CFA Level IEconomicsMedium
When the price of Good X increases by 5%, the quantity demanded of Good Y increases by 15%. What is the cross-price elasticity of demand, and what does it imply about the relationship between X and Y?
- A+3.0; X and Y are substitutes
- B-3.0; X and Y are complements
- C-0.33; X and Y are substitutes
- D+0.33; X and Y are complements
Show answer & explanationAnswer & explanation
Correct answer: A. +3.0; X and Y are substitutes
Cross-price elasticity = %ΔQ_Y / %ΔP_X = 15%/5% = 3.0. A positive cross-price elasticity indicates the goods are substitutes, since a price increase in X raises demand for Y.
Why the other options are wrong
- B. Sign is wrong; the elasticity here is positive, not negative.
- C. Sign and classification are both incorrect.
- D. Magnitude is inverted and complements require a negative sign.
Cross-Price Elasticity of Demand
Measures the responsiveness of quantity demanded of one good to a price change in another good.
- Positive value = substitutes
- Negative value = complements
- Zero value = unrelated (independent) goods
Memory trick: Positive sign = Partners in substitution; Negative sign = Necessary complement.