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 .

Point PED graph

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 PED graph

Point elasticity

We can continue to work out other elasticities:

Point PED Graph

For your own practice, work out the missing figures.

 


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