# Difference between Point and Arc Elasticity of Demand

When calculating elasticity of demand there are two possible ways.

1. Point elasticity of demand takes the elasticity of demand at a particular point on a curve (or between two points)
2.  Arc elasticity measures elasticity at the mid point between the two selected points:

Formula for point elasticity of demand is:

PED=

% 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

Arc elasticity measures the mid point between the two selected points:

#### 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.

### Unitary 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.

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## 2 thoughts on “Difference between Point and Arc Elasticity of Demand”

1. shfu says:

Your example of difference between arc and point elasticities is not correct since point elasticity is suppose to measure a very small change between two points. However, in your example, the different between the two points is too large and therefore the answer is neither point elasticity nor mid-point elasticity.

1. sileshi says:

When we use point & when arc? can we use both all the time?