Cross-Price Elasticity of Demand: Formula, Examples, and How to Read It

Cross-price elasticity of demand (XED) measures how much the quantity demanded of one good responds when the price of a *different* good changes, and its formula is the percentage change in the quantity demanded of Good B divided by the percentage change in the price of Good A. The number does two jobs at once: its sign tells you whether the two goods are substitutes, complements, or unrelated, and its size tells you how strong that relationship is. A firm that learns its product has an XED of +2.5 with a rival's product knows a rival price cut will hammer its sales; a firm whose product has an XED of −1.8 with a partner good knows the two rise and fall together. This guide gives you the formula, worked calculations in both directions, a full interpretation grid, and the real business decisions XED drives.

The formula

Cross-price elasticity of demand is:

XED = (% change in quantity demanded of Good B) / (% change in price of Good A)

Two goods are involved, and the order matters: you are asking how B's *quantity* reacts to A's *price*. Contrast this with ordinary price elasticity of demand, which uses a good's *own* price in the denominator. Swapping in the price of a *different* good is the entire twist that turns own-price elasticity into cross-price elasticity. The formal definition lives in the glossary entry on cross-price elasticity of demand.

To compute each percentage change, use the standard formula, new minus old, divided by old, times 100:

% change = ((new value − old value) / old value) x 100

For precise answers, especially over larger price moves, economists often use the midpoint method, which divides the change by the *average* of the old and new values so the elasticity comes out the same whether the price rose or fell. But for exam-level work the simpler new-minus-old-over-old version is usually accepted, and it is what the worked examples below use.

Worked example 1: substitutes

A streaming service raises its price from $10 to $12 a month, a 20% increase. Over the following quarter, monthly signups for a competing service rise from 40,000 to 46,000, a 15% increase, as price-sensitive viewers switch.

Step 1, price change of Good A: (12 − 10) / 10 x 100 = +20%.

Step 2, quantity change of Good B: (46,000 − 40,000) / 40,000 x 100 = +15%.

Step 3, divide: XED = (+15%) / (+20%) = +0.75.

The result is positive, so the two services are substitutes: a price rise in one raised demand for the other. The magnitude, 0.75, is less than 1, meaning the response is real but not enormous, roughly what you would expect for services that compete but are not perfect stand-ins for each other. Any time both percentages carry the same sign, XED is positive and you have substitutes.

Worked example 2: complements

A game console maker cuts the price of its console from $500 to $400, a 20% decrease. Sales of games for that console rise from 2 million to 2.6 million copies a month, a 30% increase, because more consoles in homes means more game buyers.

Step 1, price change of Good A: (400 − 500) / 500 x 100 = −20%.

Step 2, quantity change of Good B: (2.6M − 2M) / 2M x 100 = +30%.

Step 3, divide: XED = (+30%) / (−20%) = −1.5.

The result is negative, so consoles and games are complements: a lower console price raised demand for games. The magnitude, 1.5, is greater than 1, signaling a strong complementary link, which is exactly why console makers often sell hardware cheaply to drive game sales. Whenever the two percentages carry opposite signs, XED is negative and you have complements. For the intuition behind classifying pairs this way, see our guide on substitutes vs complements.

The interpretation grid

Here is the full map from an XED value to its meaning. Commit the sign logic first, then the magnitude:

• XED > 0 (positive): substitutes. Both goods move the same way. Larger positive numbers mean closer substitutes. Two nearly identical products (say two brands of the same generic drug) can have a large positive XED; loosely related substitutes have a small positive one.
• XED < 0 (negative): complements. The goods move in opposite directions. More negative numbers mean stronger complements. Cars and gasoline, or printers and ink, carry sizable negative values.
• XED = 0 (or very close): unrelated / independent goods. A price change in one leaves the other's demand essentially untouched. Toothpaste and lawnmowers, for instance.
• Magnitude greater than 1: the cross-response is *elastic*, meaning the quantity of B reacts more than proportionally to A's price. The relationship is strong.
• Magnitude between 0 and 1: the cross-response is *inelastic*, meaning B's quantity reacts less than proportionally. The relationship is weak.

