What is the cross price elasticity of demand for good B with respect to the price of good A?

Understanding Cross-Price Elasticity

While explaining cross-price elasticity, there are three categories of product relationships to examine.

1. First, there are products that are closely related to one another – sometimes known as substitute products. These products compete for the same customers in the market.
2. Second, there are products that are consumed together. The demand for one product directly affects the consumption of related products. These products are known as complementary products.
3. The final group belongs to products that are entirely unrelated to one another. These products do not affect the consumption of one another.
4. By having a clear understanding of the concepts behind product relationships, business owners can strategically compete in their industry or stock their inventories accordingly. For example, lowering the price of printers could lead to increased purchases of toners and ink. The more printers consumers buy, the more revenues are generated by selling complementary products.

Cross-Price Elasticity Formula

Where:

• Qx = Average quantity between the previous quantity and the changed quantity, calculated as (new quantityX + previous quantityX) / 2
• Py = Average price between the previous price and changed price, calculated as (new pricey + previous pricey) / 2
• Δ = The change of price or quantity of product X or Y

Note: In cross-price elasticity, unlike in income elasticity, the ΔQx and ΔPy are calculated by finding the averages between the change in either price or quantity demanded.

Cross-Price Elasticity of Substitute Products

For substitute products, an increase in the price of a substitute product increases the demand for the competing product. This is often because consumers always try to maximize utility. The less they spend on something, the higher the perceived satisfaction.

Similarly, when the competing product price is reduced, the mirroring effect is depicted by an increase in demand for the substitute product. In either of these scenarios, the change will either drive a negative or a positive cross-price elasticity. For cross-price elasticity, where there is an increase in the price of the competing products, there will be a positive coefficient.

Practical Example

Two competing airlines – A and B – are a perfect example of substitute products. If Airline A decides to increase their flights’ round-trip ticket price by even a small margin, consumers will likely notice the difference. As a result, more people will opt for Airline B because it is cheaper.

Categories of Substitute Products

Substitute products can be categorized as either close or weak.

Close Substitutes

A close substitute is realized when a minimal increase in price leads to a large demand increase of the substitute product. The graph below shows this interpretation.

Weak Substitutes

For a weak substitute, a large increase in the price of product X will lead to only a small increase in demand for product Y. See the graph below for the interpretation.

Cross-Price Elasticity of Complementary Products

Complementary products have the opposite effect. If the price of one product increases, the demand for the complementary product decreases. To consumers, the increased joint cost will force them to buy less.

Practical Example

An example of a complementary product is an eBook reader. If the price of an eBook reader drops, the consumption of eBooks and audiobooks will increase because more consumers can afford the reader.

Categories of Complementary Products

Complementary products can either be close or weak complements.

Close Complements

In the case of a strong complement product, a minimal price decrease leads to a large increase in demand for the complement product. The graph below shows this impact.

Weak Complements

For weak complementary products, a large price decrease leads to a small increase in demand for the complementing products. The graph below shows this shift.

Cross-Price Elasticity of Unrelated Products

Unrelated products do not affect one another. This means the cross-effect elasticity is zero, and the graph would be represented by a vertical line.

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In This Article

What Is Cross Elasticity of Demand?

Ever wonder how a change in the price of Coca-Cola affects demand for Pepsi? Or how a price rise of Smucker’s jelly affects demand for Skippy’s peanut butter? Cross price elasticity of demand helps you answer such questions.

Cross price elasticity of demand (XED) is a measure of how demand for one good changes in response to a change in the price of another good. The other good might be a related good such as a substitute—a good that consumers buy in place of another good—or a complement (a good that’s consumed together with another good). It could also be a completely unrelated good, in which case, the cross-price elasticity will be zero.

What Is the Cross Price Elasticity of Demand Formula?

To measure the cross price elasticity of demand, divide the percentage change in quantity demanded for one good by the percentage change in the price of a second good.

Cross price elasticity of demand equals:

Percentage Change in Quantity Demanded of Good APercentage Change in the Price of Good B \frac{\text{Percentage Change in Quantity Demanded of Good A}}{\text{Percentage Change in the Price of Good B}}Percentage Change in the Price of Good BPercentage Change in Quantity Demanded of Good A​

=ΔQAQAΔPBPB= \frac{\frac{\Delta Q_{A}}{Q_{A}}}{\frac{\Delta P_{B}}{P_{B}}}=PB​ΔPB​​QA​ΔQA​​​

• ΔQAQ_{A}QA​ is the change in the quantity demanded of Good A. To find the change subtract, the initial quantity demanded from the new quantity demanded.

• QAQ_{A}QA​ is the initial quantity demanded for Good A.

• ΔPBP_{B}PB​ is the change in price of Good B. You can find this change by subtracting the initial price from the new price.

• PBP_{B}PB​ is the initial price of Good B.

