Chapter 4

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Elasticity
Chapter 4
Elasticity
1
Example 4.1
 Will the China’s trade balance (export – import)
deteriorate if RMB appreciates (say, from
1USD=8.1RMB to 1USD=7.8RMB)?
1. China’s imports become less expensive. Quantity
demanded for import may increase.
2. China’s Exports become more expensive. Quantity
demanded for export may decrease.
 The impact of RMB appreciation on the trade balance
depends on the responsiveness of import demand and
export demand to the appreciation.
2
Price Elasticity of Demand
 The Price Elasticity of Demand is a measure of the
responsiveness of the quantity demanded of a good to
a change in the price of that good.
 Formally, it is the percentage change in the quantity
demanded that results from a 1 percent change in its
price.
Percentage change in quantity demanded
Percentage change in price
3
Elasticity
 Generally, elasticity is a measure of the responsiveness
of the quantity demanded of a good to a change in the
price of that good
4
Example 4.2
 The price of pork falls by 2% and the quantity
demanded increases by 6%
 Then the price elasticity of demand for pork is
6%
-2%
= -3
Percentage change in quantity demanded
Percentage change in price
5
Example 4.3.
 If a 1 percent rise in the price of shelter caused a 2
percent reduction in the quantity of shelter demanded,
the price elasticity of demand for shelter would be
-2%
1%
= -2
6
Price Elasticity of Demand
 Measuring Price Elasticity of Demand
Percentage change in quantity demanded
Percentage change in price
 Observations
 Price elasticity of demand will always be negative (i.e., an
inverse relationship between price and quantity).
 For convenience sometimes we drop the negative sign.
7
Price Elasticity of Demand
Percentage Change in Quantity Demanded
Percentage Change in Price
Unit elastic
inelastic
Elastic
-3
-2
-1
Price elasticity
0 of demand
8
Example 4.4.
What is the elasticity of demand for sushi?
 Originally
 Price = $10/piece
 Quantity demanded = 400 pieces/day
 New
 Price = $9.7/piece
 Quantity demanded = 404 pieces/day, then
(404 - 400)/400
(9.7 - 10)/10
=
1%
-3%
=
-1
3
Inelastic!
9
Example 4.5. What is the elasticity of Hong
Kong Disney passes?
 Originally
 Price = $1600
 Quantity demanded = 10,000 passes/year
 New
 Price = $1520
 Quantity demanded = 12,000 passes/year, then
(12000 - 10000)/10000
(1520 - 1600)/1600
=
20%
-5%
= -4
Elastic!
10
Determinants of Price Elasticity of Demand
1. Availability of substitutes - the higher the number of substitutes,
the more responsive people are to price changes. Elasticity
increases with availability of substitutes.
2. Proportion of income used to buy the good - the higher the
fraction of income spent on a good, the higher is elasticity.
3. Temporary versus permanent change in price - if the price change
is temporary people react more to it. Suppose there is a one-day
sale - the response of quantity demanded that day will be much
greater than the response to quantity when prices are expected
to decrease permanently.
4. Short run versus long run - elasticity increases over time. If there
is a sudden price increase, individuals will take some time to find
other substitutes and make suitable changes. So quantity will not
respond much in the short run.
11
Example 4.6.
Price Elasticity Estimates for Selected Products
Good or service
Price elasticity
Green peas
-2.80
Restaurant meals
-1.63
Automobiles
-1.35
Electricity
-1.20
Beer
-1.19
Movies
-0.87
Air travel (foreign)
-0.77
Shoes
-0.70
Coffee
-0.25
Theater, opera
-0.18
Why is the price elasticity of demand more than 14 times larger
for green peas than for theater and opera performances?
12
A Graphical Interpretation
of Price Elasticity
 For small changes in price
ΔQ Q
Price elasticity   
 ( ΔQ / ΔP )( P / Q)
ΔP P
Where Q is the original quantity and P is the original
price.
13
A Graphical Interpretation
of Price Elasticity
 For small changes in price
ΔQ Q
ΔP P
 P  1 

Pr ice elasticity at A   
Q
slope
 

A
P
Price
Price elasticity   
P
P-
P
Q
D
Q
Q+
Quantity
Q
14
Example 4.7. Calculating Price Elasticity of Demand
slope 
20
D
vertical intercept
 20

 4
horizontal intercept
5
16
8 1
8
2
A  x


3 4
12
3
Price
12
A
8
Question:
What is the price elasticity
of demand when P = $8?
4
1
2
3
4
5
Quantity
15
Example 4.8. Price Elasticity and the
Steepness of the Demand Curve
What is the price elasticity of Demand for D1 & D2 when P = $4?
12
D1


