1 Economic Concepts · 1.1 Microeconomics: demand, production, markets and factor pricing
1.1.2 Elasticity of demand and supply: price, income and cross elasticity and their measurement
Elasticity measures how strongly quantity responds to a change in price, income or another good's price: percentage change in quantity ÷ percentage change in the cause.
- APPSC Paper I
- Advanced level
- 8 min read
- Free
Core facts
- Concept of price elasticity of demand: Alfred Marshall.
- Price elasticity of demand: eₚ = (% change in Qd) ÷ (% change in P) = (ΔQ/ΔP) × (P/Q). Sign is negative (law of demand); exams usually quote the absolute value.
- Five degrees of price elasticity:
| Value | Name | Demand curve |
|---|---|---|
| e = 0 | Perfectly inelastic | Vertical |
| 0 < e < 1 | Relatively inelastic | Steep |
| e = 1 | Unitary elastic | Rectangular hyperbola |
| e > 1 | Relatively elastic | Flat |
| e = ∞ | Perfectly elastic | Horizontal |
- Measurement methods: (1) percentage (proportionate) method, (2) total outlay / expenditure method (Marshall), (3) point (geometric) method, (4) arc method (midpoint formula).
- Total outlay rule: price and total expenditure move in opposite directions → elastic; same direction → inelastic; unchanged → unitary.
- Point method: e = lower segment ÷ upper segment of a straight-line demand curve. Midpoint → e = 1; X-axis → e = 0; Y-axis → e = ∞.
- Income elasticity eᵧ = % ΔQ ÷ % ΔY: > 1 luxury, 0 to 1 necessity, < 0 inferior good, = 0 neutral.
- Engel's law (Ernst Engel, 1857): as income rises, the share of income spent on food falls (food has income elasticity below 1).
- Cross elasticity eₓᵧ = % ΔQx ÷ % ΔPy: positive → substitutes, negative → complements, zero → unrelated.
- Elasticity of supply eₛ = % ΔQs ÷ % ΔP (positive). Straight supply line through the origin → eₛ = 1; cutting the price axis → eₛ > 1; cutting the quantity axis → eₛ < 1.
- Determinants of eₚ: substitutes (more → elastic), nature (necessity → inelastic; luxury → elastic), share of income (small → inelastic, e.g. salt, matchbox), number of uses, time (long run → more elastic), habits, whether purchase can be postponed.
Explained
1. Percentage method.
Example 1. Price of a good rises from ₹10 to ₹11 and quantity demanded falls from 100 to 80 units. Find eₚ. Solution. % ΔQ = −20/100 = −20%; % ΔP = 1/10 = 10%. eₚ = −20 ÷ 10. Answer: −2 (elastic) Total outlay check: 10 × 100 = ₹1,000 before, 11 × 80 = ₹880 after. Price up, outlay down → elastic, as found.
2. Point elasticity of a linear demand curve.
Example 2. Q = 100 − 5P. Find eₚ at P = 10 and at P = 8. Solution. dQ/dP = −5. At P = 10, Q = 50: e = −5 × 10/50 = −1. At P = 8, Q = 60: e = −5 × 8/60 = −0.67. Geometric check: the curve meets the price axis at ₹20, so e = P/(20 − P): 10/10 = 1 and 8/12 = 0.67. Answer: 1 at ₹10 (midpoint); 0.67 at ₹8 A straight-line demand curve has the same slope everywhere but different elasticity at every point.
3. Income elasticity.
Example 3. Monthly income rises from ₹20,000 to ₹25,000; demand for milk rises from 10 to 12 litres a week. Solution. % ΔQ = 20%; % ΔY = 25%. eᵧ = 0.8. Answer: 0.8 – normal good, a necessity
4. Cross elasticity.
Example 4. The price of tea rises from ₹100 to ₹120 a packet and demand for coffee rises from 50 to 60 packets. Solution. (10/50) ÷ (20/100) = 0.2 ÷ 0.2. Answer: +1 – tea and coffee are substitutes
5. Elasticity of supply.
Example 5. Price rises from ₹20 to ₹25 and quantity supplied from 100 to 130 units. Solution. (30/100) ÷ (5/20) = 0.30 ÷ 0.25. Answer: 1.2 – relatively elastic supply
6. Uses of elasticity. A seller raises revenue by raising price only when demand is inelastic; the Government taxes inelastic goods (petrol, tobacco, salt in the past) for steady revenue; devaluation helps exports only if foreign demand is elastic; "paradox of plenty" – a bumper crop with inelastic demand lowers farmers' total revenue.
