When calculating elasticity of demand there are two possible ways.
- Point elasticity of demand takes the elasticity of demand at a particular point on a curve (or between two points)
- Arc elasticity measures elasticity at the mid point between the two selected points:
Formula for point elasticity of demand is:
% Δ Q / Q
% Δ P / P
To get more precision, you can use calculus and measure an infinitesimal change in Q and Price ( where ð = very small change) This is the slope of the demand curve at that particular point in time.
Arc elasticity measures the mid point between the two selected points:
Example of Difference between Point and Arc Elasticity A to B
Point elasticity A to B
- Quantity increase from 200 to 300 = 100/200 = 50%
- Price falls from 4 to 3 = 1/4 = -25%
- Therefore PED = 50/ -25 = – 2.0
Mid Point Elasticity A to B
- Mid point of Q = (200+300) / 2 = 250
- Mid Point of P = (3+4) / 2 = 3.5
- Q % = (100/250) = 40%
- P % = 1/3.5 = 28.57
- PED = 40/-28.57 = - 1.4
(or ( 3.5/250) * 100/1 = - 1.4)
Readers Question: I wonder if you could possibly help with the problem we encountered when were tying to calculate PED and a change in Total Revenue in a random example.
By taking random numbers we have found ourselves in a situation where TR has not increased when the price increased, given that D was price inelastic.The figures are as follows:
- Price increased from 10-20, (10/10 = 100% increase in price)
- QD had fallen from 10-5 units. (5/10 = 50% fall in price
- Surely, it gives PED of -0.5? – yes using PED
This suggests that D is price inelastic, hence TR should have increased. But it did not. Before the price was raised it equalled: 10×10=100 and after the rise in price: 20×5=100. It remained constant. Could you possibly explain why this has occurred?
All textbooks say that TR should increase when P is raised and D is price inelastic. It should work for any numbers as we can draw a demand curve through these two points (whether a straight line or hyperbolic). Does this imply that if demand is price inelastic and P rises TR may EITHER increase or stay the same, or is there a much complicated answer?
Using Arc elasticity of demand
we get a different elasticity of demand
Firstly we find the midpoint of Q and P. For Q This is (10+20)/2. For P this is 1(0+5)/2 = 7.5
- QD = 10/15 = 66% increase in quantity
- Price = 5/7.5 = 66% fall in price.
Therefore PED = 66/66 = 1.0 This explains why the revenue remained the same.
Elasticity and Revenue
The thing with a straight line is that the elasticity varies. At the top left, quantity is showing a big % increase, compared to price.
Therefore, it makes a big difference whether we use point elasticity of arc elasticity.
This will be a rectangular hyperbola
With this shape, the % change is constant.
Note for A Level Students
It is not needed to know the difference between point and arc elasticity. I teach just point elasticity. That is why your calculations were correct. But, outcome confusing.