Questions: Income and Cross-Price Elasticity

Question 1

As incomes rise in a city, ridership on public buses falls significantly. What does this tell us about bus rides?

• A. Bus rides are a luxury good — demand grows faster than income
• B. Bus rides are an inferior good — demand falls as income rises
• C. Bus rides are a complement to cars — their prices are linked
• D. The income elasticity of bus rides is between 0 and 1

Answer: (B)

An inferior good is one with a negative income elasticity of demand (E_I < 0): as income rises, consumers substitute away from it toward preferred alternatives. Bus rides often fit this pattern in cities — as people earn more, they shift to cars, rideshares, or other modes. 'Inferior' is a technical term describing the income-demand relationship, not a quality judgment. Many inferior goods (generic staples, inexpensive fast food) are perfectly serviceable — they're inferior only in the economic sense.

Question 2

The cross-price elasticity of demand for butter with respect to the price of margarine is +0.8. This tells you that butter and margarine are:

• A. Complements — they are often consumed together and the elasticity is positive
• B. Substitutes — when margarine gets more expensive, consumers switch to butter
• C. Unrelated goods — a cross-price elasticity below 1.0 indicates no relationship
• D. Normal goods — the positive sign confirms both are normal goods

Answer: (B)

A positive cross-price elasticity means the goods are substitutes: when the price of margarine rises, quantity demanded of butter increases as consumers switch. A negative cross-price elasticity would indicate complements — goods consumed together, so that a price rise in one reduces demand for both. The magnitude (0.8) tells you how close the substitutes are; the sign tells you the relationship. The positive/negative sign is the key diagnostic, not the magnitude relative to 1.

Question 3

An inferior good is defined as a good of low quality or low social status that consumers prefer less.

• T. True
• F. False

Answer: False

This is the most common misconception about inferior goods. 'Inferior' in economics refers strictly to the income-demand relationship: a good is inferior if its income elasticity is negative — that is, if demand for it falls as consumer income rises. The good need not be low quality. Bus rides, instant noodles, and generic store brands may be perfectly fine products; they are 'inferior' only because higher-income consumers tend to substitute away from them. A Giffen good — theoretically possible but rare — is even more extreme: demand rises as its own price rises.

Question 4

A positive cross-price elasticity between goods X and Y means that when the price of Y rises, quantity demanded of X increases.

• T. True
• F. False

Answer: True

This is the definition of substitutes via cross-price elasticity. E_XY = (%ΔQ_X) / (%ΔP_Y) > 0 means these variables move in the same direction: when P_Y rises, Q_X rises. Consumers facing a pricier Y switch to X as an alternative. The reverse relationship also holds: if the price of X rises, demand for Y increases. Complements have negative cross-price elasticity — when P_Y rises, consumers buy less of Y and therefore also less of X.

Question 5

Why does the sign of income elasticity matter more than the magnitude when classifying a good, and give an example of an inferior good that is not obviously 'cheap' or low-quality?

Model answer: The sign determines the category: positive = normal good, negative = inferior good. Magnitude then subdivides within categories (E_I > 1 = luxury; 0 < E_I < 1 = necessity). An example of a surprising inferior good: margarine itself in some contexts (as incomes rise, consumers switch to butter); public transit in car-owning societies; or rice as a staple in rapidly developing countries where wealthier households shift to more diverse diets.

Sign first, magnitude second is the right classification order because the sign is a categorical fact about consumer preferences — it tells you which direction demand moves with income. Once you know the good is normal (E_I > 0), the magnitude separates luxuries from necessities. For inferior goods, magnitude tells you how steeply demand falls with income. The surprising examples (public transit, generic staples) reinforce that inferiority is about behavior, not quality.