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 = 88-80/84 = -0.09524
- % change in price = (14-10)/12 = 0.3333
- PED = -0.09524 /0.3333
**= -0.28571**

**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 = 0.90909
- The % change in Price would be 4/10 = -40
- Therefore PED would be 0.90909/-40 =
**-0.22727**

#### 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 )

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(change in P / average P)