How this instrument works
Cross-price elasticity of demand (XED) measures how the quantity demanded of one good, A, responds in percentage terms to a percentage change in the price of a separate good, B. That single number does something ordinary price elasticity cannot: its sign is the finding. A positive XED means A and B are substitutes — raise B's price and shoppers buy more A instead. A negative XED means they are complements — raise B's price and demand for A falls too, because the two are usually bought as a pair. A reading near zero means the two goods barely interact in anyone's basket.
The formula is a ratio of two percentage changes rather than raw amounts, which is what lets it compare goods priced in entirely different units — a $0.10 rise in the price of margarine against a change in pounds of butter sold, or a $2 airfare surcharge against hotel-night bookings. That unit-free ratio is also exactly what competition regulators lean on when they ask whether two products compete in the same market: a version of that test asks whether a modest, sustained price rise in one product would push enough buyers toward a rival that the price rise stops paying off, and cross-price elasticity is the number that answers it.
A measured XED is a local reading, not a fixed constant attached to a pair of goods. It reflects one starting price, one quantity, one population, and one stretch of time — a coffee-and-creamer pairing measured during a price spike can read differently than the same pairing measured in ordinary conditions, and habits take time to shift, so a number gathered too soon after a price move can understate the true substitution or complementarity once buyers adjust.
- Enter the % change in quantity demanded of A — the observed or assumed swing in how much of good A people bought.
- Enter the % change in price of B — positive for a price rise in the other good, negative for a price cut.
- Read Cross-price elasticity of demand (XED) in the result: check the sign first, then the size.
- Flip the sign on either field to see a price cut instead of a rise — the story flips (substitute to complement or back) even when the size of the number stays the same.
Worked example — margarine's price, butter's demand
Say good B is margarine and good A is butter. Margarine's price rises 20% and, as shoppers switch, the quantity of butter demanded rises 10%. Divide the two: XED = 10 ⁄ 20 = 0.5. The positive sign says butter and margarine behave as substitutes in this data — a price rise in one goes with more purchases of the other — and 0.5 is a moderate reading, well short of the near-1-or-higher values you would expect between two near-identical store brands of the same product.
Keep the same 20% price rise in B but flip A's response to a 10% fall in quantity demanded instead, and the ratio becomes -0.5. Same size, opposite sign, and now the story is complements: think printer prices up 20% while ink-cartridge sales drop 10% because fewer new printers left the shelf. One sign-flip separates the two relationships on this sheet, which is why reading the sign is the first step, not an afterthought.
Questions
What does a positive cross-price elasticity mean?
It means the two goods are substitutes. In this ratio, a rise in good B's price came with a rise in quantity demanded of good A, so buyers shifted toward A. The larger the positive value, the closer the substitution — a reading near or above 1 points to close substitutes like two brands of the same product, while a small positive value points to weak, partial substitution.
What does a negative value mean?
It means the goods are complements — typically bought together, like phones and cases, or coffee and creamer. A price rise in B comes with a fall in demand for A because the higher cost of the pair discourages the whole combination, not just B on its own. The more negative the reading, the tighter that pairing.
How is this different from ordinary price elasticity of demand?
Ordinary (own-price) elasticity relates a good's quantity to its own price and is almost always negative, since demand curves slope down. Cross-price elasticity relates good A's quantity to a different good B's price, so nothing forces the sign one way — the sign itself is what the calculation reveals about how the market treats the two goods.
Why do competition regulators use this number?
Agencies reviewing mergers ask whether two products compete in the same market. One accepted test asks whether a hypothetical monopolist raising one product's price by a modest, sustained amount would lose enough sales to a rival that the price rise doesn't pay off; a high cross-price elasticity between the two products supports treating them as one market, while a low or negative reading argues for separate ones.
Can the same two goods show different XED values in different studies?
Yes. Cross-price elasticity is measured at a specific starting price and quantity, for a specific population, over a specific stretch of time, so it is a local reading rather than a fixed property of the two goods. The same pair can test as closer substitutes near one price range and weaker substitutes near another, and estimates drawn from different customer groups or seasons will not always agree.
What's the most common misreading of this figure?
Assuming the sign is fixed by which good gets labeled A and which gets labeled B. Swap the roles — measure how B's quantity responds to A's price instead — and the two elasticities describe the same relationship from opposite sides. They usually agree in sign but rarely match in exact size, so it pays to check which good's quantity and which good's price sit in the ratio you're reading.
References
- FTC & DOJ — Merger Guidelines (2023), market definition and substitution
- OpenStax, Rice University — Principles of Microeconomics, cross-price elasticity
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.