As an example, say you want to know how a change in the price of hot dogs affects demand for hot dog buns. You observe that when the price of hot dogs increases from $6.50 to $7.02, the sale of hot dog buns falls from 1000 units to 910 units. Using the formula above, you can calculate the cross price elasticity as:

XED=ΔQAQAΔPBPB=910−10001000÷7.02−6.506.50=−0.090.08=−1.125\text{XED}= \frac{\frac{\Delta Q_{A}}{Q_{A}}}{\frac{\Delta P_{B}}{P_{B}}}=\frac{910-1000}{1000}\div \frac{7.02-6.50}{6.50}=\frac{-0.09}{0.08}=-1.125XED=PB​ΔPB​​QA​ΔQA​​​=1000910−1000​÷6.507.02−6.50​=0.08−0.09​=−1.125

This cross price elasticity of demand tells us that an 8% price increase for hot dogs is associated with a 9% decrease in demand for hot dog buns. The fact that the cross price elasticity is greater than 1 in absolute terms tells you that the percent change in the quantity demanded is larger than the percent change in the price of hot dogs.

Understanding Types of Cross Elasticity of Demand

Cross price elasticity of demand can be negative, positive, or zero.

Negative Cross Price Elasticity of Demand

The cross price elasticity of demand will be negative when two goods are complements.

Complementary products are goods that are consumed together. If the price of one good goes down, demand for its complement will increase and vice versa. The quantity change in one good and the price change in the second good will always move in opposite directions for complements. This is what makes the cross price elasticity negative.

As an example, think of peanut butter and jelly. Because these goods are frequently consumed together, if the price of jelly falls, consumer demand for peanut butter will increase. If the price of jelly goes up, consumer demand for peanut butter will decrease.

Positive Cross Price Elasticity of Demand

Cross price elasticity of demand will be positive when two goods are substitutes.

Substitute goods are goods that can be used to satisfy the same demand. If the price of a good goes down, demand for its substitute will decrease and vice versa. In this way, the quantity change and the price change will always move in the same direction for substitutes. This is what makes the cross price elasticity positive.

As an example, think of Pepsi and Coca-cola. If you assume the two brands of soda are substitutes, if the price of Coke falls, consumer demand for Pepsi will fall because more consumers will choose to buy Coke over Pepsi. If the price of Coke increases, demand for Pepsi will increase as consumers shift away from Coke and start buying more Pepsi.

When Cross Price Elasticity of Demand Is Zero

Cross price elasticity of demand will be zero when two goods are unrelated.

When two goods are unrelated, the price of one good should have no effect on demand for the other. This is why the cross price elasticity of two unrelated goods will be zero.

Understanding the Magnitude of Cross Price Elasticity

Elasticities can take on any value.

When the cross price elasticity coefficient is less than -1 or greater than 1, the cross price elasticity is elastic. In the case of two substitutes, this means that the two goods are strong substitutes where one good can easily replace the other. In the case of complements, this means the two goods are strong complements that are frequently purchased together.

When cross price elasticity is between -1 and 0 for complementary goods and between 0 and 1 for substitute goods, the cross price elasticity is inelastic. This indicates that the two goods are either weak complements or weak substitutes.

The figure below summarizes what you need to know to interpret the cross price elasticity of demand. Remember, when the cross price elasticity is positive the two goods are substitutes. When the value is negative, the two goods are complements, and when the value is zero, the two goods are unrelated.

Cross Price Elasticity Versus Other Types of Elasticity

What Is Elasticity?

In general, elasticity measures the responsiveness of one thing to a change in another.

4 Types of Elasticity

Cross price elasticity of demand is just one type of elasticity you’ll learn about in economics.

Other types of elasticity you might come across in your economics courses are:

• Price Elasticity of Demand - This measures how the quantity demanded of a good changes in response to a change in its price. Unlike cross price elasticity, price elasticity of demand relates quantity demanded for a good to its own price rather than the price of another good.

• Price Elasticity of Supply - This measures how the quantity supplied for a product changes in response to a change in its price.

• Income Elasticity of Demand - This measures how quantity demanded for a good changes in response to changes in the income of consumers who buy the good.

Cross Price Elasticity of Demand Examples

Check your understanding of cross price elasticity by answering these three questions.

1. The price of Colgate toothpaste falls from $4.50 to $4.32. As a result, sales of Aquafresh toothpaste decrease from 20,000 units to 19,000 units. Without doing the calculation, do you expect the cross price elasticity of demand for Aquafresh to be positive or negative?

2. Calculate the cross price elasticity of demand for Aquafresh toothpaste using the information from Question 1.

3. If honey and tea are weak complements, the cross price elasticity of demand for honey with respect to changes in the price of tea should be:

a) Less than -1

b) Between -1 and 0

c) Between 0 and 1

d) Greater than 1

Solutions:

1. A positive cross elasticity of demand should be the result, since Aquafresh and Colgate toothpaste are substitutes.

2. −100020,000÷−0.184.50=−0.05−0.04=1.25\frac{-1000}{20,000} \div \frac{-0.18}{4.50}= \frac{-0.05}{-0.04}= 1.2520,000−1000​÷4.50−0.18​=−0.04−0.05​=1.25

3. B. Two goods that are weak complements should have cross price elasticity of demand that is between -1 and 0.

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