## Arc and point elasticity of demand

#### Arc elasticity

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.