Bologna prices and cheese purchases

Cross-price elasticity of demand measures how the quantity demanded of one good responds to a price change in another. Divide the percentage change in quantity demanded of cheese by the percentage change in the price of bologna.

The price of bologna rose 2 percent and the quantity of cheese demanded fell 5 percent, so the elasticity is -5% / +2% = -2.5.

The sign tells you the relationship. A negative value means a price rise in one good lowers demand for the other, so the two are used together: complements, as in a bologna and cheese sandwich. A positive value would mean substitutes. The size, 2.5, says cheese purchases moved two and a half times as much, in percentage terms, as the bologna price did.

Each choice

• A. The relationship is right but the fraction is upside down: 2 / 5 = 0.4. The response in quantity always goes on top and the triggering price change on the bottom.
• B. Both the division and the sign are off. The fraction is flipped, and a drop in cheese purchases after bologna gets pricier points to complements, not substitutes.
• C (correct). A negative cross-price elasticity signals complements, and the quantity change always goes on top of the fraction.
• D. The size is right but the sign was dropped. The quantity of cheese fell, so the numerator is negative, and that negative sign is the evidence the goods are complements.
• E. This has the fraction flipped and also pairs a negative value with substitutes. Substitutes have a positive cross-price elasticity, so these two parts contradict each other.