gathered. An article in the New York Times contained the following statement from the Centers for Disease Control and Prevention: "A 10 percent increase in the price of cigarettes reduces consumption by 3 percent to 5 percent." Given this information, compute the range of the price elasticity of demand for cigarettes. Explain whether the demand for cigarettes is elastic, inelastic, or unit elastic. If cigarette manufacturers raise prices, will their revenue increase or decrease? Briefly explain.

Short answer

The price elasticity of demand for cigarettes ranges from -0.3 to -0.5. Cigarette demand is inelastic since the magnitude of price elasticity is less than 1. As a result, if cigarette manufacturers raise their prices, their revenue will increase.

Step-by-step solution

Compute the Price Elasticity of Demand

Using the formula for price elasticity of demand which is \( \frac{\% Change in Quantity Demanded}{\% Change in Price} \), look at the two scenarios given. In the first scenario, a 10% increase in price leads to a 3% decrease in quantity demanded. So, the price elasticity of demand is \( \frac{-3\%}{10\%} = -0.3 \). In the second scenario, a 10% increase in price leads to a 5% decrease in quantity demanded. So, the price elasticity of demand is \( \frac{-5\%}{10\%} = -0.5 \). Therefore, the price elasticity of demand ranges from -0.3 to -0.5.

Classify the Demand

The demand for a good is said to be inelastic if the magnitude of price elasticity is less than 1 and elastic if the magnitude is greater than 1. In this case, the price elasticities calculated are -0.3 and -0.5. So the magnitudes, which are 0.3 and 0.5 respectively, are less than 1. Hence, it can be concluded that the demand for cigarettes is inelastic.

Determine Effect on Revenue

In case of inelastic demand, an increase in price results in an increase in total revenue. This is because the percentage change in quantity demanded is less than the percentage change in price. Therefore, if cigarette manufacturers raise prices, their revenue will increase.

Key concepts

Inelastic Demand

Inelastic demand occurs when the quantity demanded of a product does not change significantly in response to price changes. This concept is crucial when evaluating products like cigarettes, which are often found to have inelastic demand. When demand is inelastic, consumers are relatively unresponsive to changes in price. They may reduce their consumption slightly, but not by a large margin.

In the case of cigarettes, economists have found that a 10% increase in price results in only a 3% to 5% decrease in quantity demanded. This is a small change, indicating inelastic demand. To determine price elasticity, we use the formula:
\[ \text{Price Elasticity of Demand} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}} \]

For cigarettes, we find elasticity values of

• -0.3 when a 10% price increase leads to a 3% quantity decrease, and
• -0.5 when the quantity decreases by 5% instead.

Since both values (0.3 and 0.5 when taking the absolute values) are less than 1, the demand is inelastic. This means cigarette consumers are likely to continue buying even if prices rise.

Revenue Impact

One interesting effect of inelastic demand is its impact on revenue. With inelastic demand, price increases lead to increased revenue. This is because the drop in quantity demanded is proportionally smaller than the price hike.

For cigarette companies, this means raising prices will likely increase their total revenue, despite a slight decline in sales volume. The concept relies on the idea that the lost sales from higher prices are outweighed by the higher prices of the remaining sales. So, even if fewer cigarettes are sold, the higher price per pack covers the lost sales, resulting in an overall revenue increase.

This is a strategic advantage for businesses with inelastic products, as they can adjust pricing to boost profits without materially shrinking their customer base. However, the ethical and public health implications of such strategies, especially with products like cigarettes, remain a point of discussion.

Cigarette Consumption

Cigarette consumption is a classic example of a product with inelastic demand. Various factors contribute to this, including addiction, limited alternatives, and habitual use. Many smokers find it challenging to quit or reduce consumption even when prices rise, due to nicotine addiction.

Cigarette smoking patterns are often deeply ingrained, making consumers less sensitive to price changes compared to other products. Even with tax hikes or stricter regulations, reductions in smoking rates tend to be gradual rather than immediate or significant.

While price can influence consumption levels, other factors are also at play, such as public health campaigns, smoking cessation programs, and societal shifts in attitudes towards smoking. These external influences can gradually impact demand more than price fluctuations alone. Understanding these dynamics helps explain why cigarette manufacturers might respond to inelastic demand by increasing prices, knowing that consumption will decrease only slightly.