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.

point elasticity

 

 

Arc Elasticity

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

arc elasticity

 

 

 

Example of Difference between Point and Arc Elasticity A to B

Demand_curve-wiki

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

price_elasticity_of_demand_and_revenue.svg

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

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.

Related

2 Responses to Difference between Point and Arc Elasticity of Demand

  1. shfu April 21, 2013 at 11:29 am #

    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.

    • sileshi May 2, 2013 at 9:43 am #

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