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Chapter 6: Problem 5

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

Expert verified
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

01

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.
02

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.
03

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.

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Most popular questions from this chapter

According to a news story about the bus system in the Lehigh Valley in Pennsylvania, "Ridership fell 14 percent ... after a 33 percent increase" in bus fares. Based on this information, is the demand for bus trips price elastic or price inelastic? Explain your answer in terms of the five determinants of price elasticity.

The elasticities reported in this Apply the Concept were calculated using price data for many brands of beer. Why might price elasticity estimates be less reliable if they use data for only one brand of beer?

Suppose that the following table gives data on the price of rye and the number of bushels of rye sold in 2017 and 2018 : $$ \begin{array}{c|c|c} \hline \text { Year } & \begin{array}{c} \text { Price (dollars per } \\ \text { bushel) } \end{array} & \text { Quantity (bushels) } \\ \hline 2017 & \$ 3 & 8 \text { million } \\ \hline 2018 & 2 & 12 \text { million } \\ \hline \end{array} $$ a. Calculate the change in the quantity of rye demanded divided by the change in the price of rye. Measure the quantity of rye in bushels. b. Calculate the change in the quantity of rye demanded divided by the change in the price of rye, but this time measure the quantity of rye in millions of bushels. Compare your answer to the one you computed in (a). c. Assuming that the demand curve for rye did not shift between 2017 and \(2018,\) use the information in the table to calculate the price elasticity of demand for rye. Use the midpoint formula in your calculation. Compare the value for the price elasticity of demand to the values you calculated in (a) and (b).

If the demand for orange juice is inelastic, will an increase in the price of orange juice increase or decrease the revenue that orange juice sellers receive?

Write the formula for the price elasticity of demand. Why isn't elasticity just measured by the slope of the demand curve?
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