If a decrease in the price of good X results in a decrease in the quantity of Y demanded,

Question

BlackTom AI · Accepted Answer

Cross-price elasticity of demand (Exy) is defined as the percentage change in quantity demanded of good Y divided by the percentage change in the price of good X: Exy = (%ΔQy) / (%ΔPx). The sign of Exy indicates the relationship between goods: Exy < 0 implies complements (when the price of X falls, demand for Y rises); Exy > 0 implies substitutes (when the price of X falls, demand for Y falls). Step-by-step reasoning: 1. Identify the direction of changes. The question states a decrease in the price of X and an influence on quantity demanded of Y. For cross-price elasticity to be negative, the percentage change in Qy must be opposite in sign to the percentage change in Px. 2. Apply the definition. Let ΔPx < 0 (price of X falls). If the resulting ΔQy > 0 (quantity demanded of Y increases), then Exy = (%ΔQy)/( %ΔPx) = (positive)/(negative) = negative. 3. Interpret the sign. A negative Exy means the two goods are complements: consumers buy more of Y when X becomes cheaper because the goods are used together. Why the correct answer is correct: - A negative cross elasticity indicates that a fall in the price of X raises demand for Y; economically, this is the hallmark of complementary goods. Thus, Exy < 0 correctly describes a complementary relationship. Why the other options are incorrect: - "There is not sufficient information..." is wrong because the direction of change in price and quantity is sufficient to determine the sign of Exy. - "Good X and good Y are substitutes" is incorrect: substitutes produce a positive cross elasticity (a fall in X’s price reduces demand for Y). - "Good X and good Y are complements" describes the economic relationship implied by a negative cross elasticity, but the answer format requested the sign statement, so the more precise statement given (that Exy is negative) directly characterizes the relationship. Conclusion: The cross-price elasticity of demand for good Y is negative, which confirms the provided answer.

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