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Elasticity
• Reading: 2.4-2.5, 4.3
• Supply-Demand model can predict the direction
of changes in P & Q.
• It can also predict the degree of change in P & Q.
• Income up → P up. Will P goes up only slightly
or greatly? This depends on the slope of S and D
curves.
What would be the price and quantity
response if income increases?
Case 1
D
Price
Case 2
S
S
P0
P0
D
Q0
Quantity
Q0
Quantity
Elasticity
• Slope (∆P/∆Q) can help indicate the response of Q to P
(∆Qd/∆P, ∆Qs/∆P; ∆ means change in …).
• But slope is not a good measurement. Its value is
different if measurement units of P or Q are different.
• P up: US$1→US$2. Q down: 200→100.
∆Q/∆P = -100/1 = -100.
• P now quoted in HK$: P up: HK$7.8→HK$15.6.
∆Q/∆P = -100/7.8 = -12.82.
Elasticity: Demand
• A better measurement of responsiveness
shouldn’t be affected by measurement unit →
elasticity
• Own-price demand elasticity:
% change in quantity demanded
Ed 
% change in price
Qd / Q d

P / P
Elasticity: Demand
• E.g. price of pork up from $10 to $11 →
quantity demanded down from 1 million
pounds to 950,000 pounds.
• P up by 10%, Qd down by 5%
• Ed = -5%/10% = -0.5
• Ed < 0 because D curve is downward-sloping.
Elasticity: Demand
•
•
•
•
•
There is a calculation problem, however.
P up from $10 to $11 → up 10%
P down from $11 to $10 → down 9%
Q down from 1 million to 950,000 → down 5%
Q up from 950,000 million to 1 million → up
5.3%
• Ed is different even for the same degree of
movement. Direction of movement matters.
Elasticity: Demand
• Explore methods to get rid of this directiondependence problem.
• For calculating elasticity for two points, we
can take an average of Q or P after and before
change.
E PD

 ΔQ

P 
ΔP  Q 
Elasticity: Demand
•
Two points of P:
$10, $11
→ average P = $10.5
• ∆P/P = 1/10.5 = 9.5%
Price
($ per unit)
•
Two points of Q:
1 million, 950,000
→ average = 975000
• ∆Q/Q = 50000/975000
= 5%
11
10
•
Ed = - 5%/9.5% = -0.53
D
9.5
10
Quantity (100K)
Elasticity: Demand
• Elasticity calculated for two points by this
method: arc elasticity of demand.
• Its value won’t be different due to the direction
of movement: from A to B, or from B to A.
• This invariance property can also be achieved
by shortening the distance between two points.
Elasticity: Demand
• The shorter the distance between point A and B,
the elasticities calculated from either direction
is closer to each other.
• When point A and B converges to one point,
the elasticity is completely “invariant” with
direction of movement.
• This is point elasticity.
Elasticity: Demand
• To measure point elasticity, we have to know the slope
of the demand curve.
 Qd   P   P   Qd 

• Ed  Qd   P    Q   P 
• Slope of a D curve = ∆P/∆Qd
• Point Ed = (P/Q)  (slope of D curve)
• E.g. Qd = 8 – 2P, ∆Qd/∆P = -2.
Point Ed at (P = 1, Qd = 6): Ed = (1/6)(-2) = -1/3
Point Ed at (P = 2, Qd = 4): Ed = (2/4)(-2) = -1
Point Elasticity
• Measuring point Ed is much easier for linear
demand function because the slope is constant.
• But even for non-linear demand function, it can
be measured. Again, use Ed = (P/Q)  (slope of D
curve).
Point Elasticity
Price
($ per unit)
•
•
•
11
Ed = ∆Qd/Qd  ∆P/P
= (P/Q)(∆Qd/∆P)
Slope = ∆P/∆Qd = -1 at A
Ed = (11/9.5)/(-1) = -1.16
at point A
A
D
9.5
Q
Elasticity: Demand
• Arc elasticity is probably more intuitive. But
economists more often use point elasticity.
• Point elasticity measures the quantity response
to a very small change in price.
Elasticity: Demand
• Patterns in elasticities:
- Elastic: % change in Qd > % change in P
(|Ed| > 1)
- Inelastic: % change in Qd < % change in P
(|Ed| < 1)
- |.| means absolute value.
- Along a demand curve, point Ed is different at
different points.
Elasticity: Demand
Price
4
EP = -
Demand Curve
Q = 8 – 2P
Elastic
Ep = -1
2
Inelastic
4
8
Q
Ep = 0
Application: Elasticity, Consumption
Expenditure, Sales Revenue
Price of x
Total expenditure
7
6
|Ed| > 1
5
|Ed| =1
Demand)
4
3
|Ed| < 1
2
1
0
1
2
3
4
5
6
• To stimulate sales,
price must be
lower.
• To increases sale
volume, sales
revenue may not
be higher.
• Px increases with
x at first and then
decreases.
• If % P reduction <
% quantity
reduction, Px
increases.
7 X
Elasticity: Demand
• Special types of D curve:
- Horizontal D curve: ∆Qd/∆P = ∞ (∆P/∆Qd =
0). Perfectly elastic at all point.
- Vertical D curve: ∆Qd/∆P = 0 (∆P/∆Qd = ∞).
Perfectly inelastic at all point.
Perfectly elastic demand
Price
EP =  at every point
D
P*
Quantity
Perfectly inelastic demand
Price
D
EP = 0 at every point
Q*
Quantity
Elasticity: Demand
•
-
Some elasticity results:
Soft drink: elastic
Toilet papers: elastic
Toothpaste: inelastic
Tissue: inelastic
Elasticity: Demand
• Income elasticity of demand:
% change in quantity demanded
EI 
% change in income
Qd / Qd
I Qd


