Chapter 6
Elasticities of Demand
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Contents:
• Elasticity of Demand
• Classification of Elasticities of Demand
• Price Elasticity of Demand
• Price Elasticity & Demand Curve
• Price Elasticity of Demand, Total Revenue &
Total Expenditure
• Income Elasticity of Demand
• Cross Elasticity of Demand
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Contents:
• Advanced Material 6.1: Price Consumption
Curve and Price Elasticity
• Advanced Material 6.2: Income Consumption
Curve and Income Elasticity
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Elasticity of Demand
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Elasticity of demand
Elasticity of demand (需求彈性, Ed)
• is a measure of the responsiveness of
the quantity demanded of a good to
a change in an exogenous variable.
•
% change in X_________
% change in exogenous variable
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Why?
Classification
of
Elasticities of Demand
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Classification according to the exogenous variable concerned
Type of elasticity of
demand
Price elasticity of demand
(價格需求彈性, pEd)
Income elasticity of demand
(所得需求彈性, iEd)
Cross elasticity of demand
(交叉需求彈性, cEd)
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Exogenous variable
concerned
Price of the good
Income
Price of related good
Classification according to the formula adopted
in calculation
Point elasticity of demand
% Δ= X2 – X1 x 100%
X1
very small
Situations applied: when the % change are _________
Arc elasticity of demand
% Δ= X2 – X1 x 100%
(X1+ X2)/2
Situations applied: when the % change are significant
_________
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Classification according to the size of the elasticity
1. Perfectly inelastic (Ed = 0)
• The exogenous variable changes but X remains unchanged
i.e. % Δ in X =_______.
0
Px
D
• In the case of price elasticity,
the demand curve is _________.
vertical
vertical
0
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X
Classification according to the size of the elasticity
2. Inelastic (Ed < 1)
 %  in exogenous variable
%  in X ____
3. Unitarily elastic (Ed = 1)
 %  in exogenous variable
%  in X ____
4. Elastic (Ed > 1)
 %  in exogenous variable
%  in X ____
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Classification according to the size of the elasticity
5. Perfectly elastic (Ed = infinity)
• A negligible change in the exogenous variable
brings an infinite change in Qd
Px
i.e. % Δ in X =_________.
infinity
• In the case of price elasticity,
horizontal
the demand curve is ___________.
0
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horizontal
D
X
Price Elasticity of Demand
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What is price elasticity?
Price elasticity of demand (價格需求彈性, pEd)
is equal to the percentage change in quantity demanded
of a good divided by the percentage change in its own
price.
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What is price elasticity? (Con’t)
According to the first law of demand,
 pEd is ________.
negative
However, if Giffen good existed,
positive
 its pEd would be ________.
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Point elasticity of demand -- on a linear demand curve (DC)
Px
Mathematical measure:
C
P1
A

ΔPx
ΔX
0
Graphical measure:
X1
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pEd
DC
B
X
at point A:
Point elasticity of demand – on a non-linear DC
Px
Mathematical measure:
C
P1
Graphical measure:
A
ΔPx
pEd
DC
ΔX
0
X1
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B
X
at point A:
Price Elasticity
&
Demand Curve
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Point elasticity of demand -- on a linear DC
Px
|pEd| > 1 (elastic)

Demand
curve
0
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M (mid-point):
|pEd|= 1 (unitarily elastic)
|pEd| < 1 (inelastic)
X
Price elasticity at points on different DCs
• If two linear DCs have the same y-intercept
Px
C
P
O
 they will have the same pEd at every price.
BA
OP
ED
=
=
pEd at point A on d1 =
AC PC
DC
= pEd at point D on d2
D
A
d1
B
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d2
E
X
Price elasticity at points on different DCs
pEd
at point A on d1 (with a smaller y-intercept)
If 2 linear DCs have different y-intercepts
Px
BA
=
AC
F
C
P
O
A
OP
=
PC
>
OP ED
=
PF
DF
 The curve with a smaller y-intercept will
have a larger
elasticity
the
curve
= pEdprice
at point
D on dthan
(with
a
larger
2
with a larger y-intercept at every price.
y-intercept)
D
d1
B
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d2
E
X
Price elasticity of points on different DCs
Px
C
F
P
O
pEd
at point A on a d1 (with a larger slope)
If 2 linear DCs intersect,
= BA = OP
AC PC
<
OP
ED
=
PF
DF
 the one with a gentler slope will have a larger
=at
point D on d2point.
D
(on elasticity
d 2)
price
pEthe
d at intersection

