Measurement of Elasticity – Point & Arc Methods

In Business Economics, it is not enough to know that demand is elastic or inelastic. We must measure price elasticity of demand. Two important methods are:

1. Point method
2. Arc method

1. Point Elasticity of Demand

Point elasticity measures elasticity at a specific point on the demand curve.

Formula (for small change in price)

Ep = (ΔQ / ΔP) × (P / Q)

Where:

• ΔQ = Small change in quantity demanded
• ΔP = Small change in price
• P = Original price
• Q = Original quantity demanded

Simple Numerical Example

Price of a pen falls from ₹10 to ₹9. Quantity demanded rises from 100 units to 120 units.

• ΔP = -1 (10 - 9)
• ΔQ = +20 (120 - 100)
• P = 10, Q = 100

Ep = (ΔQ / ΔP) × (P / Q)
   = (20 / -1) × (10 / 100)
   = -200 / 100
   = -2

Ignoring the minus sign (we know demand curve slopes down): Ep = 2 (elastic demand).

2. Arc Elasticity of Demand

Point method is not accurate when there is a large change in price. In such cases we use arc elasticity.

Formula (between two points on a demand curve)

Ep = (ΔQ / ΔP) × (P1 + P2) / (Q1 + Q2)

Where:

• P1, P2 = Two prices
• Q1, Q2 = Quantities corresponding to those prices

This formula uses average price and average quantity.

Numerical Example

Price of a commodity falls from ₹20 to ₹10. Quantity demanded increases from 40 units to 80 units.

• P1 = 20, P2 = 10 → ΔP = -10
• Q1 = 40, Q2 = 80 → ΔQ = +40

Ep = (ΔQ / ΔP) × (P1 + P2) / (Q1 + Q2)
   = (40 / -10) × (20 + 10) / (40 + 80)
   = (-4) × (30 / 120)
   = (-4) × (1/4)
   = -1

So, Ep = 1 (unitary elastic demand).

3. Point vs Arc Elasticity – Comparison

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4. Diagrammatic Idea (Conceptual)

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5. Quick Revision Points

• Point method → small change, elasticity at a point.
• Arc method → large change, elasticity between two points.
• Both are based on percentage method of price elasticity.
• Minus sign is usually ignored; we focus on magnitude of Ep.

6. Quiz Time 🎯

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