Cross elasticity of demand
Cross elasticity of demand measures how the quantity demanded of one good responds to a change in the price of another.
Change the price of one product and the demand for another can move. Cross elasticity measures how, and reveals what competes with what.
Cross elasticity of demand measures how the quantity demanded of one good responds to a change in the price of another. Its sign tells you the relationship between the two goods: positive for substitutes, negative for complements, near zero for goods that have little to do with each other.
Substitutes and complements
When two goods are substitutes, like rival brands of coffee, a rise in the price of one increases demand for the other, so cross elasticity is positive: buyers switch. When two goods are complements, used together, like printers and ink or cars and petrol, a rise in the price of one reduces demand for the other, so cross elasticity is negative: dearer cars mean less petrol sold. The stronger the relationship, the larger the number.
Defining the competition
Cross elasticity is a practical tool for working out what actually competes with what, which is rarely obvious. Two products may look similar yet barely affect each other's demand, while two that look unrelated may be close substitutes in buyers' eyes. Competition authorities use cross elasticity to define markets when judging mergers, because the real question is which products constrain each other's prices, not which sit in the same category.
Pricing across a range
For a firm selling several related products, cross elasticity matters because changing one price ripples across the others. Cutting the price of a complement can lift sales of the profitable partner, which is why razors are cheap and blades are not, or why consoles are sold near cost to drive game sales. Ignoring these cross-effects leads to pricing each product in isolation and missing how they move together.
Cross elasticity is the measure of how goods relate through price. It turns the loose notions of substitute and complement into something quantifiable, and it repeatedly shows that the boundaries of a market, and of competition, are not where intuition first places them.