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.

Point elasticity

Point elasticity is the price elasticity of demand at a specific
point on the demand curve instead of over a range of it.

To get point PED we need to re-write the basic formula to include
an expression to represent the percentage, which is the change in a
value divided by the original value, as follows:

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.

Example

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
.

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:

We can continue to work out other
elasticities:

For your own practice, work out the missing
figures.