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Chapter 6 Elasticities of Demand
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• 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
Contents:
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• Advanced Material 6.1: Price Consumption Curve and Price Elasticity• Advanced Material 6.2: Income Consumption Curve and Income Elasticity
Contents:
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Elasticity of Demand
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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.
Elasticity of demand
• % change in X_________ % change in exogenous variable
Why?
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Classification of
Elasticities of Demand
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Type of elasticity of demand
Exogenous variable concerned
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)
Classification according to the exogenous variable concerned
Price of the good
Income
Price of related good
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Classification according to the formula adopted in calculation
Point elasticity of demand
% Δ= X2 – X1 x 100%
X1
Situations applied: when the % change are _________
Arc elasticity of demand
% Δ= X2 – X1 x 100%
(X1+ X2)/2Situations applied: when the % change are _________
very small
significant
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vertical
Classification according to the size of the elasticity
• Perfectly inelastic (Ed = 0)
• The exogenous variable changes but X remains unchanged
i.e. % Δ in X =_______.
• In the case of price elasticity,
the demand curve is _________.
D0
vertical
Px
X0
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Classification according to the size of the elasticity
2. Inelastic (Ed < 1) % in X ____ % in exogenous variable
3. Unitarily elastic (Ed = 1) % in X ____ % in exogenous variable
4. Elastic (Ed > 1) % in X ____ % in exogenous variable
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horizontal
D
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
i.e. % Δ in X =_________.
• In the case of price elasticity,
the demand curve is ___________.
infinity
horizontal
Px
X0
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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.
good the of price in %
demanded quantity in %Edp
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What is price elasticity? (Con’t)
According to the first law of demand, pEd is ________.negative
positive
However, if Giffen good existed, its pEd would be ________.
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ΔPx
ΔXX
X1
P1
0
C
B
A
Px
DC
Point elasticity of demand -- on a linear demand curve (DC)
1
1
X X
P
P
X
1
1
X X
P
P
X
Mathematical measure:
pEd at point A:
Graphical measure:
OX
BX
CP
OP
AC
AB
1
1
1
1 OX
BX
CP
OP
AC
AB
1
1
1
1
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ΔPx
ΔX
Point elasticity of demand – on a non-linear DC
XX1
P1
0
C
B
A
Px
DC
1
1
X X
P
P
X
1
1
X X
P
P
X
Mathematical measure:
pEd at point A:
Graphical measure:
OX
BX
CP
OP
AC
AB
1
1
1
1 OX
BX
CP
OP
AC
AB
1
1
1
1
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Price Elasticity Price Elasticity &&
Demand Curve Demand Curve
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X0
Px
Demand curve
M (mid-point): |pEd|= 1 (unitarily elastic)
|pEd| > 1 (elastic)
|pEd| < 1 (inelastic)
Point elasticity of demand -- on a linear DC
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AD
d1 d2 XO
Px
B
C
P
E
pEd at point A on d1 =BAAC
=OPPC
EDDC
=
= pEd at point D on d2
Price elasticity at points on different DCs• If two linear DCs have the same y-intercept
they will have the same pEd at every price.
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pEd at point A on d1 (with a smaller y-intercept)
=OPPF
EDDF
= pEd at point D on d2 (with a larger y-
intercept)
>
Price elasticity at points on different DCs
A D
XO
Px
B
C
P
Ed1
d2
F OPPC
=BAAC
=If 2 linear DCs have different y-intercepts
The curve with a smaller y-intercept will have a larger price elasticity than the curve with a larger y-intercept at every price.
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D (on d2)
XO
Px
A on (d1)
B
C
P
E
F
d1 d2
pEd at point A on a d1 (with a larger slope)
OPPF
EDDF
=
= pEd at point D on d2
(with a smaller slope)
<
Price elasticity of points on different DCs
OPPC
=BAAC
=If 2 linear DCs intersect,
the one with a gentler slope will have a larger price elasticity at the intersection point.
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Price Elasticity of Demand, Total Revenue &
Total Expenditure
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Total expenditure paid by a consumer
= Price x Quantity transacted (or P x Q)
= Total revenue received by a producer
Price elasticity, total expenditure (TE) and total revenue (TR)
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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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D2
P2
X2
in TRin TR in TRin TR
Increase in demand
D P & Q TR
Px
XD1
S1
P1
X10
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D2
P2
X2
Decrease in demand
D P & Q TR Px
X
D1
S1
P1
X10
in TRin TR in TRin TR
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Increase in supply
P but X
Δ in TR depends onthe relative % Δ inP & Q, i.e., the pEd.
