Cross elasticity of demand measures how much the quantity demanded of one product changes when the price of a different product changes. If coffee gets pricier and tea sales climb, that shift is cross elasticity at work.
The number tells you whether two products compete, complement each other, or have nothing to do with each other. Pricing, product, and marketing teams use it to predict what a rival’s price move will cost them.
In this guide, we’ll cover the formula, worked examples, what the result means, how businesses and regulators use it, and how to measure it with survey research.
What is cross elasticity of demand?
Cross elasticity of demand (also called cross price elasticity of demand, or XED) is the percentage change in quantity demanded of Good A divided by the percentage change in the price of Good B. It captures how closely two products are linked in the minds of buyers.
The sign of the result matters most:
- Positive: The goods are substitutes.
- Negative: The goods are complements.
- Near zero: Buyers treat the goods as unrelated.
Economists hold other factors constant when they calculate it, such as income and tastes. That rule isolates the price effect of the second product.
Cross elasticity vs price elasticity vs income elasticity
These three measures are easy to confuse. All three describe demand, but each one asks about a different trigger.
| Measure | What changes | What responds | Typical question |
|---|---|---|---|
| Cross elasticity of demand | Price of a different product | Quantity demanded of your product | If a rival cuts prices, how many customers do we lose? |
| Price elasticity of demand | Price of the same product | Quantity demanded of that product | If we raise our price, how much do sales fall? |
| Income elasticity of demand | Consumer income | Quantity demanded | Do buyers purchase more as they earn more? |
For the own-price version, see our guide to price elasticity.
How do you calculate cross elasticity of demand?
You calculate it by dividing the percentage change in quantity demanded of Good A by the percentage change in the price of Good B. The calculation takes four steps.
- Record the starting and ending price of Good B.
- Record the starting and ending quantity demanded of Good A.
- Convert each change to a percentage: (new minus old) divided by old, times 100.
- Divide the quantity change for Good A by the price change for Good B.
Formula:
XED = % change in quantity demanded of Good A ÷ % change in price of Good B
Worked example: Coffee and tea
A café raises its coffee price from $4 to $5, a 25% increase. Over the same period, its tea sales rise from 200 to 230 cups a day, a 15% increase.
XED = 15% ÷ 25% = +0.6
The result is positive, so coffee and tea are substitutes. The size is below 1, so the link is real but not strong. Some coffee drinkers switch to tea. Most stay loyal to coffee.
The midpoint method for bigger price changes
The simple formula gives different answers depending on which price you treat as the starting point. The midpoint method fixes that by dividing each change by the average of the old and new values.
- Percentage change = (new minus old) ÷ ((new plus old) ÷ 2) × 100
- Coffee from $4 to $6 is a 40% change
- Tea from 100 to 130 cups is a 26.09% change
- XED = 26.09% ÷ 40% = +0.65
Use the midpoint method whenever prices move by more than about 10%.
What do positive, negative, and zero values mean?
The sign of the result tells you how two products relate, and the size tells you how strongly. A result above +1 or below -1 signals a strong link, while a result between -1 and +1 signals a weak one.
- Positive (substitutes): Buyers switch from the pricier product to the cheaper one. Coffee and tea are a classic pair. The higher the value, the closer the substitutes.
- Negative (complements): Buyers use the two products together. When gasoline gets pricier, demand for large, fuel-hungry vehicles falls. The more negative the value, the tighter the pairing.
- Zero (independent goods): A price change in one product has no effect on the other. Bread and televisions fit here.
A strong positive value is a warning sign for sellers. It means customers will switch quickly when a rival lowers its price.
What are real examples of cross elasticity?
Real markets show a wide range of values, from strongly competing goods to loosely linked ones. The table below uses published estimates, so you can see what typical numbers look like.
| Product pair | Relationship | Cross elasticity |
|---|---|---|
| Butter and margarine | Substitutes | +0.81 |
| Beef and pork | Substitutes | +0.28 |
| Entertainment and food | Complements | -0.72 |
Source: Wikipedia, Cross elasticity of demand.
Butter and margarine score high because buyers see them as close alternatives. Beef and pork score lower because many shoppers choose by habit, cuisine, or occasion.
Researchers also study newer markets. One study of the Norwegian car market estimated direct and cross price elasticities for gasoline, diesel, hybrid, and battery electric cars. Studies like this show how a price change on one fuel type shifts demand across the others.
How do businesses use cross elasticity of demand?
Businesses use cross elasticity to decide how to price against competitors, how to bundle products, and how to manage their own product lines. The same number answers all three questions, but the action differs by relationship type.
Setting prices against close substitutes
- Estimate how many customers you would lose to a rival’s discount before you react.
- Match the price only when the cross elasticity is high and the product is hard to tell apart from the rival’s.
- Compete on quality, service, or brand when the cross elasticity is low.
- Watch for price changes on substitutes when you forecast sales for the next quarter.
Pricing and bundling complements
Complements reward a different strategy. A printer maker can sell the printer cheaply because ink sales make up the margin. A game console works the same way, with games and accessories carrying the profit.
Negative cross elasticity also guides bundling:
- Strong complements justify a bundle discount that lifts sales of both.
- Weak complements rarely justify one, because buyers purchase them separately anyway.
Avoiding cannibalization in your own product line
Cross elasticity applies inside a company too. A new “lite” plan might pull customers from the premium plan instead of winning new ones. Estimate the cross elasticity between your own products before launch, so you know how much new revenue is truly new. A price test on the new plan shows the pull before you commit.
