Cross-price elasticity of demand (XED) measures how the quantity demanded of one good responds when the price of a different good changes. It helps identify whether goods are substitutes, complements, or unrelated.2.5.3 Cross-Price Elasticity of Demand (XED)
What is cross-price elasticity of demand?
Cross-price elasticity of demand (XED) is a measure used in microeconomics to determine how the quantity demanded of one product (Good A) changes when there is a change in the price of another product (Good B).
The formula for XED is:
XED = (Percentage change in quantity demanded of Good A) ÷ (Percentage change in price of Good B)
This measure helps identify the nature of the relationship between two goods. Depending on whether the XED is positive, negative, or zero, the goods are classified as substitutes, complements, or unrelated, respectively.
Economists and businesses use XED to assess how pricing decisions, changes in market conditions, or new products will affect demand across different goods.
Important notes about interpreting XED
The sign (positive or negative) tells us the type of relationship between the two goods.
The magnitude (absolute value) tells us how strong that relationship is.
A higher absolute value indicates a stronger relationship.
A lower absolute value indicates a weaker relationship.
Let’s explore the three possible types of relationships using XED: substitutes, complements, and unrelated goods.
Substitutes: XED > 0
When the XED is positive, it means the two goods are substitutes. This means that as the price of one good increases, the demand for the other good increases because consumers switch to the alternative.
Definition: Substitutes are goods that serve a similar function or satisfy similar consumer needs. If one becomes more expensive, consumers tend to shift their purchases to the other.
Example:
Tea and coffee are common substitutes. If the price of coffee rises, some consumers may choose to buy tea instead, increasing the demand for tea.
Suppose the price of coffee increases by 10%, and as a result, the quantity demanded for tea increases by 8%. The XED would be:
XED = 8% ÷ 10% = +0.8
This positive value confirms a substitute relationship.
Characteristics of substitute goods:
They compete in the same market or serve similar consumer functions.
The closer the substitute, the higher the positive XED value.
Examples include:
Butter and margarine
Coke and Pepsi
Streaming services like Netflix and Disney+
Bus rides and train rides
Strong vs. weak substitutes:
Strong substitutes (e.g., Coke vs. Pepsi) may have XED values greater than +1.
Weak substitutes (e.g., butter vs. olive oil) may have lower positive values such as +0.2 or +0.3.
Businesses monitor the XED of substitute goods closely. If a competitor’s price changes, it can significantly impact demand for their own product.
Complements: XED < 0
When the XED is negative, it indicates the two goods are complements. This means that as the price of one good increases, the demand for the other good decreases because they are used together.
Definition: Complementary goods are typically used in combination, so if one becomes more expensive, the other becomes less attractive or useful.
Example:
Cars and gasoline are complements. If the price of gasoline rises sharply, consumers may drive less or delay purchasing new cars, reducing car demand.
Suppose the price of gasoline increases by 20%, and the quantity of cars demanded falls by 10%. The XED would be:
XED = -10% ÷ 20% = -0.5
This negative value confirms a complementary relationship.
Characteristics of complementary goods:
They are usually consumed or used together.
The closer the complementarity, the more negative the XED value.
Examples include:
Printers and ink cartridges
Smartphones and mobile apps
Video game consoles and games
Electric cars and charging stations
Strong vs. weak complements:
Strong complements (e.g., console and console-exclusive games) may have XED values like -1.2.
Weak complements (e.g., chips and salsa) may have XED values like -0.2.
Firms use this information to create bundling strategies or co-marketing efforts. For instance, selling a printer at a discount with the expectation of future ink cartridge sales.
Unrelated goods: XED = 0
Sometimes, two goods are unrelated, meaning that a change in the price of one does not affect the demand for the other. In these cases, the XED is zero.
Definition: Unrelated goods have no consumer or market connection. The demand for one is unaffected by changes in the price of the other.
Example:
Bread and televisions are unrelated goods. If the price of televisions increases, it is highly unlikely that the demand for bread will change.
Suppose the price of televisions increases by 15%, and there is no change in the demand for bread. Then:
XED = 0% ÷ 15% = 0
Characteristics of unrelated goods:
No link in consumer preference or usage.
XED equals zero, showing independence between the goods.