The single most tested idea is the sign, so if you remember nothing else: positive equals substitutes, negative equals complements, zero equals unrelated. The magnitude then grades how strong that link is. This sits alongside the other elasticity concepts, elastic demand and inelastic demand, that you will meet in the elasticity module.

How XED differs from the other elasticities

Elasticity is a family of measures, and it is easy to mix them up. All of them divide a percentage change in some quantity by a percentage change in something that drives it. What differs is the driver in the denominator:

• Price elasticity of demand uses the good's own price. It is almost always negative (higher price, lower quantity) and measures how sensitive buyers are to that good's price. The rare Giffen good, whose demand curve slopes up, is the only exception.
• Cross-price elasticity of demand uses another good's price. Its sign classifies the relationship between the two goods.
• [Income elasticity of demand](/glossary/income-elasticity-of-demand) uses consumer income. Its sign tells you whether a good is normal (positive) or inferior (negative).

Keeping the denominators straight is half the battle. Own price, other good's price, and income are three different drivers producing three different elasticities. You can practice all three with the calculators on the calculate hub: the cross-price elasticity calculator, the price elasticity of demand calculator, and the income elasticity of demand calculator. If a problem also asks how a price change affects a firm's revenue, the total revenue test is the companion tool.

Business uses of cross-price elasticity

XED is not just an exam concept; firms estimate it from real sales data to make concrete decisions.

Pricing against rivals. A company that knows its product is a strong substitute for a competitor's (high positive XED) also knows it is exposed: a rival price cut will pull its customers away fast. That shapes how aggressively it must match discounts and how much pricing power it really has. A low XED with rivals, by contrast, signals a differentiated product that can hold a price premium.

Bundling and complement pricing. When a firm sells two complements (negative XED), it can profit by pricing them as a system rather than in isolation. The razor-and-blades model, cheap razor, expensive blades, works precisely because the two are strong complements: a low razor price lifts blade demand. Console makers, printer makers, and coffee-pod makers all play the same game. Knowing the XED between the anchor product and its consumable tells the firm how much it can afford to discount the anchor.

Antitrust and market definition. Regulators use cross-price elasticities to decide whether two products belong in the same market. If two goods have a high positive XED, buyers treat them as close substitutes, so a proposed merger between their makers gets more scrutiny because the combined firm would face less competition. XED is a working tool in competition policy, not just a classroom formula.

Forecasting. A retailer that knows the XED between its products can predict how a promotion on one item will cannibalize or lift sales of others, and plan inventory accordingly. Complements get stocked together; substitutes get watched for cannibalization.

Common mistakes to avoid

Three errors trip students up most often. First, dropping the sign: cross-price elasticity keeps its sign because the sign carries the classification, unlike own-price elasticity where the negative is often assumed and stated as an absolute value. Never report XED as a bare magnitude. Second, flipping which good is which: the denominator is the price of the good whose price *changed*, and the numerator is the quantity of the *other* good. Reversing them gives a different number. Third, confusing XED with income elasticity: a negative XED means complements, but a negative *income* elasticity means an inferior good. Same sign, completely different meaning, because the denominators differ.

Putting it together

Cross-price elasticity of demand answers a precise question: when the price of one good moves, how much does demand for another good move, and in which direction? Divide the percentage change in the second good's quantity by the percentage change in the first good's price. A positive result means substitutes, a negative result means complements, and a result near zero means the goods are unrelated. The magnitude grades the strength of the link. Firms use those numbers to price against rivals, bundle complements, and define markets; students use them to shift demand curves the right way on exam day. Run your own numbers through the cross-price elasticity calculator, build the broader intuition in the elasticity module, and pair this with the substitutes vs complements guide so the sign rule becomes second nature.