## Arc Elasticity of Demand

Definition: Arc elasticity of demand measures the elasticity at the midpoint between two points on a curve.

#### Formula for Average of 'midpoint' elasticity of demand

(change in Q / average Q )
---------------------------
(change in P / average P)

or:

Arc elasticity measures elasticity at the mid point between the two selected points:

#### Example of Arc Elasticity of Demand:

• Price increases from 10p to 12p.
• Quantity falls from 40 to 20.
• Mid point of price = (12+10) / 2 = 11
• Mid point of quantity = (40+20) / 2 = 30

PED = % change Q.D/ % change in price

The % change in quantity is 20 / 30 = - 0.667

The % change in price is 2p / 11 = 0.18

Therefore PED = -0.667 / 0.18 = - 3.7

#### Point elasticity A to B

• Quantity increase from 200 to 300 = 100/200 = 50%
• Price falls from 4 to 3 = 1/4 = -25%
• Therefore PED = 50/ -25 =  – 2.0

Arc (Mid Point) Elasticity A to B

• Mid point of Q = (200+300) / 2 = 250
• Mid Point of P = (3+4) / 2 = 3.5
• Q % = (100/250) = 40%
• P % = 1/3.5 = 28.57
• PED = 40/-28.57 = - 1.4

(or ( 3.5/250)  * 100/1 = - 1.4)

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