Questions: Substitutes and Complements: Cross-Price Elasticity

Question 1

The price of gasoline rises 20%, and you observe that sales of large SUVs fall substantially. What does this tell you about the cross-price elasticity of SUVs with respect to gasoline?

• A. It is positive — gasoline and SUVs are substitutes
• B. It is negative — gasoline and SUVs are complements
• C. It is zero — the relationship is coincidental, not causal
• D. It is positive — higher gasoline prices increase demand for any vehicle

Answer: (B)

When the price of gasoline rises, demand for SUVs falls. Cross-price elasticity ε_XY = (% ΔQ_SUV) / (% ΔP_gas) is negative here (price up, quantity down). A negative cross-price elasticity means the goods are complements — they are used together, so a price increase in one reduces demand for both. This makes intuitive sense: owning and driving an SUV requires gasoline, so when gas gets more expensive, SUVs become more expensive to operate and demand for them falls.

Question 2

If the cross-price elasticity of demand for tea with respect to the price of coffee is +1.8, what would you predict when the price of coffee rises significantly?

• A. Demand for tea will fall, since coffee and tea are used together
• B. Demand for tea will rise, since consumers shift away from expensive coffee toward tea
• C. Demand for tea is unaffected — tea drinkers and coffee drinkers are entirely separate consumer groups
• D. Demand for tea will fall slightly, as tea and coffee are weak substitutes

Answer: (B)

A positive cross-price elasticity (+1.8) means coffee and tea are substitutes. When coffee's price rises, consumers shift toward tea — the quantity demanded of tea increases. The magnitude (+1.8) indicates close substitutability: consumers are fairly responsive to price differences between the two goods, and a significant price increase in coffee would produce a substantial increase in tea demand.

Question 3

If the cross-price elasticity of demand between two goods is negative, it means they are substitutes.

• T. True
• F. False

Answer: False

This reverses the rule. A POSITIVE cross-price elasticity means substitutes: when the price of Y rises, demand for X rises (consumers switch to X). A NEGATIVE cross-price elasticity means complements: when the price of Y rises, demand for X falls (because Y and X are used together, less Y means less X). Remember: positive = substitutes (they go in opposite directions — one up, consumers switch to the other); negative = complements (they move together — one more expensive, both demanded less).

Question 4

A cross-price elasticity of +0.1 indicates weaker substitutability than a cross-price elasticity of +1.5 — meaning consumers would switch less readily between the goods when one's price changes.

• T. True
• F. False

Answer: True

The magnitude of cross-price elasticity measures the intensity of the relationship. A value of +0.1 means a 10% price increase in good Y causes only a 1% increase in demand for X — consumers barely respond by switching. A value of +1.5 means the same 10% price increase causes a 15% increase in demand for X — consumers switch readily. Both are positive (substitutes), but +1.5 describes much closer substitutes. Airlines, for example, track high cross-price elasticities between competing routes because even small price differences cause large passenger shifts.

Question 5

A grocery store discounts chips by 30% and notices that salsa sales increase significantly. What does this reveal about the cross-price elasticity between chips and salsa, and what does it imply about the relationship between these goods?

Model answer: When the price of chips falls, demand for salsa rises — this means the cross-price elasticity of salsa with respect to chip prices is negative (price of chips down → quantity of salsa up). A negative cross-price elasticity means the goods are complements: they are consumed together, so making one cheaper increases demand for both. The observation implies that chips and salsa are strong enough complements that chip promotions reliably drive salsa revenue. Grocery chains exploit this by discounting one good in a complementary pair to boost total basket value.

This connects the quantitative concept to real pricing strategy. The same logic explains why printers are sold cheaply (or at a loss) while ink cartridges are priced high — the negative cross-price elasticity between printers and ink means the two must be considered jointly. Understanding complementarity allows firms to optimize across product lines rather than pricing each item in isolation.