Which of the following is true of the cross-price elasticity of demand?

• A. A positive cross-price elasticity indicates that the two goods are substitutes.
• B. Cross-price elasticity of demand is always negative.
• C. A cross-price elasticity of zero means the goods are complements.
• D. A negative cross-price elasticity indicates that the two goods are unrelated.

Answer: (A)

Verified step by step guidance

1. Understand the definition of cross-price elasticity of demand: it measures the responsiveness of the quantity demanded of one good to a change in the price of another good. Mathematically, it is given by the formula: \[\text{Cross-price elasticity} = \frac{\% \text{ change in quantity demanded of Good A}}{\% \text{ change in price of Good B}}\]
2. Interpret the sign of the cross-price elasticity: - If the cross-price elasticity is positive, it means that an increase in the price of Good B leads to an increase in the quantity demanded of Good A, indicating that the goods are substitutes. - If the cross-price elasticity is negative, it means that an increase in the price of Good B leads to a decrease in the quantity demanded of Good A, indicating that the goods are complements.
3. Consider the case when the cross-price elasticity is zero: this implies that changes in the price of Good B have no effect on the quantity demanded of Good A, meaning the goods are unrelated or independent.
4. Evaluate the given statements based on these interpretations: - A positive cross-price elasticity indicates substitutes. - Cross-price elasticity is not always negative; it can be positive or zero depending on the relationship between goods. - A zero cross-price elasticity means goods are unrelated, not complements. - A negative cross-price elasticity indicates complements, not unrelated goods.
5. Conclude that the correct statement is the one that says a positive cross-price elasticity indicates that the two goods are substitutes.