Chapter 5: Problem 22

What is the formula for the cross-price elasticity of demand?

Short Answer

Expert verified

The formula for the cross-price elasticity of demand (CPED) is: \[ CPED = \frac{\% \:Change \:in \:Quantity \:Demanded \:of \:Good \:A}{\% \: Change \:in \:Price \:of \:Good \:B} \] To calculate CPED, first find the percentage changes in the quantity demanded of Good A and the price of Good B using the formula \[ \%\: Change = \frac{New \:Value - Old\: Value}{Old\: Value} * 100 \] and then apply the CPED formula by dividing the percentage change in the quantity demanded of Good A by the percentage change in the price of Good B.

Step by step solution

Understanding Cross-Price Elasticity of Demand Formula

The cross-price elasticity of demand (CPED) is calculated by taking the percentage change in the quantity demanded of one good divided by the percentage change in the price of another good. It can be positive, negative, or zero, which indicates whether the goods are substitutes, complements, or not related. The formula for CPED is: \[ CPED = \frac{\% \:Change \:in \:Quantity \:Demanded \:of \:Good \:A}{\% \: Change \:in \:Price \:of \:Good \:B} \]

Identifying the Components of the Formula

To better understand the formula, let's identify each component: 1. \% Change in Quantity Demanded of Good A: This represents the percentage change in the quantity demanded for Good A as a result of a change in the price of Good B. 2. \% Change in Price of Good B: This represents the percentage change in the price of Good B.

Calculating the Percentage Changes

In order to find the cross-price elasticity of demand, we first need to calculate the percentage changes for both the quantity demanded of Good A and the price of Good B. The formula for percentage change is: \[ \%\: Change = \frac{New \:Value - Old\: Value}{Old\: Value} * 100 \] We will apply this formula to both the quantity demanded of Good A and the price of Good B.

Applying the Formula

Using the formula for cross-price elasticity of demand and the calculated percentage changes, we can now apply the formula to find the CPED by dividing the percentage change in the quantity demanded of Good A by the percentage change in the price of Good B.

Interpreting the Results

Once we have calculated the cross-price elasticity of demand, we can interpret the results: 1. If the CPED is positive, it means the goods are substitutes. This indicates that as the price of Good B increases, the quantity demanded for Good A increases as well. 2. If the CPED is negative, it means the goods are complements. This indicates that as the price of Good B increases, the quantity demanded for Good A decreases. 3. If the CPED is zero or close to zero, it means the goods are unrelated or have very minimal relationships. A change in the price of Good B will not have a significant impact on the quantity demanded for Good A.