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 midpoint 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 (Arc) 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)


Arc-elasticity

Example of calculating Arc Elasticity of Demand

ped-arc-inelastic-demand

Arc ‘mid-point’ elasticity

  • The mid point of Q = (80+88)/2 = 84
  • The mid-point of P =(10+14)/2 =12
  • % change in Q = 88-80/84 = -0.09524
  • % change in price = (14-10)/12  = 0.3333
  • PED = 0.333/-0.9524 = -0.285

Comparison with measuring elasticity as point A to B

If we calculated elasticity from point A to B. We would take the starting point as the reference.

  • The % change in Q would be 8/88 = 10%
  • The % change in Price would be 4/10 = -40%
  • Therefore PED would be 10/-40 = -0.25

 

Example 2

arc-elasticityPrice has increased from $50 to $120 (change in price of $70)

Quantity has fallen from 40 to 20 (change in quantity of 20)

Using arc-elasticity of demand

PED =

Change in Q (20) /midpoint (30) = – 0.66666
Change in p (70) /midpoint (85)  = 0.823529

PED = – 0.809


If we calculated PED from points B to A.

% change in QD would be 20/40 (50%

% change in price would be 70/50 (140%)

PED = -0.35

If we calculated PED from points A to B

% change in QD would be 20/20 (100%)

% change in price would be 70/120 (58%)

PED = -1.72

point-arc-elasticity


Readers Question: I wonder if you could possibly help with the problem we encountered when we’re trying 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

9 thoughts on “Difference between Point and Arc Elasticity of Demand

  1. Dear Tejvan Pettinger

    I really must express my gratitude for the help you freely gave me to pass my Economics class. I realize how busy you are and know that it took a lot of time to get me ready for the test. I know I was on the verge of failing the class, and I could not get my head around the language at all. Your patience was much appreciated, and it is through your help that I have managed to pass the class with one of the best marks.

    You are the sort of family friend that anyone would love.

    Sincerely,
    Melusi Ntombela
    South Africa, University of Zululand

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