Cross Elasticity measures

Question

BlackTom AI · Accepted Answer

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

1. Relevant knowledge points and concepts
- Definition: Cross-price elasticity of demand (Exy) = (% change in quantity demanded of good X) / (% change in price of good Y).
- Interpretation: Exy > 0 implies substitutes (increase in Py raises Qx); Exy < 0 implies complements (increase in Py lowers Qx); Exy = 0 implies independent goods.
- Distinction from own-price elasticity: Own-price elasticity relates Qx to changes in Px (same good), not to Py (different good).

2. Step-by-step reasoning
- Identify the variables: quantity of product X (Qx) and price of a different product Y (Py).
- Compute percent changes using the standard formula: %Δ = (new − old) / old × 100.
- Divide the percent change in Qx by the percent change in Py to get Exy.
- Use the sign and magnitude of Exy to infer relationship (substitute/ complement/ independent).

3. Example calculation (all intermediate steps)
- Suppose Qx rises from 100 units to 120 units when Py rises from $10.00 to $11.00.
- %ΔQx = (120 − 100) / 100 × 100 = 20%.
- %ΔPy = ($11 − $10) / $10 × 100 = 10%.
- Exy = %ΔQx / %ΔPy = 20% / 10% = 2.0 → positive, so X and Y are substitutes.

4. Why the correct answer is correct
- The correct choice matches the formal definition of cross-price elasticity: sensitivity of purchases (quantity demanded) of one product to price changes of another product.

5. Why the other options are incorrect
- Options referring to changes in quality are about quality effects, not cross-price relationships; cross elasticity deals with prices, not quality.
- The option about “preferences” is imprecise: economics measures changes in quantity demanded, not raw preferences; preferences are underlying but not the measured statistic.
- The option about sensitivity to changes in “the price of the product” describes own-price elasticity, not cross-price elasticity.

Conclusion: The correct answer is “how sensitive people's purchases of one product are in response to changes in the price of a different product,” which matches the provided answer.

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