Cross-Price Elasticity of Demand (XED)

Cross-Price Elasticity of Demand (XED) measures how sensitive the quantity demanded of one good is to a change in the price of another good.

It is used to determine whether two goods are Substitutes or complements.

X E D = \frac{% change in quantity of Product B}{% change in price of Product A}

XED is directional – generally not symmetric.

{XED}_{B, A} = \frac{% Δ Q_{B}}{% Δ P_{A}} vs. {XED}_{A, B} = \frac{% Δ Q_{A}}{% Δ P_{B}}

These two values are not equal in most real-world cases.

Market power, brand loyalty, search costs, habit formation, adjustment costs
Only under very restrictive conditions (e.g., homogeneous goods with symmetric consumer preferences) would they be equal.

Scenario	Calculation	Result
Price of tea ↑ 20% → Quantity of coffee ↑ 10%	$$ \text{XED}_{\text{Coffee, Tea}} = \frac{10%}{20%} = 0.5 $$	Substitutes
Price of coffee ↑ 20% → Quantity of tea ↑ 30%	$$ \text{XED}_{\text{Tea, Coffee}} = \frac{30%}{20%} = 1.5 $$	Substitutes

→ Both positive (substitutes), but 0.5 ≠ 1.5.

Always specify the direction:

Do not assume $$ \text{XED}{B,A} = \text{XED} $$.