I / I
Qd I
Elasticity: Demand
• EI > 0, normal good
• EI < 0, inferior good (nothing to do with
inferior quality)
• EI > 1, superior good. Income share of
superior good increases with income.
• Some facts associated with EI:
- Necessities usually have EI between 0 and 1.
- Luxury goods usually have high EI.
Elasticity: Demand
• Cross-price elasticity of demand: it measures
how the price of a good affects the quantity
demanded of another good.
% change in quantity demanded of good X
E XY 
% change in price of good Y
QX / QX
PY QX


PY / PY
QX PY
Elasticity: Demand
• EXY > 0. X and Y are substitutes. E.g. coffee
and tea. P of coffee up, D for tea goes up →
Qd of tea up.
• EXY < 0. X and Y are complements. E.g. coffee
and coffee mate. P of coffee up, D for coffee
mate down → Qd of coffee mate down.
Elasticity: Supply
• Own-price elasticity of supply:
% change in quantity supplied
E s
% change in price
Qs / QS
P Qs


P / P
Qs P
Elasticity: Supply
• For an upward-sloping S curve, Es > 0.
• For a horizontal S curve, Es = 0.
• Since S curve may be down-sloping (not often
happens), Es < 0 is possible.
• Elastic supply: |Es| > 1
• Elastic supply: |Es| < 1
Elasticity: Long run vs Short run
• P up. Q will change. But when will we
measure the change in Qs, or Qd?
• Time is important because it takes time for
consumers to change their consumption habit,
and for firms to change their production
capacity.
Elasticity: Long run vs Short run
• Long run: enough time is allowed for
consumers or producers to fully adjust to the P
change.
• Short run: time is not enough for this complete
adjustment.
Elasticity: Long run vs Short run
• It is widely believed that D is more elastic in
LR than in SR.
• Reason: (1) When P up, it takes time to change
consumption habit. (2) It takes time to search
substitutes for a good.
• This phenomenon is called “second law of
demand”. But this “law” is not widely
recognized to be “law”.
Elasticity: Long run vs Short run
Price
DSR
•People cannot easily
adjust consumption in
short run.
•In the long run, people
tend to drive smaller and
more fuel efficient cars.
DLR
Quantity of Gasoline
Elasticity: Long run vs Short run
• Counterexample: (Steven Cheung) P up for
cross-harbour tunnel, Qd drops in SR, recovers
in LR.
• Reason: Substitutes for the tunnel (other
tunnels) are well known, need no time to
search. In contrast, consumers find out
substitutes for the tunnel are not so useful as
initially imagined. Revert to tunnel finally.
Elasticity: Long run vs Short run
• Counterexample: (Pindyck & Rubinfeld)
Durable goods are more elastic in SR than in
LR.
• Reason: Consumers hold a much larger stock
of old durables than newly produced durables
per year. Replacing old durables takes time.
E.g. P for cars up, delay replacing old cars, Qd
for new cars drop sharply. Old cars gradually
wear out and must be replaced. Qd picks up
again.
Elasticity: Long run vs Short run
Price
DLR
•Initially, people may put
off immediate car
purchase
•In long run, older cars
must be replaced.
DSR
Quantity of Cars
Elasticity: Long run vs Short run
• For the same reason, income elasticity is also
smaller in SR but higher in LR. Changing
habit and searching substitutes takes time.
• Again, for durables, EI more inelastic in LR.
Income down, Qd for new cars down sharply.
Old cars gradually wear out. Qd picks up again.
Elasticity: Long run vs Short run
• Elasticity for petrol (in US):
Years after the price change
(oil shock 1974):
1
2
3
5
10 20
Ed
-0.11 -0.22 -0.32 -0.49 -0.82 -1.17
EI
0.07 0.13 0.20 0.32 0.54 0.78
Elasticity: Long run vs Short run
• Elasticity for cars (in US):
Years after the price change
(1980s-1990s):
1
2
3
5
10 20
Ed
-1.20 -0.93 -0.75 -0.55 -0.42 -0.40
EI
3.00 2.33 1.88 1.38 1.02 1.00
Elasticity: Long run vs Short run
• Durables: D is more elastic in SR. The
business is more pro-cyclical than nondurables. Indicators of economic fluctuation.
E.g. sales of new houses frequently cited as
signs of economic recovery.
Elasticity: Long run vs Short run
• Normally, supply is also more elastic in LR
than in SR.
• In SR, there are fixed factors or production
capacity constraint. Even P up, Qs can’t
expand beyond capacity. Can only pay workers
to work overtime. In LR, Qs can expand more.
• This is the so-called Le Châtelier principle.