Income and Cross-price Elasticity
Income elasticity of demand divides percentage quantity change by percentage income change. A positive value indicates a normal good, a negative value an inferior good, and a value above one often a luxury.
Cross-price elasticity of demand divides the percentage change in demand for A by the percentage price change of B. Positive values suggest substitutes, negative values complements, and near-zero values a weak relationship.
Read signs and magnitudes
If income rises 10% and restaurant demand rises 15%, income elasticity is 1.5: a strongly income-responsive normal good. If bus trips fall 4%, income elasticity is −0.4: inferior for this sample, without any quality judgment.
| Income elasticity | Classification |
|---|---|
| below 0 | inferior |
| 0 to 1 | necessity-like normal good |
| above 1 | luxury-like normal good |
If tea price rises 5% and coffee demand rises 3%, cross-price elasticity is +0.6, suggesting substitutes. Printer prices rising and ink demand falling produces a negative value, suggesting complements. Relationships depend on population, use, and time; simultaneous shocks must be controlled before interpreting causally.
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Classifications depend on population, period, and market definition. One food may be normal for low-income households but barely respond at high income. Correlation also does not establish causation; estimates should control for simultaneous taste, season, and income changes.
KNOWLEDGE QUIZ
Three market research files
A research team reports three controlled comparisons. Use the reported percentages directly and keep signs. The first two concern another good's price; the third concerns income.
Tea price +5%, coffee quantity +3%; printer price +10%, ink quantity −8%; income +10%, bus trips −4%.
- Identify numerator and denominator and calculate each elasticity.
- Classify the relationships and explain the sign economically.
- Using constant local responses, predict coffee demand after tea price rises 2%. State why an uncontrolled survey could mislead.