How do economists measure the responsiveness of demand to income and to the prices of other goods?
Topic 2.5 Other Elasticities: calculate and interpret the income elasticity of demand (normal versus inferior goods) and the cross-price elasticity of demand (substitutes versus complements).
A focused answer to AP Microeconomics Topic 2.5, covering income elasticity of demand and the normal-versus-inferior distinction, cross-price elasticity of demand and the substitute-versus-complement distinction, and how the sign and size of each elasticity are interpreted, with worked exam-style questions.
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What this topic is asking
Topic 2.5 extends elasticity beyond a good's own price to two further measures: how demand responds to income and to the prices of other goods. The College Board wants you to calculate and interpret the income elasticity of demand (which tells you whether a good is normal or inferior) and the cross-price elasticity of demand (which tells you whether two goods are substitutes or complements). The sign of each elasticity carries the meaning, so unlike own-price elasticity you keep the sign.
Income elasticity of demand
The sign tells you the type of good:
- Positive income elasticity, a normal good: demand rises as income rises. If the value is greater than 1, the good is a luxury (income-elastic, demand grows faster than income); if between 0 and 1, it is a necessity (income-inelastic).
- Negative income elasticity, an inferior good: demand falls as income rises, because consumers switch to better alternatives (for example, away from generic noodles toward restaurant meals).
This connects to the demand topic: an income change shifts the demand curve, and its income elasticity tells you the direction (right for normal, left for inferior) and the strength of the shift.
Cross-price elasticity of demand
The sign tells you the relationship:
- Positive cross-price elasticity, substitutes: a higher price of B raises demand for A, because buyers switch from B to A (tea and coffee, butter and margarine).
- Negative cross-price elasticity, complements: a higher price of B lowers demand for A, because the goods are consumed together (cars and petrol, printers and ink).
- Near zero: the goods are unrelated.
The larger the absolute value, the stronger the relationship: a cross-price elasticity of 2 means very close substitutes, while 0.1 means weak ones.
Try this
Q1. A good has an income elasticity of demand of . State whether it is normal or inferior. [1 point]
- Cue. The negative sign means demand falls as income rises, so it is an inferior good.
Q2. The cross-price elasticity between two goods is . State the relationship between them. [1 point]
- Cue. A positive value means they are substitutes, and the large size means they are close substitutes.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2018 (style)1 marksMultiple choice. A good with a negative income elasticity of demand is (A) a normal good. (B) an inferior good. (C) a luxury. (D) a complement. (E) a Giffen good only.Show worked answer →
The answer is (B). A negative income elasticity means that as income rises, demand for the good falls, the defining feature of an inferior good (consumers switch away as they get richer).
(A) and (C) have positive income elasticity. (D) describes a cross-price relationship, not an income one. (E) is not what the sign alone identifies; a negative income elasticity simply marks an inferior good.
AP 2021 (style)4 marksFree response. When the price of tea rises by 10 percent, the quantity of coffee demanded rises by 6 percent; separately, when consumer income rises by 5 percent, the quantity of bus rides demanded falls by 2 percent. (a) Calculate the cross-price elasticity between tea and coffee. (b) State whether tea and coffee are substitutes or complements and why. (c) Calculate the income elasticity of demand for bus rides. (d) State whether bus rides are a normal or inferior good and why.Show worked answer →
A four-point elasticities FRQ.
(a) (1 point): cross-price elasticity = percent change in quantity of coffee / percent change in price of tea = 6 / 10 = 0.6 (positive).
(b) (1 point): a positive cross-price elasticity means tea and coffee are substitutes, because a higher price of tea raises demand for coffee.
(c) (1 point): income elasticity = percent change in quantity / percent change in income = -2 / 5 = -0.4 (negative).
(d) (1 point): a negative income elasticity means bus rides are an inferior good, because demand falls as income rises.
Related dot points
- Topic 2.1 Demand: state the law of demand, distinguish a change in quantity demanded from a change in demand, and identify the determinants that shift the demand curve.
A focused answer to AP Microeconomics Topic 2.1, covering the law of demand, the difference between a movement along and a shift of the demand curve, the determinants of demand, and the income and substitution effects, with worked exam-style questions.
- Topic 2.3 Price Elasticity of Demand: calculate price elasticity of demand using the midpoint formula, classify demand as elastic, inelastic, or unit elastic, apply the total revenue test, and identify the determinants of elasticity.
A focused answer to AP Microeconomics Topic 2.3, covering the price elasticity of demand, the midpoint formula, elastic versus inelastic versus unit elastic demand, the total revenue test, perfectly elastic and inelastic cases, and the determinants of elasticity, with worked exam-style questions.
- Topic 2.4 Price Elasticity of Supply: calculate price elasticity of supply using the midpoint formula, classify supply as elastic, inelastic, or unit elastic, and explain why time is the key determinant.
A focused answer to AP Microeconomics Topic 2.4, covering the price elasticity of supply, the midpoint formula, elastic versus inelastic versus unit elastic supply, the perfectly elastic and inelastic extremes, and why time is the chief determinant, with worked exam-style questions.
- Topic 2.6 Market Equilibrium and Consumer and Producer Surplus: find equilibrium price and quantity, identify consumer and producer surplus on a graph, and explain why the competitive equilibrium maximizes total surplus (allocative efficiency).
A focused answer to AP Microeconomics Topic 2.6, covering how supply and demand determine equilibrium price and quantity, the measurement of consumer and producer surplus, total surplus, and why the competitive equilibrium is allocatively efficient, with worked exam-style questions.
- Topic 1.6 Marginal Analysis and Consumer Choice: explain diminishing marginal utility, and use the utility-maximizing rule (equal marginal utility per dollar) to find the consumption bundle that maximizes total utility given a budget.
A focused answer to AP Microeconomics Topic 1.6, covering total and marginal utility, the law of diminishing marginal utility, and the utility-maximizing rule that equalises marginal utility per dollar across goods, with worked exam-style questions.
Sources & how we know this
- AP Microeconomics Course and Exam Description — College Board (2023)