Other examples:
Apples and car tires
Books and shampoo
Milk and headphones
Knowing when goods are unrelated helps firms understand that price changes in those markets won’t affect their own sales or pricing strategy.
Business relevance of XED
Understanding cross-price elasticity is useful in a wide variety of business and policy contexts. It can help companies anticipate customer behavior, shape pricing strategy, and manage competition.
Pricing strategies for substitutes:
If a firm knows its product is a close substitute for a competitor’s, it may respond to a price increase by the competitor with advertising or only a small price increase, knowing that consumers may switch.
Firms may also use price-matching policies to keep XED effects neutralized.
Pricing strategies for complements:
A business might sell a primary product at a low price and profit from complementary goods. This is known as the razor-and-blades model.
For example, game consoles are often priced near cost, while games and accessories generate profits.
Firms can also offer bundles to encourage consumers to purchase both complementary items at once.
XED and product development:
When launching new products, businesses can assess whether they are likely to cannibalize sales of existing products or complement them.
Understanding cross-price elasticity also helps companies decide whether to enter new markets where products are substitutes or complements to existing offerings.
Graphical analysis of XED
Graphs help illustrate how the demand for one good changes as the price of another changes. Let’s look at how this applies to substitute and complementary goods.
Substitutes: Demand curve shift to the right
When the price of Good B increases, and Good A is a substitute, the demand curve for Good A shifts to the right.
Example: Price of coffee rises → demand for tea increases.
On a graph, this is shown as a new, higher demand curve for tea.
This demonstrates a positive relationship between the price of coffee and the demand for tea.
Complements: Demand curve shift to the left
When the price of Good B increases, and Good A is a complement, the demand curve for Good A shifts to the left.
Example: Price of gasoline increases → demand for cars decreases.
On a graph, this is shown as a new, lower demand curve for cars.
This represents a negative relationship between the price of gasoline and the demand for cars.
Calculating XED step-by-step
To calculate cross-price elasticity of demand accurately, follow this three-step process using percentage changes:
Step 1: Calculate the percentage change in quantity demanded of Good A
Use the midpoint formula:
% change in quantity demanded = [(Q2 - Q1) / ((Q2 + Q1) ÷ 2)] × 100
Where:
Q1 = original quantity demanded
Q2 = new quantity demanded
Step 2: Calculate the percentage change in price of Good B
Also using the midpoint formula:
% change in price = [(P2 - P1) / ((P2 + P1) ÷ 2)] × 100
Where:
P1 = original price
P2 = new price
Step 3: Apply the XED formula
XED = (% change in quantity demanded of Good A) ÷ (% change in price of Good B)
Example:
Suppose the price of coffee rises from 6, and the quantity demanded of tea increases from 100 to 130 units.
% change in quantity demanded of tea = [(130 - 100) / (130 + 100) ÷ 2] × 100
= (30 / 115) × 100
≈ 26.09%% change in price of coffee = [(6 - 4) / (6 + 4) ÷ 2] × 100
= (2 / 5) × 100
= 40%XED = 26.09% ÷ 40% = +0.65
Interpretation: Since XED is positive and less than 1, tea and coffee are substitutes, but not very close ones.
Elasticity and strength of the relationship
Just as with price elasticity of demand, XED can be classified as elastic or inelastic, depending on the absolute value.
Elastic cross-price elasticity (|XED| > 1): A large change in quantity demanded in response to a price change. Indicates strong substitutes or complements.
Inelastic cross-price elasticity (|XED| < 1): A small change in quantity demanded. Indicates weak substitutes or complements.
Understanding whether a relationship is elastic or inelastic helps firms make better strategic decisions regarding pricing, advertising, and product placement.
FAQ
Yes, cross-price elasticity of demand (XED) can be very useful for analyzing products offered by the same company, especially when they serve similar or related functions. For example, a beverage company that produces both soda and flavored water may want to know whether the two goods are substitutes. If the XED between them is strongly positive, it means that a price increase for soda may lead consumers to switch to the flavored water, and vice versa. This can help the company avoid “cannibalization,” where one product reduces the sales of another within the same firm. It also assists in designing pricing strategies that maximize overall revenue. If the goods are complements—like a console and a specific type of controller—the company can bundle them or adjust prices to promote joint sales. Therefore, XED is a valuable internal tool for managing product lines and understanding how price changes affect demand within a company’s own offerings.