X
S2
Px
D
S1
P1
X1
P2
X20
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S2
a. Demand is elastic
P2
X2
When supply increases, if demand is elastic,
• %in X % in P
• TR
Px
XD
S1
P1
M
in TR
in TR
X10
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S2
b. Demand is unitarily elastic
%in X %in P
TR remains constant
in TR
in TRP2
X2
Px
XD
S1
P1
M
X1
0
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S2
c. Demand is inelastic
%in X % in P
TR
Px
XD
S1
P1
M
in TR
in TR
X1
P2
X20
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P but X
Decrease in supply
Px
XD
S1
S2
P2
P1
X1X20
Δ in TR depends onthe relative % Δ in P & Q, i.e., the pEd
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S2
a. Demand is elastic
When supply decreases, if demand is elastic,
• % in X % in P
• Δ in TR
Px
X
D
S1
P2
X2
P1
M
X1
in TR
in TR
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S2
b. Demand is unitarily elastic
% in X = % in P
TR remains constant Px
XD
S1
P1
M
in TR
in TR X1
P2
X2
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S2
c. Demand is inelastic
%in X % in P
Δin TR
P2
X2
D
M
Px
X
S1
P1
X1
in TR
in TR
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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
% 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 /smaller than one.
For a unitarily elastic demand:
equal to
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Xx
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1. Number of close substitutes:
more close substitutes
more elastic demand.
Factors affecting price elasticity
Why?
Why?
2. Degree of necessity:
necessities & habit-forming goods
less elastic demand.
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3. Number of possible uses:
more different uses more elastic demand.
Factors affecting price elasticity (Con’t)
Why?
4. Durability:
more durable more elastic demand.
5. Proportion of income spent:
a larger proportion of one’s expenditure
more elastic demand.
Why?
Why?
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6. Time of adjustment:
longer time for adjustment more elastic demand
(Second law of demand)
Shift of DC as time passes
Px
X
P0
P1
X0 X3X2X1 X40
Why?
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Q6.7:
The demand for salt is inelastic. List all possible reasons.
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Income Elasticity of Demand
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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.
incomein %
demandedquantity in %Edi
What is income elasticity?
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Superior good X is _________ related to income. iEd is ________.
luxuries necessities
positive
(Options: positive / negative / luxuries / necessities / positively / negatively )
iEd 1
iEd 1
positively
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Inferior good
X is _________ related to income.
iEd is __________.negative
(Options: positive / negative / luxuries / necessities positively / negatively)
negatively
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X
II1
X1
C 0
B
A ΔX
Δ I
Good X is an inferior good
Graphical measure:
Mathematical measure:
CI
OI
OX
BX
AC
AB
1
1
1
1di A point at E
1
1
X
I
I
X
X
II1
X1
C0
B
A ΔXΔ I
Good X is a superior good
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Cross Elasticity of Demand
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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).
Y good of pricein %
X good of demandedquantity in % Edc
What is cross elasticity?
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The cross elasticity of substitutes is positive, why?
The cross elasticity of complements is negative, why?
Cross elasticity of demand
when PY Y and X (substitute of Y) thus, PY and X are positively related.
when PY Y and X (complement of Y) thus, PY and X are negatively related.
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•Graphical measure:
•Mathematical measure:1
1
X
P
P
X Y
Y
PY
X
C
0B
A
ΔX
ΔPY
X1
PY1
Good X and good Y are substitutes
PY
X
C
0 B
A
ΔX
ΔPY
X1
PY1
Good X and good Y are complements
CP
OP
OX
BX
AC
AB
Y
Y
1
1
1
1dc A point at E
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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 Camera Map
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Advanced Material 6.1:Price elasticity and price consumption curve
As income remains unchanged and the expenditure ongood Y , the expenditure on good X must __________.
As the expenditure on good X (when Px and X ),the % in X must be ___________ the % in PX.
So, the demand for good X must be the demand for good X must be _______.
If PCC is _upward sloping_, when Px, both the consumption of good X and good Y __________.
PCCY
X0
increase
decrease
smaller than
inelastic
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Shape of PCC
Consumption and
expenditure on Y
Expenditure on X
(= I - PY Y)
Relative size
of % Δ in
X () and P
x ()
Price elasticity
of demand for X
Upward sloping %in X
%in Px
Horizontal Unchanged Unchanged
%in X
% in Px
Downward sloping
%in X
% in Px
< Inelastic
>
=
Elastic
Unitarily elastic
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Price elasticity and price consumption curve
• Graphical measure:
PCC (|pEd|<1)
Y
X0
PCC (|pEd|=1)
Y
X0
PCC (|pEd|>1)
Y
X0
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ICC1
ICC2
ICC5
ICC4
ICC3
Shape of ICC
iEd of X
iEd of Y
ICC1
ICC2
ICC3
ICC4
ICC5
Y
XI1 I3I20
Advanced Material 6.2:Income elasticity and income consumption curve
+ve-ve
+ve0
+ve+ve
0+ve
-ve+ve
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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?