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.