Forecasting demand and sizing markets
Demand forecasts improve when they include the prices of related goods. A beverage brand that tracks a rival’s promotions can predict dips in its own volume. Pair the forecast with research on how to test market demand when you launch something new. A short checklist helps:
- Track rival prices and promotions weekly.
- Log your own price changes and campaigns.
- Compare the sales dip or lift with each rival move.
How do regulators use cross elasticity in antitrust cases?
Regulators use cross elasticity to decide which products compete in the same market. If a price rise on one product sends buyers to another, the two products likely belong to the same market.
The best-known US example is the Cellophane case. DuPont sold most of the cellophane in the country, but the courts weighed whether other flexible wrapping materials were close substitutes. High cross elasticity with those materials suggested DuPont did not hold a monopoly. The case is still taught as a lesson in defining markets.
The same logic applies to mergers. If two firms sell close substitutes, a merger removes a competitor and can push prices up. Antitrust agencies study how customers divert from one product to another when prices change.
Governments also use cross elasticity in tax and public health policy:
- A tax on one product can push buyers to a cheaper substitute.
- That shift changes the policy’s real effect.
What affects the size of cross elasticity?
Cross elasticity depends on how easily buyers can swap one product for another, and how long they have to adjust. Five factors drive most of the variation.
- Closeness of the products: Near-identical goods, such as two bottled water brands, show high values.
- Availability of alternatives: More substitutes in the market raise the cross elasticity of each one.
- Time horizon: Buyers switch more over months than over days, so long-run values are usually larger.
- Switching costs: Subscriptions, contracts, and loyalty programs lower the values.
- Brand loyalty and habit: Strong brands hold their buyers even when a rival cuts prices.
Remember that the relationship can change over time. New technology, shifting tastes, and advertising can turn a weak substitute into a strong one.
How can you measure cross elasticity with survey research?
You can measure cross elasticity by showing respondents products at different price levels and recording what they choose. This approach works when real sales data is thin, messy, or missing.
Market data has real problems. You rarely see a rival’s exact prices and sales, and promotions or stock-outs distort the signal. Survey research controls the variables instead.
The process runs in four steps:
- Define the products and the competitor whose price you want to test.
- Build choice tasks where each product appears at several price points.
- Collect responses from a representative sample of real buyers.
- Model the choices, then simulate a price change on one product while you hold your price fixed.
Conjoint analysis is the standard method for step 4. In one example, we found a product’s share of preference rose from 10% to 11% after a competitor raised its price by 10%. The implied cross elasticity was 1.0.
For a simpler first pass, the Van Westendorp price sensitivity meter shows an acceptable price range before you run a full choice study.
How does QuestionPro support cross elasticity research?
QuestionPro’s research tools cover the two hardest parts of a cross elasticity study: building the choice experiment and reaching the right buyers. The QuestionPro Market Research Software includes conjoint analysis for pricing and product studies.
Conjoint tasks let you vary your price and a competitor’s price in the same survey. The resulting data feeds a simulator that shows how your share shifts when the rival’s price moves. That is a direct view of cross-elasticity, without waiting for a real price war.
QuestionPro Audience adds a pre-screened panel, so you can reach US consumers or B2B decision-makers who fit your market. Targeted sampling matters here, because the wrong respondents give you a misleading elasticity.
What are the limitations and common mistakes?
Cross elasticity is a useful signal, but it is easy to misread. Most errors come from weak data or from treating one number as permanent.
- Ignoring other factors: Income, season, and advertising all move demand. If they change at the same time as price, the result is unreliable.
- Using tiny price changes: A 1% change can give noisy results. Test meaningful price steps.
- Mixing up the direction: The cross elasticity of A to B often differs from B to A. A premium brand may lose few buyers to a budget rival, while the budget brand loses many to the premium one.
- Treating the number as fixed: Values shift with time, promotions, and market entry.
- Choosing the wrong respondents: Survey results only hold if the sample reflects real buyers.
- Skipping own-price context: Read cross elasticity next to your own price elasticity. Our guide to measuring price sensitivity explains how.
Why cross elasticity of demand deserves a place in your pricing toolkit
Cross elasticity of demand turns a vague sense of “we compete with them” into a number you can act on. It tells you which rivals can hurt you, which products help you, and where your own offers overlap.
Start with the products closest to yours. Calculate the figure from sales data where you have it, and run a survey where you do not. Then revisit the number each year, because markets rarely stay still.
Frequently Asked Questions (FAQs)
Yes. A value of zero means a price change in one product has no effect on demand for the other, so the goods are unrelated. Bread and televisions are a typical example, and firms can usually ignore each other’s prices in that case.
No. The effect of Product A’s price on Product B’s demand often differs from the reverse. A well-known brand may lose few customers to a cheaper rival, while the cheaper rival loses many buyers when the famous brand discounts.
It depends on the number of products, price levels, and segments in the study. Each segment you want to analyze needs enough respondents on its own. Smaller samples give wide error ranges, so check precision before you act on the results.
Online shopping lets buyers compare prices in seconds, which usually raises cross elasticity between similar products. Price-tracking apps and search tools lower switching costs, so a rival’s discount can pull sales away faster than in a physical store.
Yes. Before launch, estimate how much of your new product’s sales would come from your existing products, which is cannibalization, and how much from competitors. A high cross-elasticity with your own product means a smaller net gain.
