Arc elasticity of demand (arc PED) is the value of PED over a range
of prices, and can be calculated using the standard formula:
More formally, we can say that PED is the ratio of the quantity
demanded to the percentage change in price.
We can then invert the denominator, to
get:
We can reverse the order of the
multiplication, so this can be rewritten as:
Elasticity has now been spilt into two parts, the
over
which
is the ratio of the change in quantity to the change in price – this is
the gradient of the demand curve – and
/
,
which is related to the actual point on the curve at which a measurement
is made.
For example, consider the demand schedule for a hypothetical product. We can now calculate the point elasticity at point . To find the gradient we have taken the nearest point, at .
point  p (£)  qd  PED 

10  2  

9  4  

8  6  

7  8  

6  10  

5  12  

4  14  

3  16  0.37 

2  18  

1  20 
When calculating the elasticity of demand, for all goods with a
downward sloping demand curve, you should get a negative value.
We can repeat this for point
. The gradient
stays the same, as it is linear, but the
and
change,
to:
point  p (£)  qd  PED 

10  2  

9  4  

8  6  2.66 

7  8  

6  10  

5  12  

4  14  

3  16  0.37 

2  18  

1  20 
point  p (£)  qd  PED 

10  2  

9  4  4.50 

8  6  2.66 

7  8  

6  10  1.20 

5  12  0.83 

4  14  0.57 

3  16  0.37 

2  18  0.29 

1  20 
For your own practice, work out the missing
figures.