Cross-Price Elasticity of Demand
Plain definition
Cross-price elasticity measures how the quantity demanded of one good responds to a price change in another good: (percentage change in quantity demanded of good A) divided by (percentage change in price of good B). The sign reveals the relationship: positive for substitutes, negative for complements.
In economics
Cross elasticity defines markets for competition analysis: if two brands' cross elasticity is large and positive, they compete in the same market. Merger regulators and firms use it to identify real substitutes and complements, and to predict how a rival's price move will shift their own demand curve.
Example
If a 10 percent rise in the price of tea raises coffee demand by 8 percent, the cross elasticity is +0.8 — substitutes. If a 10 percent rise in petrol prices cuts car demand by 6 percent, the cross elasticity is -0.6 — complements.
People mix up what the sign and the size mean. The sign tells you the relationship (positive = substitutes, negative = complements); the size tells you how strong it is. A cross elasticity of -0.1 and +3.0 are not comparable as small versus large numbers — the first is a weak complement, the second a strong substitute.