Page 76 - DECO405_MANAGERIAL_ECONOMICS

Unit 5: Elasticity of Demand

P = New price – Old price = 4 – 3 = 1 Notes
Q = New quantity – Old quantity = 2000 – 3250 = – 1250
Substituting,

( 1250) 3
e = ( ) 1.15
p 1 3250
(b) When price falls from 4 to 3 per unit,
P, the old price = 4

Q, the old quantity (from the table) = 2000
New price = 3
New quantity = 3250 units
P = New price – Old price = 2000 – 3250 = –1250
Q = 3250 – 2000 = 1250
Substituting,

e =
p

The question is, how is it that we get different demand responses for the same range of price
change? The answer is that our initial quantity demanded and price have been different. When
we calculate for price fall, they are 2000 for initial quantity demanded and 4 for initial price.
When we calculate it for price rise they are 3250 for initial quantity demanded and 3 for initial
price. Hence elasticity tends to depend on our choice of the initial situation. However, demand
response should be the same for the same finite stretch of the demand curve. To get rid of this
dilemma created by the choice of the initial situations, we take the arithmetic mean of the two
quantities Q and the mean of the two prices P. This gives us the concept of arc elasticity of
demand.
Q P 0 P 1
Arc elasticity =
Q 0 Q 1 P
Q P 0 P 1
or, e =
P Q 0 Q 1
Where Q and Q are the two quantities corresponding to the two points on the demand curve.
0 1
Similarly P and P are the two prices.
0 1

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