Price elasticity of demand

Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price.

$\text{PED} = \dfrac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$

Three steps to calculate:

1. Calculate % change in quantity demanded = $(Q_{new} - Q_{old})/Q_{old} \times 100$.
2. Calculate % change in price = $(P_{new} - P_{old})/P_{old} \times 100$.
3. Divide: PED = step 1 / step 2.

Worked example. Price rises from $10 to$12. Quantity demanded falls from 100 to 90.

• %ΔQ = (90 - 100)/100 × 100 = -10%.
• %ΔP = (12 - 10)/10 × 100 = +20%.
• PED = -10 / +20 = -0.5.

The negative sign. PED is almost always negative because price and quantity move in opposite directions (law of demand). Mark schemes typically accept the absolute value |PED| for categorisation, but show the negative in your calculation and switch to |PED| when classifying.

A common shortcut. If you only need to know the category (elastic vs inelastic), you can compare the percentages without dividing:

• |%ΔQ| > |%ΔP| → ELASTIC.
• |%ΔQ| < |%ΔP| → INELASTIC.
• |%ΔQ| = |%ΔP| → UNIT ELASTIC.

Cambridge tip. Mark schemes for PED calculation questions reward 1 mark per percentage change + 1 for the formula + 1 for the answer. Show all four steps. Final-answer-only loses three of the four marks.

1. Perfectly inelastic — |PED| = 0.

• Quantity demanded does not change when price changes.
• Vertical demand curve.
• Rare. e.g., life-saving medicine for which no substitute exists. Insulin for a diabetic.

2. Inelastic — 0 < |PED| < 1.

• Quantity demanded changes by a SMALLER % than price.
• Steep demand curve.
• Examples: petrol (in the short run), salt, basic food.
• Consumers don't respond strongly to price.

3. Unit elastic — |PED| = 1.

• Quantity demanded changes by the SAME % as price.
• Total revenue stays constant.
• Often a reference point in theory; rare exactly in practice.

4. Elastic — |PED| > 1.

• Quantity demanded changes by a LARGER % than price.
• Flat demand curve.
• Examples: branded goods with substitutes (Coca-Cola), luxury goods, holidays.
• Consumers respond strongly to price.

5. Perfectly elastic — |PED| = ∞.

• Any price increase causes quantity to fall to zero.
• Horizontal demand curve.
• Theoretical extreme — rare in real markets.

The categorical rule of thumb.

| |PED| | Category | Curve | Example | |---|---|---|---|---| | 0 | Perfectly inelastic | Vertical | Life-saving medicine | | 0-1 | Inelastic | Steep | Petrol, salt | | 1 | Unit elastic | (Constant revenue) | Reference point | | >1 | Elastic | Flat | Luxury goods | | ∞ | Perfectly elastic | Horizontal | Theoretical |

Cambridge tip. Mark schemes test category-VALUE pairs. Make sure you can match each category to its numerical range and to a typical example.

1. Availability of substitutes.

More substitutes → more ELASTIC (consumers can switch). Few substitutes → INELASTIC.

Examples.

• Coca-Cola (many substitutes: Pepsi, generic colas, water) → elastic.
• Petrol for car drivers (few substitutes in the short run) → inelastic.

2. Necessity vs luxury.

Necessity → INELASTIC (must buy regardless of price). Luxury → ELASTIC (can be foregone).

Examples.

• Insulin for a diabetic (necessity) → very inelastic.
• A luxury holiday → elastic.

3. Proportion of income spent on the good.

Small share of income → INELASTIC (consumer barely notices). Large share of income → ELASTIC.

Examples.

• Salt (cents per kg, tiny share) → inelastic.
• A car (large share of income) → elastic.

4. Time period.

Short term → INELASTIC (no time to adjust). Long term → ELASTIC (consumers find substitutes, change habits).

Example: petrol.

• Short-run PED ≈ -0.2 (inelastic). Drivers can't change cars overnight.
• Long-run PED ≈ -0.7 (more elastic). Eventually drivers buy more efficient cars or switch to public transport.

Cambridge tip. 8-mark "explain determinants of PED" questions appear most series. Memorise these four factors and have an example ready for each.

Total revenue (TR) = Price × Quantity.

When price changes, BOTH P and Q change — but the SIZE of each change determines whether revenue rises or falls. PED tells you which dominates.

Inelastic demand (|PED| < 1).

Quantity changes by a SMALLER % than price. So:

• Price rise → quantity falls a little → REVENUE RISES (price effect dominates).
• Price fall → quantity rises a little → REVENUE FALLS.

Elastic demand (|PED| > 1).

Quantity changes by a LARGER % than price. So:

• Price rise → quantity falls a lot → REVENUE FALLS (quantity effect dominates).
• Price fall → quantity rises a lot → REVENUE RISES.

Unit elastic (|PED| = 1).

Both changes are equal in % terms. Revenue stays constant.

Worked example. A bus company is considering a 10% fare increase. PED = -0.4 (inelastic).

• Quantity falls by 0.4 × 10% = 4%.
• Net effect: roughly +6% on revenue (price up 10%, quantity down 4%).
• Revenue RISES.

The decision rule for firms. Firms with INELASTIC demand can raise prices to raise revenue. Firms with ELASTIC demand should LOWER prices to raise revenue.

Worked example: government tax. Indirect taxes are most often imposed on goods with INELASTIC demand (cigarettes, fuel) — because consumers can't easily reduce consumption, the government raises revenue without much fall in tax-base quantity.

Cambridge tip. Mark schemes for PED-revenue questions ALWAYS test both directions (inelastic and elastic). Make sure you can apply the rule both ways.