Crosselasticity

Crosselasticity, commonly referred to as the cross-price elasticity of demand, measures how the quantity demanded of one good responds to a change in the price of another good. It is defined as E_xy = (%ΔQ_x) / (%ΔP_y), or equivalently as the ratio of the percentage change in Q_x to the percentage change in P_y. The concept assumes other factors remain constant (ceteris paribus).

Interpretation: If E_xy > 0, the goods are substitutes; if E_xy < 0, they are complements; if E_xy ≈ 0, they are unrelated. The magnitude indicates the strength of the relationship: larger absolute values reflect stronger responsiveness. The estimates can vary by product, market, and time period.

Examples: Substitutes: a rise in the price of tea raises the quantity demanded of coffee, yielding a positive XED. Complements: a rise in the price of milk lowers the quantity demanded of cereal, yielding a negative XED. Calculation example: a 5% price increase for good Y causing a 2% decrease in Q_x gives E_xy = -0.40. In practice, arc elasticity or log changes are often used to reduce bias in larger changes.

Applications and limitations: XED helps with pricing strategy, competitive analysis, and demand forecasting by indicating how tightly related two goods are. Limitations include dependence on the price range observed, possible changes in substitution patterns over time, and the assumption that other factors stay constant. Data quality and model specification also affect estimates. See also: price elasticity of demand, income elasticity of demand, substitutes and complements.