Price elasticity of demand: measurement, determinants and importance
Price elasticity of demand measures how strongly quantity demanded responds to a price change. It tells a firm whether a price rise will raise or cut revenue.
Meaning and formula
Price elasticity of demand (PED) is the percentage change in quantity demanded divided by the percentage change in price: PED = %ΔQd ÷ %ΔP. Because price and quantity move in opposite directions, PED is negative; economists usually read its absolute value. If quantity changes by a larger percentage than price, demand is elastic (|PED| > 1). If it changes by a smaller percentage, demand is inelastic (|PED| < 1). Three methods are used: the percentage method, the midpoint (arc) method for larger changes, and the point method on a demand equation.
Degrees of price elasticity
| Type | Value of |PED| | Shape of demand curve | Example |
|---|---|---|---|
| Perfectly inelastic | 0 | Vertical | A life-saving medicine, in the short run |
| Inelastic | Between 0 and 1 | Steep | Rice, salt, electricity, fuel |
| Unit elastic | 1 | Rectangular hyperbola | Total spending stays the same |
| Elastic | Greater than 1 | Flat | One brand of biscuits, restaurant meals |
| Perfectly elastic | Infinity | Horizontal | One farmer's crop in a large market |
Worked example 1: percentage method and total revenue
A tea packer raises the price of a 400 g tea packet from Rs. 400 to Rs. 440. Monthly sales fall from 1,000 packets to 850. Find the PED and the effect on total revenue.
- %ΔP = (440 − 400) ÷ 400 × 100 = 40 ÷ 400 × 100 = 10%.
- %ΔQd = (850 − 1,000) ÷ 1,000 × 100 = −150 ÷ 1,000 × 100 = −15%.
- PED = −15% ÷ 10% = −1.5, so |PED| = 1.5: demand is elastic.
- TR before = 400 × 1,000 = Rs. 400,000. TR after = 440 × 850 = Rs. 374,000.
- Change in TR = 374,000 − 400,000 = −Rs. 26,000.
PED = −1.5 (elastic). Raising the price cut revenue by Rs. 26,000 a month, as the total revenue test predicts for elastic demand.
Worked example 2: midpoint (arc) method
When the price of a bus fare card rises from Rs. 200 to Rs. 250, the number sold falls from 600 to 500 a day. Find the arc elasticity using the midpoint method.
- Midpoint quantity = (600 + 500) ÷ 2 = 550. Midpoint price = (200 + 250) ÷ 2 = 225.
- %ΔQd = (500 − 600) ÷ 550 = −100 ÷ 550 = −0.1818 (−18.18%).
- %ΔP = (250 − 200) ÷ 225 = 50 ÷ 225 = 0.2222 (22.22%).
- PED = −0.1818 ÷ 0.2222 = −(100 × 225) ÷ (550 × 50) = −22,500 ÷ 27,500 = −9/11 ≈ −0.82.
- Check with revenue: TR before = 200 × 600 = Rs. 120,000; after = 250 × 500 = Rs. 125,000. Revenue rose, which fits inelastic demand.
Arc PED ≈ −0.82 (inelastic). The midpoint method gives the same answer whether price rises or falls.
Worked example 3: point elasticity on a demand equation
Demand for coconuts is Qd = 6,000 − 20P. Find the point elasticity at P = Rs. 100, Rs. 150 and Rs. 200. Use PED = (ΔQ/ΔP) × (P/Q), where ΔQ/ΔP = −20.
- At P = 100: Q = 6,000 − 2,000 = 4,000. PED = −20 × 100 ÷ 4,000 = −2,000 ÷ 4,000 = −0.5 (inelastic).
- At P = 150: Q = 6,000 − 3,000 = 3,000. PED = −20 × 150 ÷ 3,000 = −3,000 ÷ 3,000 = −1.0 (unit elastic).
- At P = 200: Q = 6,000 − 4,000 = 2,000. PED = −20 × 200 ÷ 2,000 = −4,000 ÷ 2,000 = −2.0 (elastic).
On a straight-line demand curve, elasticity changes along the line: −0.5 at Rs. 100, −1 at the midpoint Rs. 150, and −2 at Rs. 200.
The total revenue test
| Demand is | Price rises | Price falls | Pricing lesson |
|---|---|---|---|
| Elastic (|PED| > 1) | TR falls | TR rises | Cut price to raise revenue |
| Inelastic (|PED| < 1) | TR rises | TR falls | Raise price to raise revenue |
| Unit elastic (|PED| = 1) | TR unchanged | TR unchanged | Price change does not affect revenue |
Determinants of price elasticity of demand
- Availability of close substitutes: many substitutes → elastic (one brand of soap); few → inelastic (electricity).
- Necessity or luxury: necessities such as rice are inelastic; luxuries such as foreign holidays are elastic.
- Share of income spent: a box of matches (tiny share) is inelastic; a car (large share) is elastic.
- Time period: demand is more elastic in the long run, as buyers find substitutes (e.g. solar panels after electricity tariffs rise).
- Habit and addiction: cigarettes and alcohol have inelastic demand.
- Definition of the market: 'food' is inelastic; one brand of biscuits is elastic.
Practical importance of elasticity calculations
- Pricing: a firm raises price on inelastic products and uses discounts on elastic ones.
- Taxation: governments place excise taxes on goods with inelastic demand (cigarettes, liquor, fuel) because sales, and so tax revenue, fall little.
- Price discrimination: charge more in the market with inelastic demand (business travellers, peak-hour users).
- Exports and exchange rates: if foreign demand for exports is elastic, a weaker rupee raises export earnings.
- Farm incomes: with inelastic demand, a bumper harvest lowers prices so much that farmers' total revenue can fall.
- Wage bargaining: unions can win wage rises more easily where demand for the product is inelastic.
Vegetable demand is inelastic, so a bumper harvest can make prices collapse at wholesale centres such as Dambulla, and farmers earn less in total. A tea brand with loyal buyers (inelastic demand) can pass on a cost rise; a brand with many close rivals cannot.
Structured question: “Price rises from Rs. 200 to Rs. 250 and quantity falls from 600 to 500. Calculate arc elasticity and comment.” Midpoint method: −(100/550) ÷ (50/225) = −9/11 ≈ −0.82, inelastic, so revenue rises (Rs. 120,000 → Rs. 125,000).
Essay: “Explain price elasticity of demand, its measurement, determinants and practical importance to business.” Define and give the formula, show degrees with diagrams, work one calculation, explain the total revenue test, list determinants and business uses.
Short answer: “State the total revenue test for elastic demand.” When demand is elastic, a price rise lowers total revenue and a price cut raises it.
Elastic = Easily stretched: buyers react strongly. TR test: price and revenue move together when demand is inelastic, opposite when elastic.