# Arc and point elasticity

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## 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.

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