Arc and point elasticity of demand
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 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
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
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
We can continue to work out other elasticities:
For your own practice, work out the missing figures.