When Uber raises surge pricing, some riders immediately switch to Lyft. When coffee prices spike, demand for tea rises. When printer prices fall sharply, ink cartridge sales increase. In each case, a price change in one good shifts demand for a different good. Cross-price elasticity puts a number on exactly how much — and whether the relationship is substitution or complementarity.
The formula
Cross-Price Elasticity of Demand (XED) = % Change in Quantity Demanded of Good A ÷ % Change in Price of Good B
The sign of the result classifies the relationship:
- Positive XED: when B's price rises, demand for A rises → A and B are substitutes
- Negative XED: when B's price rises, demand for A falls → A and B are complements
- Near zero: the goods are largely unrelated
Reading the result
A cross-price elasticity of +1.5 between Lyft and Uber means that a 10 percent increase in Uber's price raises Lyft's ridership by 15 percent — strong substitution. A cross-price elasticity of –0.6 between smartphones and phone cases means a 10 percent rise in smartphone prices reduces phone case demand by 6 percent — moderate complementarity.
The magnitude matters for business strategy. A high positive XED means competing products are close substitutes and pricing decisions directly drive switching. A high negative XED means the firm's product is tightly tied to the performance of another — making it vulnerable to shocks in the complementary market.
Worked example
A coffee roaster tracks demand for its ground coffee when supermarket instant coffee prices change. Over two quarters, instant coffee prices rose 12 percent. The roaster's unit sales rose 4 percent over the same period, with no changes to its own pricing or marketing.
XED = +4% ÷ +12% = +0.33
A positive value confirms the two products are substitutes. The relatively small magnitude (0.33) suggests the substitution is modest — many instant coffee buyers prefer it for reasons beyond price and don't fully cross over to ground coffee when instant gets more expensive.
Where it's used
Antitrust regulators use cross-price elasticity to define the boundaries of a relevant market — if the XED between two products is high, they compete closely and should be analyzed as part of the same market. The DOJ Antitrust Division's merger guidelines rely on this logic: two firms cannot be said to have a combined monopoly if buyers readily substitute to outside products (high XED with competitors). Firms use it to monitor competitive threats and price coordination across product portfolios.
