Cross-Price Elasticity

Cross-price elasticity of demand (often abbreviated XED or E_xy) quantifies the percentage change in quantity demanded of good X resulting from a one percent change in the price of good Y. Formally:

E_xy = (%Δ Quantity demanded of X) / (%Δ Price of Y)

The sign of the coefficient is what matters most for classification:

• Positive XED → the two goods are substitutes. When the price of Y rises, consumers switch toward X. Example: butter and margarine, or Pepsi and Coca-Cola.
• Negative XED → the goods are complements. A higher price for Y reduces demand for X because they are consumed together. Example: petrol and cars, or printers and ink cartridges.
• Zero (or near-zero) XED → the goods are unrelated or independent in consumption.

The magnitude indicates the strength of the relationship: a value near zero implies weak linkage, while a large absolute value implies the goods are close substitutes or strong complements.

Cross-price elasticity is central to several policy and research domains relevant to IR and economic governance. Competition authorities such as the European Commission's DG COMP and the U.S. Department of Justice use it to define relevant product markets in antitrust cases—if two products have a high positive XED, they likely belong in the same market, affecting merger reviews. The U.S. Horizontal Merger Guidelines and the "SSNIP test" (small but significant non-transitory increase in price) rely implicitly on cross-elasticity reasoning.

In trade policy, cross-price elasticities help estimate how tariffs on one import affect demand for domestic substitutes or for complementary inputs, informing WTO dispute calculations of nullification and impairment. In energy and climate analysis, XED between fossil fuels and renewables shapes carbon-pricing models used by the IEA and IPCC working groups.

Estimates are typically derived from econometric demand systems such as the Almost Ideal Demand System (AIDS) developed by Deaton and Muellbauer (1980).