Calculation of PED using the formula

Price Elasticity of Demand (PED)

Price elasticity of demand measures how the quantity demanded of a good changes in response to a change in its price.

Formula

The elasticity of demand is calculated as:

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

Using the midpoint (arc) method, the formula becomes:

\$\text{PED} = \frac{(Q2 - Q1)/\left(\frac{Q1+Q2}{2}\right)}{(P2 - P1)/\left(\frac{P1+P2}{2}\right)}\$

Step‑by‑step calculation

1. Record the initial price \(P1\) and quantity demanded \(Q1\).
2. Record the new price \(P2\) and new quantity demanded \(Q2\).
3. Calculate the percentage change in quantity demanded:

   \$\% \Delta Q = \frac{Q2 - Q1}{\frac{Q1+Q2}{2}}\times 100\%\$

4. Calculate the percentage change in price:

   \$\% \Delta P = \frac{P2 - P1}{\frac{P1+P2}{2}}\times 100\%\$

5. Divide the two percentages to obtain PED:

   \$\text{PED} = \frac{\% \Delta Q}{\% \Delta P}\$

Example

Suppose the price of a cup of tea rises from £1.00 to £1.20 and the quantity demanded falls from 1000 cups to 850 cups.

Calculations:

• Midpoint of price: \((1.00+1.20)/2 = 1.10\)
• Midpoint of quantity: \((1000+850)/2 = 925\)
• Percentage change in quantity:

  \$\frac{850-1000}{925}\times100\% = -16.22\%\$

• Percentage change in price:

  \$\frac{1.20-1.00}{1.10}\times100\% = 18.18\%\$

• PED:

  \$\frac{-16.22\%}{18.18\%} = -0.89\$

Interpretation: The demand for tea is inelastic (|PED| < 1), so the percentage change in quantity demanded is smaller than the percentage change in price.

Suggested diagram: A demand curve showing the two price‑quantity points and the slope.