# Arc Elasticity of Demand

Definition: Arc elasticity of demand measures elasticity between two points on a curve – using a mid-point between the two curves.

On most curves, the elasticity of a curve varies depending on where you are. Therefore elasticity needs to measure a certain sector of the curve.

### Calculating Arc Elasticity of Demand

To calculate arc elasticity of demand we first take the midpoint in between. #### Once we have the midpoint, we calculate the PED in the usual way #### Example of calculating Arc Elasticity of Demand • The mid point of Q = (80+88)/2 = 84
• The mid-point of P =(10+14)/2 =12

• % change in Q = (14-10)/12  = 0.3333
• % change in price = 88-80/84 = -0.9524
• PED = 0.333/-0.9524 = -0.35

Comparison with measuring elasticity as point A to B

If we calculated elasticity from point A to B. We would take the starting point as the reference.

• The % change in Q would be 8/88 = 10%
• The % change in Price would be 4/10 = -40%
• Therefore PED would be 10/-40 = -0.25

#### Example 2 Price has increased from \$50 to \$120 (change in price of \$70)

Quantity has fallen from 40 to 20 (change in quantity of 20)

#### Using arc-elasticity of demand

PED =

Change in Q (20) /midpoint (30) = – 0.66666
Change in p (70) /midpoint (85)  = 0.823529

PED = – 0.809

If we calculated PED from points B to A.

% change in QD would be 20/40 (50%

% change in price would be 70/50 (140%)

PED = -0.35

If we calculated PED from points A to B

% change in QD would be 20/20 (100%)

% change in price would be 70/120 (58%)

PED = -1.72

#### Formula for Average or ‘midpoint’ elasticity of demand

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