(with a smaller slope)
A on (d1)
d1
d2
B
E
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X
Price Elasticity of Demand,
Total Revenue &
Total Expenditure
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Price elasticity, total expenditure (TE) and
total revenue (TR)
Total expenditure paid by a consumer
= Price x Quantity transacted
(or P x Q)
= Total revenue received by a producer
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Change in TE and TR
When demand or supply changes,
price & quantity transacted vary.
Subsequently, total expenditure
& total revenue are affected.
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Increase in demand
D  P  & Q   TR 
Px
S1
P2
 in TR
P1
D2
D1
0
X1
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X2
X
Decrease in demand
D  P  & Q   TR 
Px
S1
P1
in TR
P2
D1
0
D2
X2
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X1
X
Increase in supply
P but X 
Δ in TR depends on
the relative % Δ in
P & Q, i.e., the pEd.
Px
S1
S2
P1
P2
D
0
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X1
X2
X
a. Demand is elastic
Px
S1
P1
P2
When supply increases,
if demand is elastic,
S2
M
• %in X  %  in P
• TR 

 in TR
 in TR
D
0
X1 X2
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X
b. Demand is unitarily elastic
%in X  %in P
Px
S1
TR remains constant
S2
P1
M

P2
 in TR
D
0
X1
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X2
X
 in TR
c. Demand is inelastic
%in X  %  in P
Px
TR 
S1
M
P1
P2
0
S2

 in TR
D
X1
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X2
X
 in TR
Decrease in supply
P but X 
Px
S2
S1
Δ in TR depends on
the relative % Δ in
P2
P & Q, i.e., the pEd
P1
D
0
X2
X1
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X
a. Demand is elastic
Px
S2
When supply decreases,
if demand is elastic,
S1
• %  in X  %  in P
P2
P1
M

 in TR
 in TR
• Δ in TR 
D
X2 X1
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X
b. Demand is unitarily elastic
Px
%  in X = %  in P
S2
TR remains constant
S1
P2
M

P1
 in TR
 in TR
D
X2
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X1
X
c. Demand is inelastic
%in X  %  in P
Px
Δin TR 
S2
M
P2
P1
S1

 in TR
D
X2 X1
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X
 in TR
Q6.6:
(a) If the demand is inelastic, to increase the TR,
should a producer raise the price or
should he cut the price?
(b) After raising the price of a good, a producer
finds that the total revenue falls.
What is the reason?
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Unit elasticity and total revenue
For a unitarily elastic demand:
% Δ in X = % Δ in P
TR remains constant despite a change in P or Q.
If one spends the whole amount (or a fixed amount)
of his income on a good no matter what its price is,
its pEd must be equal to / greater
than
equal
to /smaller than one.
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x
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X
Factors affecting price elasticity
1. Number of close substitutes:
more close substitutes
 more elastic demand.
Why?
2. Degree of necessity:
necessities & habit-forming goods
 less elastic demand.
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Why?
Factors affecting price elasticity (Con’t)
3. Number of possible uses:
more different uses  more elastic demand. Why?
4. Durability:
more durable  more elastic demand.
Why?
5. Proportion of income spent:
a larger proportion of one’s expenditure
 more elastic demand.
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Why?
6. Time of adjustment:
longer time for adjustment  more elastic demand
(Second law of demand)
Px
P0
Why?
P1
0
X0X1X2 X3
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X4
Shift of DC
as time passes
X
Q6.7:
The demand for salt is inelastic.
List all possible reasons.
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Income Elasticity of Demand
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What is income elasticity?
Income elasticity of demand (所得需求彈性, iEd)
is equal to the percentage change in quantity demanded
divided by the percentage change in income.
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Superior good
 X is _________
positively related to income.
 iEd is ________.
positive

