ECOS2001 · Intermediate Microeconomics
Comparative Statics & Elasticity
Comparative statics asks how the optimal bundle moves when income or a price changes. Tracing the optimum as income rises gives the income offer curve and the Engel curve (normal goods have demand rising with income, inferior goods falling); tracing it as a price changes gives the price offer curve and the ordinary demand curve (downward-sloping, except a Giffen good). Elasticity puts numbers on responsiveness: own-price elasticity classifies demand as elastic, unit-elastic or inelastic; cross-price elasticity signs substitutes versus complements; and income elasticity signs normal, luxury and inferior goods.
What this chapter covers
- 01Income offer curve and Engel curve; normal vs inferior goods
- 02Price offer curve and the ordinary demand curve; the Giffen exception
- 03Homothetic preferences: demand scales linearly with income
- 04Own-price elasticity ε = (∂x/∂p)(p/x); elastic, unit, inelastic
- 05Cross-price elasticity: positive for substitutes, negative for complements
- 06Income elasticity η: normal > 0, luxury > 1, inferior < 0
Own-price elasticity along a linear demand
- 1 markQuantity at p = 20: x = 100 − 2·20 = 100 − 40 = 60 units.
- 1 markSlope of demand with respect to price: ∂x/∂p = −2.
- 1 markOwn-price elasticity formula: ε = (∂x/∂p)·(p/x).
- 2 marksSubstitute: ε = (−2)·(20/60) = −2·(1/3) = −0.667.
- 1 markSince |ε| = 0.667 < 1, demand is inelastic at this price — a 1% price rise cuts quantity by about 0.67%, so revenue would rise.
Key terms
- Engel curve
- The relationship between income and the quantity demanded of a good, holding prices fixed; upward-sloping for normal goods, downward for inferior goods.
- Giffen good
- A good whose demand rises when its price rises, because a strong inferior-good income effect overwhelms the substitution effect; ∂x/∂p > 0.
- Own-price elasticity (ε)
- The percentage change in quantity per percentage change in own price, ε = (∂x/∂p)(p/x); |ε| > 1 elastic, = 1 unit-elastic, < 1 inelastic.
- Cross-price elasticity
- The percentage change in one good's quantity per percentage change in another good's price; positive for substitutes, negative for complements.
Comparative Statics & Elasticity FAQ
Why does elasticity change along a straight-line demand curve?
Because elasticity is the slope times the ratio p/x, and although the slope is constant, p/x falls steadily as you move down the curve. Demand is elastic at high prices (low quantity) and inelastic at low prices (high quantity), passing through unit-elastic at the midpoint.
What is the link between elasticity and revenue?
If demand is elastic (|ε| > 1) a price rise lowers total revenue; if inelastic (|ε| < 1) a price rise raises revenue; at unit elasticity revenue is at its maximum. This makes elasticity the key to pricing decisions.
Exam move
Practise computing all three elasticities from a demand function, and remember the sign conventions (cross-price and income elasticities) classify the good. Be ready to say in one sentence what the number means for revenue or for the normal/inferior label.
