Name both goods and keep their roles distinct.
Cross elasticity of demand (XED, also called CED) is the percentage change in demand for good A divided by the percentage change in the price of good B, other things equal, including A's own price. A positive value indicates substitutes in the stated relationship; a negative value indicates complements. A zero estimate indicates no measured cross-price response under those conditions. A larger absolute magnitude generally indicates a stronger response to the other good's price, but the direction of the relationship still comes from the sign. XED of A with respect to B need not equal XED of B with respect to A.
- Formula
- Cross elasticity of demand (XED, also called CED) = percentage demand change for good A / percentage price change of good B. A is the good whose demand responds; hold its own price fixed.
- Sign
- Positive XED suggests substitutes: buyers switch towards A when B becomes dearer. Negative XED suggests complements: goods used together, so a higher B price reduces demand for A.
- Direction
- The response of A to B's price need not match the response of B to A's price.
Use both market names
Substitutes
A higher B price can increase demand for A as buyers switch. The coefficient is positive under that relationship.
Complements
A higher B price can reduce demand for A when they are used together. The coefficient is negative.
Magnitude
Use absolute size to compare responsiveness while retaining the sign for the relationship. -2 is a stronger proportional response than -0.4, not a weaker one because it is more negative.
Limits
An estimate of zero concerns the specified data and conditions. Market definitions, consumer groups, budgets and time can change the measured relationship.
| Sign | Relationship | B price rises |
|---|---|---|
| Positive | Substitutes | A demand rises |
| Negative | Complements | A demand falls |
| Zero | No measured response in this comparison | A demand unchanged |
Worked example: Rail fares and bus demand
Rail fares rise by 10%. Demand for bus journeys rises by 6% at each given bus fare, holding income, service quality and other relevant determinants unchanged. Use these stated percentage changes.
- Label A as bus journeys and B as rail journeys. XED of bus demand with respect to rail fare is +6%/+10% = +0.6.
- The positive sign supports the substitute relationship: some passengers switch towards buses when rail becomes relatively dearer.
- Bus demand shifts right. It is not a movement caused by the bus fare, since that own price is held constant in the demand comparison.
- The reverse response need not have the same coefficient. Nor does this demand increase guarantee exactly 6% more bus journeys after any bus-fare adjustment.
Watch out for this
XED uses the percentage change in the same good's own price.
That would be PED. XED connects demand for one good to the price of another, with both goods named.
Check your understanding
The price of games consoles falls by 10%, and demand for compatible games rises by 15%, other things equal. What is XED of game demand with respect to console price?
- +1.5, so they are substitutes.
- -1.5, supporting complementarity in this comparison.
- -0.67, because price must go in the numerator.