1
 4  1 
D1    



12
2
4
6



 4  1 
D2    
 2


6
4
 12 
Price
6
Observation
If two demand curves
have a point in
common, the steeper
curve must be less
elastic with respect to
price at that point.
4
D2
4
6
Quantity
12
16
Example 4.9. Price Elasticity Regions along
a Straight-Line Demand Curve
12
When P = $4
When P = $1


 4  1 
D    
 2


6
4
 12 


1
 1  1 
D    

5
 10  6 
 12 
Price
6
4
Observation
Price elasticity varies at every
point along a straight-line
demand curve
D
1
4
6
10
12
Quantity
17
Price Elasticity Regions along
a Straight-Line Demand Curve
Observation
Price elasticity varies at
every point along a straightline demand curve
a
  1
Price
  1
  1
a/2
b/2
Quantity
b
18
Perfectly Elastic Demand Curve
Perfectly elastic
Price
demand (elasticit y  - )
Quantity
If the price increases a little, the quantity demanded will drop to zero.
If the price drops a little, the quantity demanded will increase a lot.
19
Perfectly Inelastic Demand Curve
Perfectly inelastic
Price
demand (elasticity  0)
Quantity
The quantity demanded is not responsive to any change in price.
20
Elasticity and Total Expenditure
 Total Expenditure = P x Q
 Market demand measures the quantity (Q) at each
price (P)
 Total Expenditure = Total Revenue
21
Example 4.10. The Demand Curve for Movie Tickets
Price ($/ticket)
12
Price ($/ticket)
10
8
6
Total expenditure ($/day)
12
10
8
6
4
2
0
1000
1600
1800
1600
1000
0
0
4
2
0
1
2
3
4
5
6
Quantity (100s of tickets/day)
22
Total Expenditure as a Function of Price
Total revenue is at a maximum at the midpoint
on a straight-line demand curve.
12
1,800
1,600
Total expenditure ($/day)
Price ($/ticket)
10
8
6
4
2
0
1
2
3
4
5
Quantity (100s of tickets/day)
6
1,000
0
2
4
6
8
10
12
Price ($/ticket)
23
Example 4.11.
 What happens to total expenditure on shelter when the
price is reduced from $12/sq yd to $10/sq yd?
Price ($/sq yd)
16
14
12 E
10
8
6
4 F
2
0 
Reduction in expenditure from
sale at a lower price
Increase in expenditure from
additional sales
When price goes down,
total expenditure will
rise [fall] if the gain
from sale of additional
units is larger [smaller]
than the loss from the
sale of existing units at
the lower price.
G
4 6
8 10 1214 16
Quantity (sq yds/wk)
24
Example 4.12. Elasticity and Total Expenditure
 Should a rock band raise or lower its price to increase total
revenue?
 Assume P=$20, Q=5,000, and =-3.
 Total revenue = $20 x 5,000 = $100,000/week
 If P is increased 10%,
 Q will decrease 30%
 Total revenue = $22 x 3,500 = $77,000/week
 If P is lowered 10%,
 Q will increase 30%
 Total revenue = $18 x 6,500 = $177,000/week
Note: Cost does not change with Q. Maximizing total revenue is the
same as maximizing total profit.
25
Elasticity and Total Expenditure
If demand is...
A price increase will...
A price reduction will...
reduce total
expenditure
elastic
  
P x
Q
=
increase total
expenditure
P
Q
increase total
expenditure
inelastic
  
Px
Q =
PQ
P
x
Q = PQ
reduce total
expenditure
Px
Q =
PQ
26
A demand curve with constant elasticity
P
Unitary elastic: PxQ=k
Q
27
Example 4.13.
 A director of a big bus company said, "For each 1 percent fare
hike, we lose 0.2 percent of our riders." We can conclude that:
a. a fare increase will increase total revenue.
b. demand for bus service will go up as fares increase.
c. demand is price elastic.
d. a 10 percent fare hike will produce a 20 percent reduction in riders.
e. the price elasticity is -5.
 We are told that when DP/P = 1%, DQ/Q = -0.2%.
 Elasticity = (DQ/Q)/(DP/P) = -0.2.
(inelastic)
So answer a is correct. A fare increase will increase total revenue.
28
Cross-Price Elasticity of Demand
 The percentage by which quantity demanded of the first
good changes in response to a 1 percent change in the
price of the second good
 Substitute Goods
When the cross-price elasticity of demand is
positive
 Complement Goods
When the cross-price elasticity of demand is
negative
29
Income Elasticity of Demand
 The percentage by which quantity demanded changes
in response to a 1 percent change in income
 Normal Goods
Income elasticity is
positive
 Inferior Goods
Income elasticity is
negative
30
The Price Elasticity of Supply
 Price Elasticity of Supply
 The percentage change in the quantity supplied that
occurs in response to a 1 percent change in price
DQ Q
Price elasticity of supply 
DP P
 P  1 

