Applying XED — Substitutes and Complements

Idea

Cross elasticity of demand measures how the demand for one good responds to a change in the price of another, capturing the relationship between related goods. Its sign identifies the relationship; its magnitude measures how close that relationship is.

Mechanism

With

$CED = \frac{\%\,\text{change in quantity demanded of Good X}}{\%\,\text{change in price of Good Y}}$

• Substitutes (CED > 0). The goods satisfy similar wants, so a rise in the price of Good Y raises demand for Good X — they move in the same direction. If a 5% rise in the price of hardcopy books raises e-book demand by 10%, the CED of e-books with respect to hardcopy books is $+10\%/+5\% = +2$.

• Complements (CED < 0). The goods are used jointly, so a rise in the price of Good Y lowers demand for Good X — they move in opposite directions. If a 20% rise in the price of cars lowers petrol demand by 5%, the CED of petrol with respect to cars is $-5\%/+20\% = -0.25$.

The magnitude reflects closeness: a closer substitute or complement produces a larger $|CED|$. E-books are a closer substitute for hardcopy books than audiobooks, so a rise in hardcopy prices raises e-book demand more than audiobook demand, and the e-book CED is larger.

Considerations

CED must be kept apart from derived demand, which links goods in an input–output relationship (flour and bread) rather than two final goods. For evaluation, CED tells a firm how exposed it is to rivals’ pricing (high positive CED with a substitute) and to shocks in the price of a complement (negative CED), and tells a government which markets a price intervention will spill over into.