1
 luxuries
iEd

iEd  1
 necessities
(Options: positive / negative / luxuries / necessities
/ positively / negatively )
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Inferior good
 X is _________
negatively related to income.
 iEd is __________.
negative
(Options: positive / negative / luxuries / necessities
positively / negatively)
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X
I1

I
X1
Mathematical measure:
Graphical measure:
X
X1
X
Good X is a
superior good
A

ΔX
ΔI
B
X1
Good X is an
inferior good

A
ΔI
ΔX
B
C 0
I1
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I
0
C
I1
I
Cross Elasticity of Demand
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What is cross elasticity?
Cross elasticity of demand (交叉需求彈性, cEd)
is equal to the percentage change in quantity demanded
of a good (e.g., good X) divided by the percentage
change in price of another good (e.g., good Y).
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Cross elasticity of demand
The cross elasticity of substitutes is positive, why?
when PY  Y and X (substitute of Y)
thus, PY and X are positively related.
The cross elasticity of complements is negative, why?
when PY  Y and X (complement of Y)
thus, PY and X are negatively related.
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•Mathematical measure:
•Graphical measure:
PY
PY
Good X and good Y
are substitutes
Good X and good Y
are complements
C
A

PY1
0
B
PY1
ΔPY
ΔX
X1
C
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X
0
A
ΔPY 
ΔX
X1
B
X
Q6.9:
For each of the following commodities, suggest a
good with a positive cross elasticity and a good with
a negative cross elasticity related to the commodity.
Shoes
Pencil
Broom
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Camera
Map
Advanced Material 6.1:
Price elasticity and price consumption curve
If PCC is _upward sloping_, when Px, both the
consumption of good X and good Y __________.
increase
As income remains unchanged and the expenditure on
good Y  , the expenditure on good X must __________.
decrease
As the expenditure on good X  (when Px  and X ),
the %  in X must be ___________
smaller than the %  in PX.
Y
So, the demand for good X must be
_______.
inelastic
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PCC
0
X
Shape of
PCC
Consumption Expenditure Relative size
Price
and
on X
elasticity
of % Δ in
expenditure (= I - PY  Y) X () and of demand
on Y
for X
Px ()
Upward
sloping
%in X < Inelastic
%in Px
Horizontal
Downward
sloping


Unchanged Unchanged

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
%in X = Unitarily
elastic
%  in Px
%in X > Elastic
%  in Px
Price elasticity and price consumption curve
Y
PCC
(|pEd|=1)
• Graphical measure:
Y
PCC
(|pEd|<1)
0
X
Y
0
PCC
(|pEd|>1)
X
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0
X
Advanced Material 6.2:
Income elasticity and income consumption curve
Y
ICC2
ICC3
ICC1
0
I1
ICC4
ICC5
I2
I3 X
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Shape
of ICC
ICC1
iEd
of
X
-ve
iEd
of
Y
+ve
ICC2
0
+ve
ICC3
+ve
+ve
ICC4
+ve
0
ICC5
+ve
-ve
Correcting Misconceptions:
1. The gentler the slope of a demand curve,
the larger its price elasticity.
2. A price rise must raise the total revenue.
3. If one spends a fixed amount of his income on a
good, his demand for the good is perfectly inelastic.
4. It is impossible for all the goods consumed to be
luxuries, because one must consume some necessities.
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Survival Kit in Exam
Question 6.1:
After a rise in the price of coffee,
what will happen to the total revenues of
(a) coffee,
(b) sugar and
(c) tea respectively?
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