The availability and closeness of substitutes directly affect the magnitude of the cross-price elasticity of demand. The more similar two goods are in function, quality, and price, the higher the positive XED value will be. This is because consumers can easily switch from one product to another in response to even small changes in price. For example, if two brands of bottled water are nearly identical in every aspect, a price increase in one will likely lead to a significant increase in demand for the other, resulting in a high XED, such as +2.0. On the other hand, if the substitutes are less similar—like butter and cooking oil—the XED will still be positive but lower, perhaps closer to +0.3 or +0.5. Markets with many close substitutes tend to be highly competitive, as firms are more vulnerable to consumer switching. In contrast, products with fewer or more distant substitutes will typically have a lower cross-price elasticity.
Yes, time significantly affects the cross-price elasticity of demand. In the short run, consumers may not immediately change their purchasing habits in response to a change in the price of a related good. This means that XED values in the short run may appear lower because consumers need time to adjust to price differences, especially if it involves changing routines, learning new products, or incurring switching costs. Over the long run, however, consumers have more flexibility and access to information, which allows them to seek alternatives or complementary goods more effectively. As a result, XED tends to become larger—either more positive or more negative—over time. For instance, if gas prices rise, people may not reduce their car usage right away, but over months or years, they may switch to public transportation or purchase fuel-efficient vehicles. This means that the complementarity between fuel and cars becomes more evident over time, and XED becomes more negative in the long run.
Cross-price elasticity plays a critical role in decisions involving mergers and acquisitions, especially when firms produce related goods. Regulators and firms alike use XED to assess how closely related the products of two merging companies are in terms of consumer demand. If two firms produce strong substitutes (high positive XED), a merger could reduce market competition, potentially allowing the new entity to raise prices without losing significant market share. In such cases, antitrust authorities may block or restrict the merger to protect consumer welfare. On the other hand, if the goods are complements (strong negative XED), the merger might lead to efficiency gains, such as product bundling or reduced transaction costs, and might be more favorably viewed by regulators. Firms also use XED data during acquisitions to evaluate the potential impact on demand for their existing product lines and to identify whether the new products will support or compete with what they already offer.
Yes, cross-price elasticity of demand between the same two goods can change over time due to shifts in consumer preferences, market conditions, and technological developments. For example, two goods that are initially weak substitutes might become stronger substitutes if one of them improves in quality, becomes more widely available, or gains consumer trust. A good illustration is ride-sharing apps and traditional taxis. When ride-sharing first emerged, it may have had a low XED with taxis due to limited availability. Over time, as it became more accessible and affordable, consumers increasingly saw it as a substitute, and the XED became more positive. Similarly, complements can weaken or strengthen their relationship. For example, if video game consoles shift toward digital game downloads, the complementarity between consoles and physical game discs may decline, reducing the magnitude of the negative XED. Changes in income, culture, advertising, and policy can also impact how goods relate, making XED values dynamic rather than fixed.
Practice Questions
Suppose the price of digital cameras increases by 20%, and as a result, the quantity demanded of memory cards falls by 10%. Calculate the cross-price elasticity of demand (XED) and explain what the result implies about the relationship between digital cameras and memory cards.
The cross-price elasticity of demand (XED) is calculated by dividing the percentage change in quantity demanded of memory cards (-10%) by the percentage change in the price of digital cameras (+20%). XED = -10% ÷ 20% = -0.5. Since the XED is negative, this indicates that digital cameras and memory cards are complementary goods. The negative value means that as the price of cameras rises, the demand for memory cards falls, showing that they are typically used together. A value of -0.5 suggests a moderately weak complementary relationship between the two goods.
A firm discovers that the cross-price elasticity of demand between its energy drink and a rival brand is +1.4. What does this value indicate, and how should the firm use this information in its pricing strategy?
A cross-price elasticity of demand of +1.4 indicates that the two energy drinks are strong substitutes. The positive value shows that as the rival brand’s price increases, the quantity demanded for this firm’s drink increases. Since the value is greater than one, the relationship is elastic, meaning consumers are highly responsive to price differences. The firm can use this to its advantage by keeping its price slightly lower than the competitor’s to attract more buyers. This sensitivity implies that strategic pricing could significantly increase market share if the firm responds to competitors’ price changes.
