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Elasticity Formulas
Conceptually, elasticity is a measure of responsiveness.
Algebraically, it is the ratio of two percentage
changes.
When you think elasticity, you should think “responsiveness”.
When we write “%
∆
X”  this means the percentage change in X
Elasticity of Demand
– (the own price elasticity of demand) – this measures the response of quantity
demanded to a change in this good’s own price.
It can also be interpreted as follows.
If the elasticity of demand is –2, then a 1% increase in price will lead
to a 2% decrease in quantity demanded.
Likewise, if the elasticity of demand is –4, a 1% decrease in price
will lead to a 4% increase in quantity demanded.
E
D
= %
∆
Q
d
/ %
∆
P
By the 1
st
Law of Demand, this must be negative.
If %
∆
P > 0, then %
∆
Q
d
< 0
⇒
E
D
< 0
If %
∆
P < 0, then %
∆
Q
d
> 0
⇒
E
D
< 0
To keep things from being less confusing, we will often talk about the absolute value of the elasticity of
demand (remove the negative sign).
 E
D
 > 0.
There will be three relevant ranges of the elasticity of demand.

∞
< E
D
< 1, elastic
Alternatively,
1 <  E
D
 <
∞
, elastic
E
D
= 1, unit elastic
 E
D
 = 1, unit elastic
1 < E
D
< 0, inelastic
0 <  E
D
 < 1, inelastic
Also,
E
D
= 
∞
, perfectly elastic
 E
D
 =
∞
, perfectly elastic
E
D
= 0, perfect inelastic
 E
D
 = 0, perfectly inelastic
Suppose there is a 20% increase in price that leads to a 40% reduction in quantity demanded.
In this case, %
∆
P = 20%, %
∆
Q
d
= 40%
E
D
= %
∆
Q
d
/ %
∆
P =  40% / 20% = 2
This would be an elastic demand curve (E
D
 =2).
Suppose a 60% increase in price leads to a 10% reduction in quantity demanded.
In this case, %
∆
P = 60%, %
∆
Q
d
= 10%
E
D
= %
∆
Q
d
/ %
∆
P =  10% / 60% =  0.16This would be an inelastic demand curve (E
D
 =0.16).
Below, I have sketched a relatively elastic, inelastic and unit elastic curve.
I am cheating a bit.
Along any
linear demand curve is the whole range of elasticities.
Elasticities are not the same thing as the slope of
the demand curve!
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View Full DocumentRelatively elastic
Relatively inelastic
Unit elastic
P
0
P
0
P
0
P
1
P
1
P
1
D
D
D
Q
0
Q
1
Q
0
Q
1
Q
0
Q
1
Notice that for the relatively elastic curve, we see a large change in quantity demanded for a given %
change in price.
That is, demand is very responsive or elastic.
If you’d rather, the %
∆
Q
d
is larger in
magnitude than the %
∆
P.
However, for the relatively inelastic curve, we see only a modest change in quantity demanded for the
given % change in price.
We would say that this demand curve is unresponsive, or inelastic.
If you’d
rather, the %
∆
Q
d
is smaller in magnitude than the %
∆
P.
What happens to the total expenditures (spending) on a good as the price changes?
We can use the elasticity concept to determine what happens to total expenditures (total spending) as we
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 Spring '11
 KAN

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