Deeper
1. Why the arc (midpoint) formula exists. The percentage method gives different answers for a rise and a fall between the same two points, because the base differs. The arc method uses averages:
e = [ΔQ ÷ (Q₁ + Q₂)/2] ÷ [ΔP ÷ (P₁ + P₂)/2]
Example 6. For Example 1 (₹10 → ₹11, 100 → 80), find the arc elasticity. Solution. ΔQ/avg Q = 20/90 = 0.222; ΔP/avg P = 1/10.5 = 0.0952. e = 0.222 ÷ 0.0952. Answer: about −2.33
Example 7. Price falls from ₹5 to ₹4 and demand rises from 100 to 120. The percentage method gives (20/100) ÷ (1/5) = 1, "unitary". Is total outlay unchanged? Solution. Outlay falls from ₹500 to ₹480, so demand is actually inelastic over this range. The arc method gives (20/110) ÷ (1/4.5) = 0.82, consistent with the outlay test. Answer: no – the arc measure (0.82) is the reliable one
2. Elasticity, revenue and MR. MR = AR × (1 − 1/e), or e = AR ÷ (AR − MR).
- e > 1 → MR positive; e = 1 → MR = 0 (total revenue maximum); e < 1 → MR negative.
- A monopolist therefore never produces on the inelastic part of the demand curve.
Example 8. Price (AR) = ₹10 and MR = ₹5. Find e. Solution. 10 ÷ (10 − 5). Answer: 2
3. Who bears a tax. With a per-unit tax t, buyers bear t × eₛ/(eₛ + e_d) and sellers bear t × e_d/(eₛ + e_d): the side with the less elastic curve bears more.
Example 9. e_d = 2, eₛ = 1, tax ₹6 per unit. Buyers' share? Solution. 6 × 1/(1 + 2). Answer: ₹2 on buyers, ₹4 on sellers
4. Other points.
- A rectangular hyperbola demand curve (P × Q constant) has e = 1 at every point.
- Two parallel linear demand curves: at the same price, the one further from the origin is less elastic.
- Two linear curves through the same point: the flatter one is more elastic there.
- Elasticity of substitution (Hicks) and price flexibility (reciprocal of eₚ, used for farm prices) are related measures.
Common traps
- ✗ "Slope and elasticity are the same thing." ✓ Elasticity = slope term × P/Q; a straight line has constant slope but changing elasticity.
- ✗ "A vertical demand curve is perfectly elastic." ✓ Vertical = perfectly inelastic (e = 0); horizontal = perfectly elastic.
- ✗ "Price up, total outlay up → elastic." ✓ Same direction = inelastic; opposite = elastic.
- ✗ "Negative cross elasticity means substitutes." ✓ Negative = complements; positive = substitutes.
- ✗ "Income elasticity below 1 means inferior good." ✓ Inferior means below 0; between 0 and 1 is a necessity.
- ✗ "A supply line through the origin has eₛ = 0." ✓ It has eₛ = 1 whatever its slope.
- ✗ "Engel's law: spending on food falls as income rises." ✓ The share (proportion) falls; the amount may still rise.
Quick revision
- eₚ = (ΔQ/ΔP) × (P/Q); concept by Marshall.
- Vertical = 0; horizontal = ∞; rectangular hyperbola = 1.
- Outlay opposite to price → elastic; same → inelastic.
- Point method: lower ÷ upper segment; midpoint = 1.
- Arc: use averages of the two points.
- eᵧ > 1 luxury, 0–1 necessity, < 0 inferior.
- Cross: + substitutes, − complements.
- Supply line via origin: eₛ = 1.
- MR = AR(1 − 1/e); MR = 0 at e = 1.
- Less elastic side bears more of a tax.
Practise this topic. Questions on Demand, consumption & elasticity, with answers explained.
All Microeconomics: demand, production, markets and factor pricing notes · APPSC Paper I syllabus · APPSC Paper I Mock 1 with answers · Start free
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