Calculation of PED using the formula

What is Price Elasticity of Demand?

Price Elasticity of Demand measures how much the quantity demanded of a good changes when its price changes. Think of it as a “sensitivity” score: the higher the number, the more buyers react to price changes.

Formula for PED

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

In symbols: $PED = \dfrac{\Delta Q / Q}{\Delta P / P}$

Step‑by‑Step Calculation

1. Identify the initial price ($P_1$) and quantity ($Q_1$).
2. Identify the new price ($P_2$) and quantity ($Q_2$).
3. Calculate the percentage change in quantity: $\dfrac{Q_2 - Q_1}{Q_1} \times 100$.
4. Calculate the percentage change in price: $\dfrac{P_2 - P_1}{P_1} \times 100$.
5. Divide the two percentages to get $PED$.

Example Problem

Suppose the price of a video game drops from £60 to £50 and the quantity demanded rises from 2000 to 2600 units.

1. Percentage change in quantity: $\dfrac{2600-2000}{2000}\times100 = 30\%$.
2. Percentage change in price: $\dfrac{50-60}{60}\times100 = -16.67\%$.
3. $PED = \dfrac{30\%}{-16.67\%} \approx -1.80$.

Interpretation: Because |$PED$| > 1, demand is elastic. A price drop leads to a proportionally larger increase in quantity demanded.

Analogy: The Rubber Band of Demand 📉

Imagine the quantity demanded as a rubber band stretched between the price and the consumer. If the price falls (the band is pulled closer), the band stretches and more units are demanded. If the price rises (the band is pulled apart), the band snaps back and fewer units are demanded. The elasticity tells you how stretchy the band is.

Exam Tips 💡

• Remember the formula: $PED = \dfrac{(\%\Delta Q)}{(\%\Delta P)}$.
• Use absolute values when interpreting elasticity (ignore the negative sign).
• Classify: |$PED$| > 1 → elastic, |$PED$| = 1 → unit‑elastic, |$PED$| < 1 → inelastic.
• Show all steps in your calculation to earn full marks.
• When given a table, calculate the two percentage changes first.
• Check your sign: a price increase usually reduces quantity demanded, giving a negative $PED$.

Quick Check ??

Calculate the PED for a product that increases from £30 to £25 and quantity from 500 to 650 units.

1. $\Delta Q = 650-500 = 150$ → %ΔQ = $150/500 \times 100 = 30\%$.
2. $\Delta P = 25-30 = -5$ → %ΔP = $-5/30 \times 100 \approx -16.67\%$.
3. $PED = 30\% / -16.67\% \approx -1.80$.
4. Interpretation: Elastic demand.

Remember 🧠

Elasticity is a ratio, so it is unit‑free. You can use any consistent units (pounds, euros, dollars) and the result will be the same.