Cross-Price Elasticity (XED): Formula, Interpretation & Real-World Values

Cross-Price Elasticity of Demand measures the percentage change in quantity demanded of Product A when the price of Product B changes by 1%. It captures the demand linkage between any two products in a market.

Unlike own-price elasticity (which is almost always negative), cross-price elasticity can be positive, negative, or zero:
- Positive: Products are substitutes. When Brand B's price rises, demand for Brand A increases.
- Negative: Products are complements. When coffee prices rise, demand for coffee filters falls.
- Zero: Products are independent. A price change on one has no measurable effect on the other.

In FMCG, most products within the same category exhibit positive cross-price elasticity, and the magnitude tells you how close the substitution relationship really is. A cross-elasticity of 0.8 between two biscuit brands means consumers view them as near-interchangeable. A cross-elasticity of 0.1 means they occupy different mental slots.

Cross-Price Elasticity: E_AB = (%Change in Demand for A) / (%Change in Price of B)

E_AB = (dQ_A / Q_A) / (dP_B / P_B)

Interpretation guide:
- E_AB = +0.8: A 10% price increase on B drives an 8% volume gain for A (close substitutes)
- E_AB = +0.1: A 10% price increase on B drives only a 1% gain for A (weak substitutes)
- E_AB = -0.3: A 10% price increase on B causes a 3% decline in A (complements)

Volume transfer calculation:
dQ_A = Q_A x E_AB x (dP_B / P_B)

Where:
- Q_A = current volume of Product A
- E_AB = cross-elasticity from B to A
- dP_B / P_B = percentage price change on Product B

The formula is directional: E_AB and E_BA are almost never equal.

CrunchField raises its base price by 10% (from $4.29 to $4.72). The cross-elasticity estimates from scanner data predict:

CrunchField own-elasticity: -1.8
Volume loss: -18% of 2,000,000 units = -360,000 units

Volume gained by competitors:
- SweetBite (E = +0.8): gains 8% of 1,500,000 = +120,000 units
- Baker's Choice (E = +0.3): gains 3% of 2,500,000 = +75,000 units
- LuxCrisp (E = +0.1): gains 1% of 800,000 = +8,000 units
- Private Label (E = +0.5): gains 5% of 3,000,000 = +150,000 units

Total transferred to competitors: 353,000 units
CrunchField lost: 360,000 units
Unaccounted: 7,000 units (left the category)

Note how private label captured the largest absolute gain -- not because it has the highest cross-elasticity, but because its base volume is enormous. This is why cross-elasticity alone is not enough; you must weight it by competitor volume.

Cross-elasticity estimation is one of the most data-intensive exercises in FMCG pricing. Getting it wrong leads to pricing decisions that either leave money on the table or trigger unnecessary competitive reactions.

Sources of cross-elasticity estimates, ranked by reliability:
1. Econometric analysis of scanner data (best): 2-3 years of weekly sales data across stores, controlling for promotions, seasonality, and distribution changes. Requires a skilled analytics team.
2. Controlled price experiments: Deliberately vary prices in matched test/control stores. Expensive but clean.
3. Shopper panel data: Track individual households switching between brands after price changes. Good for understanding the "who" behind the numbers.
4. Expert judgment: Category managers estimating based on experience. Surprisingly accurate for directional calls, unreliable for precise magnitudes.

Common pitfalls: failing to separate promotional effects from base price effects, using too short a time window (missing lagged responses), and ignoring distribution changes that coincide with price changes.