Definition of PED

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The Allocation of Resources – Price Elasticity of Demand (PED)

Learning Objective

By the end of this lesson students will be able to:

  • Define price elasticity of demand (PED) and write the correct formula(s).
  • Calculate PED using the mid‑point (arc) method for both price rises and price falls.
  • Interpret the size of a PED value (elastic, unit‑elastic, inelastic, perfectly elastic, perfectly inelastic) and recall the numeric thresholds.
  • Identify the main determinants of PED.
  • Explain how PED affects total revenue, consumer expenditure and the decisions of households, firms, workers and government.
  • Read and label a demand‑curve diagram that shows the three elasticity zones.

1. Definition and Formulae

Price Elasticity of Demand (PED) measures the responsiveness of the quantity demanded of a good or service to a change in its price.

Two formulae are used in the Cambridge IGCSE/ A‑Level exams:

  • Standard (percentage‑change) formula \[ \text{PED}= \frac{\%\Delta Q_d}{\%\Delta P} \] where \(\%\Delta Q_d\) is the percentage change in quantity demanded and \(\%\Delta P\) is the percentage change in price.
  • Mid‑point (arc) formula – the method recommended for exam calculations because it gives the same result whether price rises or falls. \[ \text{PED}= \frac{\displaystyle\frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}}{\displaystyle\frac{P_2-P_1}{\frac{P_1+P_2}{2}}} \] \(P_1,Q_1\) are the initial price and quantity; \(P_2,Q_2\) are the new price and quantity.

Since the law of demand implies a negative relationship, the sign is usually omitted and the absolute value \(|\text{PED}|\) is reported.

2. Worked Examples

Example 1 – Price Rise

Price rises from £10 to £11 (a 10 % increase). Quantity demanded falls from 200 to 160 units (a 20 % decrease).

  1. Calculate the percentage changes using the mid‑point formula: \[ \%\Delta P = \frac{11-10}{\frac{10+11}{2}}\times100 = \frac{1}{10.5}\times100 \approx 9.52\% \] \[ \%\Delta Q_d = \frac{160-200}{\frac{200+160}{2}}\times100 = \frac{-40}{180}\times100 \approx -22.22\% \]
  2. Apply the PED formula: \[ \text{PED}= \frac{-22.22\%}{9.52\%}= -2.33 \]
  3. Take the absolute value (exam convention): \[ |\text{PED}| = 2.33 \; (>1) \] Hence demand is elastic.

Example 2 – Price Fall

Price falls from £8 to £6 (a 25 % decrease). Quantity demanded rises from 120 to 150 units (a 25 % increase).

  1. Mid‑point percentage changes: \[ \%\Delta P = \frac{6-8}{\frac{8+6}{2}}\times100 = \frac{-2}{7}\times100 \approx -28.57\% \] \[ \%\Delta Q_d = \frac{150-120}{\frac{120+150}{2}}\times100 = \frac{30}{135}\times100 \approx 22.22\% \]
  2. Apply the PED formula: \[ \text{PED}= \frac{22.22\%}{-28.57\%}= -0.78 \]
  3. Absolute value: \[ |\text{PED}| = 0.78 \; (<1) \] Hence demand is inelastic.

3. Interpreting PED Values

\(|\text{PED}|\) (absolute value) Elasticity Type Interpretation
0 < |\text{PED}| < 1 Inelastic Quantity demanded changes less than proportionally to price.
|\text{PED}| = 1 Unit‑elastic Quantity demanded changes exactly proportionally to price.
|\text{PED}| > 1 Elastic Quantity demanded changes more than proportionally to price.
|\text{PED}| = 0 Perfectly inelastic Quantity demanded does not respond to price changes (vertical demand curve).
|\text{PED}| = ∞ Perfectly elastic Any price increase drives quantity demanded to zero (horizontal demand curve).

Remember the numeric rule: elastic if > 1, unit‑elastic if = 1, inelastic if < 1.

4. Determinants of PED

Four (sometimes five) key factors explain why some goods have a higher or lower PED:

  • Availability of close substitutes – the more substitutes, the higher the PED.
  • Proportion of income spent on the good – goods that take up a large share of a consumer’s budget tend to have a higher PED.
  • Nature of the good – luxuries have a higher PED than necessities.
  • Time horizon – demand is usually more elastic in the long run because consumers have more time to adjust.
  • Brand loyalty / habit formation (optional for A‑Level) – strong loyalty reduces PED.

5. PED and Total Revenue (TR)

Total revenue is calculated as TR = P × Q. The relationship between PED and the direction of TR when price changes is shown below:

PED Category Effect of a Price Rise Effect of a Price Fall
Elastic (|\text{PED}| > 1) TR falls (quantity falls proportionally more than price rises) TR rises
Unit‑elastic (|\text{PED}| = 1) TR unchanged TR unchanged
Inelastic (0 < |\text{PED}| < 1) TR rises (quantity falls proportionally less than price rises) TR falls
Perfectly inelastic (|\text{PED}| = 0) TR rises (price rises, quantity unchanged) TR falls
Perfectly elastic (|\text{PED}| = ∞) TR falls to zero (any price rise eliminates sales) TR falls to zero (any price fall eliminates sales)

6. Using PED in Decision‑Making

  • Households – decide how much of a good to buy when its price changes; a high PED means they will switch to alternatives.
  • Firms
    • Pricing strategy – raise price only if demand is inelastic; cut price to boost revenue if demand is elastic.
    • Tax incidence – with inelastic demand, most of a tax burden falls on consumers.
    • Product positioning – develop brand loyalty or differentiate to make demand more inelastic.
  • Workers – the concept mirrors the elasticity of labour supply; a high PED for a good may affect the demand for labour in its production.
  • Government
    • Indirect taxes – choose goods with inelastic demand to raise revenue with minimal reduction in quantity sold.
    • Subsidies – subsidies on goods with elastic demand can significantly increase consumption.

7. Diagrammatic Illustration

Demand curve showing elastic, unit‑elastic and inelastic sections with PED values and total‑revenue arrows
Figure: A single demand curve divided into three zones. The upper (steep) part is inelastic (|\text{PED}| < 1), the middle is unit‑elastic (|\text{PED}| = 1), and the lower (flatter) part is elastic (|\text{PED}| > 1). Arrows illustrate the direction of total revenue when price changes.

8. Summary Checklist

  • Definition: PED = %ΔQd / %ΔP (use the mid‑point formula in exams).
  • Report the absolute value: |\text{PED}|.
  • Elasticity thresholds – > 1 (elastic), = 1 (unit‑elastic), < 1 (inelastic).
  • Determinants – substitutes, income share, nature of the good, time, (optional) brand loyalty.
  • Elastic demand → price rise → TR falls; Inelastic demand → price rise → TR rises.
  • Apply PED to pricing, tax, subsidy and production decisions for households, firms, workers and government.

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