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Chapter 6: Problem 2

If a 10 percent increase in the price of Cheerios causes a 25 percent reduction in the number of boxes of Cheerios demanded, what is the price elasticity of demand for Cheerios? Is the demand for Cheerios elastic or inelastic?

Short Answer

Expert verified
The price elasticity of demand for Cheerios is -2.5, indicating that the demand for Cheerios is elastic.

Step by step solution

01

Understand the Concept of Price Elasticity of Demand

The price elasticity of demand is calculated by the formula: \(E_{d} = \frac{\% \Delta Q}{\% \Delta P}\), where \(E_{d}\) is the price elasticity of demand, \(\% \Delta Q\) is the percentage change in quantity demanded, and \(\% \Delta P\) is the percentage change in price. An elasticity of demand greater than 1 indicates elastic demand, and less than 1 indicates inelastic demand.
02

Insert the Given Values into the Formula

The given information states that a 10% increase in price (which is \(\% \Delta P\) in the formula) leads to a 25% decrease in the quantity demanded (\(\% \Delta Q\) in the formula). However, do note that since quantity demanded decreases due to price increase, \(\% \Delta Q\) will be negative. Hence, \(E_{d} = \frac{-25\%}{10\%}\)
03

Calculate the Price Elasticity of Demand

Calculate the price elasticity of demand using the formula: \(E_{d} = \frac{-25\%}{10\%} = -2.5\)
04

Interpret the Result

The price elasticity of demand is -2.5, which means for a 10% increase in price, the quantity demanded decreases by 2.5 times. Importantly, the magnitude of \(E_{d}\) is greater than 1, indicating elastic demand. The negative sign denotes the inverse relationship between price and quantity demanded, which is expected as it follows the law of demand.

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Most popular questions from this chapter

To legally operate a taxi in New York City, a driver must have a medallion issued by the New York City Taxi and Limousine Commission, an agency of the city's government. In 2017 the number of medallions was 13,587 . In recent years the taxi industry in New York and other large cities has encountered competition from companies such as Uber, an app-based service that offers rides from drivers who own their own cars. Uber varies the prices it charges based on the demand for rides, with rides during busier periods, such as Saturday nights, having higher prices. a. What does the limitation on their number imply about the price elasticity of supply of taxi medallions? b. Is the supply of Uber rides more or less elastic than the supply of taxi rides in New York City? Briefly explain.

A study of the consumption of beverages in Mexico found that "overall, for soft drinks a \(10 \%\) price increase decreases the quantity consumed by \(10.6 \%\)." Given this information, calculate the price elasticity of demand for soda in Mexico. Is demand price elastic or price inelastic? Briefly explain. Source: M. A. Colchero, et al. "Price Elasticity of the Demand for Sugar Sweetened Beverages and Soft Drinks in Mexico," Economics and Human Biology," Vol. 19, December 2015, pp. \(129-137\).

What is the main determinant of the price elasticity of supply?

What is the midpoint formula for calculating price elasticity of demand? How else can you calculate the price elasticity of demand? What is the advantage of using the midpoint formula?

When San Francisco and other cities in California adopted soda taxes, an opinion column in the New York Times observed, "Often, the taxes don't even pinch the budgets of low-income families, because they respond by drinking less soda." What does the columnist mean when he writes that soda taxes don't "pinch the budgets" of low-income families? Shouldn't an increase in the price of soda resulting from a tax always increase the amount that families have to spend to buy soda? Briefly explain.
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