Price elasticity of supply   
 Q  slope 
31
Example 4.14. A Supply Curve for Which Price
Elasticity Declines as Quantity Rises
A  8 21 2  2
S
B
10
A
Observations:
1. Elasticity >0
2. Elasticity >1 for linear supply curve
that has a positive Y-intercept.
3. Elasticity decreases as quantity
increases.
Price
88
4
0
5
B  10 31 2  
3
22
3
Quantity
32
Example 4.15. A Supply Curve for Which Price
Elasticity is unity
A  4 / 1212 / 4  1
S
B  5 1515 5  1
B
5
Q
Price
4
0
P
A
12
The price elasticity of supply
will always equal 1 at any
point along a straight-line
supply curve that passes
through the origin.
15
Quantity
33
A challenge
 Construct an example of supply curve so that price
elasticity increases as quantity rises.
34
A Perfectly Inelastic Supply Curve
What is the price elasticity of supply of land within Central?
Price ($/acre)
S
Elasticity = 0 at every
point along a vertical
supply curve
0
Quantity of land in Central
(1,000s of acres)
35
Price (cents/cup)
A Perfectly Elastic Supply Curve
If MC is constant, then the
price elasticity of supply at every point
along a horizontal supply curve is infinite
S
14
0
Quantity of lemonade
(cups/day)
36
Determinants of Supply Elasticity
1.
2.
3.
4.
Flexibility of inputs
Mobility of inputs
Ability to produce substitute inputs
Time
37
Example 4:16. Why are gasoline prices so much more
volatile than car prices?
 Differences in markets
 Demand for gasoline is more inelastic
 Gasoline market has larger and more frequent supply
shifts
38
Greater Volatility in
Gasoline Prices than in Car Prices
S’
Gasoline
Price ($/gallon)
S
1.69
1.02
D
0
6 7.2
Quantity
(millions of gallons/day)
39
Greater Volatility in
Gasoline Prices than in Car Prices
Cars
Price ($1,000s/car)
S’
S
17
16.4
D
11 12
Quantity
(1,000s of cars/day)
Cars
40
Example 4.17. Earnings of YAO Ming
 Why does YAO Ming earn an annual basketball salary of
some US$4.5 million?
YAO Ming is a unique and essential inputs, an example of
ultimate supply bottleneck.
41
Other examples of unique and essential inputs
 Dr. Joseph YAM?
 Mr Mirko Saccani?
“The fee was agreed to be $120 million for eight years'
of unlimited [Latini]dance lessons and competitions,
and Mr Saccani would be her dancing partner and
instructor by such agreements.” (SCMP 2006-06-14,
CITY3)
Who was she, the plaintiff?
Mimi Monica Wong, head of HSBC's private banking in Asia.
42
Example 4.18. So why are the fares so different?
If you start in Kansas City and you fly to Honolulu round-trip, the
fare is a lot lower than if you start the same trip in Honolulu and fly
to Kansas City round-trip. Passengers travel on same planes,
consuming the same fuel, the same in-flight amenities, and so on.
So why are the fares so different?
By Karen Hittle, a student of
Robert Frank.
43
Example 4.18. So why are the fares so different?
 If you are starting in Kansas City and going to Honolulu, you are
probably going on vacation. You could go lots of different places.
You could go to Florida, to Barbados, to Cancun. Because
vacationers have many destinations to choose from, airlines must
compete fiercely for their business. Given economies of scale
inherent in larger aircraft, carriers have a strong incentive to fill
additional seats by targeting lower prices to the people who are
more sensitive to price – vacationers.
 But if you are starting in Honolulu on a trip to Kansas City, you are
probably not a vacationer. More likely, you either have business or
family reasons for traveling. So you are probably not shopping for
a destination if you are going to Kansas City.
 That is why the fares are so different.
44
Example 4.19.
Other things being equal, the increase in rents that occur after
rent control are abolished is smaller when
A. the own price elasticity of demand for rental homes is price
inelastic.
B. the own price elasticity of demand for rental homes is price
elastic.
C. the own price elasticity of demand for rental homes has unitary
price elasticity.
D. rented homes and owned homes are substitutes.
E. rented homes and owned homes are complements.
45
Example 4.19.
 Rent control is a form of PRICE CEILING.
 Price Ceiling is set at a price LOWER than the market equilibrium price.
 Excess demand (i.e., shortage) results.
P
D
S
Trading Loci
Pe
Price Ceiling
Q
46
Example 4.19.
 And when the Price Ceiling is lifted, the market equilibrium quantity
and price should be restored eventually.
 Price (rent) should increase.
P
D
S
Because supply is
upward sloping,
↑P → ↑ TR
Price Ceiling
Q
47
Example 4.19.
Relative inelastic
P
D
S
Pe
Price Ceiling
Relative elastic
Q
Hence, the increase in rents that occur AFTER abolishing rent
control is smaller when
(B) The own price elasticity of demand is elastic.
48
End
49
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