Arc elasticity measures how responsive quantity demanded is to price changes, using the midpoint method for consistent results. This is essential for pricing decisions and understanding consumer behavior.
Formula
The arc elasticity of demand is calculated as:
[E_d = \frac{(Q_2 - Q_1) \times (P_2 + P_1)}{(P_2 - P_1) \times (Q_2 + Q_1)}]
This is equivalent to:
[E_d = \frac{\text{Percent Change in Quantity}}{\text{Percent Change in Price}}]
Where:
- Q₁ = Initial quantity demanded
- Q₂ = New quantity demanded
- P₁ = Initial price
- P₂ = New price
Calculation Example
A product's price increases from $10 to $12, and quantity demanded decreases from 100 to 80 units:
[E_d = \frac{(80 - 100) \times (12 + 10)}{(12 - 10) \times (80 + 100)}]
[E_d = \frac{-20 \times 22}{2 \times 180} = \frac{-440}{360} = -1.22]
The elasticity of -1.22 indicates elastic demand—consumers are highly responsive to price changes.
Interpreting Elasticity Values
| Elasticity | Type | Meaning |
|---|---|---|
| |E| > 1 | Elastic | Quantity changes more than price (percentage) |
| |E| = 1 | Unit Elastic | Quantity and price change proportionally |
| |E| < 1 | Inelastic | Quantity changes less than price (percentage) |
Business Applications
Elastic Demand (|E| > 1):
- Lower prices to increase total revenue
- Common for luxury goods, products with substitutes
- Price promotions are effective
Inelastic Demand (|E| < 1):
- Can raise prices without significant volume loss
- Common for necessities, addictive products
- Focus on value over discounts
Why Use the Midpoint Method?
The midpoint (arc) method gives the same elasticity whether measuring a price increase or decrease. Simple percentage change gives different answers depending on direction, which can be misleading for business decisions.