The price of coffee rises by 20% and, as a result, demand for tea increases by 10%. What is the cross-price elasticity of demand for tea with respect to coffee price, and what does the sign tell you?
A+0.5; coffee and tea are substitutes — people switch to tea when coffee becomes more expensive
B−0.5; coffee and tea are complements — rising coffee prices reduce tea demand
C+0.5; coffee and tea are complements — the positive sign indicates they go together
D+2.0; coffee and tea are independent goods with no systematic relationship
Cross-price elasticity = (% change in quantity demanded of tea) / (% change in price of coffee) = 10% / 20% = +0.5. The positive sign indicates substitutes: when coffee gets more expensive, consumers switch to tea, raising tea demand. Complements have negative cross-price elasticity (rising price of one reduces demand for the other). The most common error is reversing the sign interpretation — positive always means substitutes.
Question 2 Multiple Choice
Gasoline prices rise sharply. A car manufacturer observes a significant drop in demand for large SUVs. What does the cross-price elasticity of demand between gasoline and SUVs reveal about their relationship?
AThey are substitutes — consumers switch from SUVs to gasoline when gas is cheaper
BThey are complements — rising gasoline prices reduce the value of SUV ownership, lowering demand for SUVs
CThey are independent goods — gasoline price changes should not systematically affect SUV demand
DThey are perfect substitutes — consumers can directly replace one with the other
The negative cross-price elasticity (higher gasoline price → lower SUV demand) signals complements. Gasoline and SUVs are consumed together — you need gas to run an SUV. When gasoline becomes more expensive, owning and operating a large SUV becomes costlier overall, reducing demand for them. This is the classic complement relationship: goods that are used jointly such that rising cost of one reduces demand for the other.
Question 3 True / False
A cross-price elasticity of −1.5 between printer ink cartridges and printers indicates that when printer prices rise, demand for ink cartridges falls — confirming that printers and ink are complements.
TTrue
FFalse
Answer: True
The negative sign is the signature of complements: when the price of one good rises, demand for the other falls. Printers and ink cartridges are consumed jointly — fewer printer purchases means fewer cartridges needed. The magnitude of −1.5 indicates a fairly strong complementary relationship: a 10% rise in printer prices leads to a 15% drop in ink cartridge demand.
Question 4 True / False
If the cross-price elasticity of demand between two goods is positive, the goods are complements — a price increase in one raises demand for the other.
TTrue
FFalse
Answer: False
This reverses the sign interpretation. A positive cross-price elasticity indicates substitutes: when the price of good B rises, consumers switch to good A, raising demand for A. Complements have negative cross-price elasticity: rising price of B reduces demand for A because they are consumed jointly. Confusing the signs is the most common error in applying cross-price elasticity.
Question 5 Short Answer
Explain why cross-price elasticity is strategically important for a business. Give an example of how the sign and magnitude would inform a pricing decision.
Think about your answer, then reveal below.
Model answer: Cross-price elasticity quantifies how a firm's demand responds to competitors' or complements' price changes. A positive cross-elasticity with a rival's product reveals a competitive threat: if the rival raises prices, customers will switch to the firm. The magnitude tells the firm how aggressively to respond — high positive elasticity means many customers are ready to switch, so the firm might hold prices to capture the inflow. A negative cross-elasticity with a complementary product signals that the firm's fortunes are tied to that product's price — e.g., a printer manufacturer should worry when ink prices rise.
The power of cross-price elasticity is turning intuitive guesses ('are these related?') into measurable, actionable numbers. A coffee shop facing rising tea prices (positive cross-elasticity with coffee) might hold its own prices stable to attract switching customers. A car manufacturer facing rising gasoline prices (negative cross-elasticity with SUVs) might pivot marketing toward fuel-efficient vehicles. Without the number, these are hunches; with it, they are data-driven decisions.