Cross Elasticity of Demand

Cross elasticity of demand measures the responsiveness of quantity demanded of one good to a change in the price of another good.

E_{xy} = \frac{\%\text{ change in quantity demanded of X}}{\%\text{ change in price of Y}}

The magnitude of $E_{xy}$ indicates the strength of the relationship:

Close complements
$E_{xy} \ll 0$ (large negative value). Example: printers and ink cartridges.
Weak complements
$E_{xy} < 0$ but close to zero. Example: coffee and sugar.
Close substitutes
$E_{xy} \gg 0$ (large positive value). Example: butter and margarine.
Weak substitutes
$E_{xy} > 0$ but close to zero. Example: tea and coffee.

Worked Example

Good X and good Y are substitutes. The price of Y increases from $10 to $12. Quantity demanded of X increases from 100 to 130 units.

Calculate $E_{xy}$ .

Solution Reveal Hide

Percentage change in price of Y:

\%\Delta P_Y = \frac{12 - 10}{10} \times 100 = 20\%

Percentage change in quantity demanded of X:

\%\Delta Q_X = \frac{130 - 100}{100} \times 100 = 30\%

Cross elasticity:

E_{xy} = \frac{30\%}{20\%} = 1.5

Since $E_{xy} > 0$ , X and Y are substitutes. The magnitude $1.5$ indicates they are relatively close substitutes.

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November 1, 2026 1 min read

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