Question

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

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

Step-by-step solution

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.

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, \(E_{d} = \frac{-25\%}{10\%}\)

Calculate the Price Elasticity of Demand

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

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.

Key concepts

Elasticity

Elasticity is a key concept in economics that measures how much one variable responds to changes in another variable. In the context of price elasticity of demand, it refers to how sensitive the quantity demanded of a good is to a change in its price. When demand is elastic, a small change in price leads to a significant change in the quantity demanded. Conversely, inelastic demand indicates that quantity demanded doesn't change much with price variations. This concept helps businesses and policymakers understand how price adjustments could impact sales and revenue.

Demand

Demand refers to the willingness and ability of consumers to purchase a certain quantity of a product at various prices. It is one of the fundamental principles of economics. The law of demand states that, all else being equal, as the price of a good decreases, the quantity demanded increases, and vice versa. Various factors such as consumer preferences, income levels, and the prices of complementary or substitute goods can influence demand. Understanding demand helps businesses set appropriate prices and develop effective marketing strategies.

Percentage Change in Quantity Demanded

The percentage change in quantity demanded is used to express how much the quantity demanded of a product changes in response to a change in price. It is calculated by dividing the change in quantity demanded by the original quantity demanded and then multiplying by 100 to convert it into a percentage.
For example, if the quantity demanded of Cheerios decreases from 100 boxes to 75 boxes due to a price increase, the percentage change in quantity demanded is ewline\[ \frac{75 - 100}{100} \times 100\ = -25\% \].
This negative percentage reflects a decrease in demand, highlighting the inverse relationship between price and quantity demanded.

Percentage Change in Price

The percentage change in price is a measure of how much the price of a product has increased or decreased over a period of time, expressed as a percentage. This calculation is essential when determining the price elasticity of demand. To find it, subtract the original price from the new price, divide by the original price, and multiply by 100.
For instance, if the price of Cheerios rises from \(2 to \)2.20, the percentage change in price can be calculated as: ewline\[ \frac{2.20 - 2}{2} \times 100\ = 10\% \].
A positive percentage indicates an increase in price, while a negative percentage would suggest a decrease.