1 chapter 4 elasticity elasticity. 2 example 4.1 will the china’s trade balance (export –...
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Chapter 4Elasticity
Elasticity
2
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.
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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
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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
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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
Percentage change in quantity demanded
Percentage change in price
6%
-2%= -3
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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
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Price Elasticity of Demand
Measuring Price Elasticity of Demand
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.
Percentage change in quantity demanded
Percentage change in price
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Price Elasticity of Demand
0
Price elasticityof demand
Elastic
Unit elastic
inelastic
-1-2-3
Price in Change Percentage
DemandedQuantity in Change Percentage
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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
Inelastic!
(404 - 400)/400
(9.7 - 10)/10=
1%
-3%=
-13
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Example 4.5. What is the elasticity of Hong Kong Disney passes?
Originally Price = $1600Quantity demanded = 10,000 passes/year
New Price = $1520Quantity demanded = 12,000 passes/year, then
Elastic!
(12000 - 10000)/10000
(1520 - 1600)/1600=
20%
-5%= -4
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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.
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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?
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A Graphical Interpretationof Price Elasticity
For small changes in price
)/)(/( elasticity Price QPΔPΔQPΔP
QΔQ
Where Q is the original quantity and P is the original price.
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A Graphical Interpretationof Price Elasticity
For small changes in price PΔP
QΔQ elasticity Price
Quantity
Pri
ce
P
D
A
Q
P - P
Q + Q
Q
P
slopeQ
P A
1 at elasticity icePr
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Example 4.7. Calculating Price Elasticity of Demand
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Quantity
Pri
ce
1
D
A
2 3 4 5
16
12
8
4
45
20
intercept horizontal
intercept vertical
slope
3
2
12
8
4
1
3
8
xA
Question:What is the price elasticityof demand when P = $8?
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Example 4.8. Price Elasticity and the Steepness of the Demand Curve
D1
D2
12
4 6 12
6
4
Quantity
Pri
ce
What is the price elasticity of Demand for D1 & D2 when P = $4?
2
1
612
1
4
41
D
2
1261
4
42
D
ObservationIf two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point.
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Example 4.9. Price Elasticity Regions along a Straight-Line Demand Curve
12
D
4 6 10 12
6
4
1
When P = $1
Quantity
Pri
ce
5
1
1261
10
1
D
2
1261
4
4
D
When P = $4
ObservationPrice elasticity varies at every point along a straight-line demand curve
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Price Elasticity Regions along a Straight-Line Demand Curve
Quantity
Pri
ce
b/2
a/2
a
b
1
1
1
ObservationPrice elasticity varies at every point along a straight-line demand curve
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Perfectly Elastic Demand Curve
Quantity
Pri
ce
)- y (elasticit demand
elastic
Perfectly
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.
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Perfectly Inelastic Demand Curve
Quantity
Pri
ce
)0 y (elasticit demand
inelasticPerfectly
The quantity demanded is not responsive to any change in price.
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Elasticity and Total Expenditure
Total Expenditure = P x QMarket demand measures the quantity (Q) at
each price (P) Total Expenditure = Total Revenue
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Example 4.10. The Demand Curve for Movie Tickets
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Quantity (100s of tickets/day)
Pri
ce (
$/ti
cket
)
1 3 4 5 6
10
8
6
4
2
0 2
Total expenditure ($/day)
12
Price ($/ticket)
010 10008 16006 18004 16002 1000
0 0
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Total Expenditure as a Function of Price
1,800
Price ($/ticket)
To
tal
ex
pe
nd
itu
re (
$/d
ay
)
2 6 8 10 12
1,600
1,000
0 4
12
Quantity (100s of tickets/day)
Pri
ce
($
/tic
ke
t)
1 3 4 5 6
10
8
6
4
2
0 2
Total revenue is at a maximum at the midpoint on a straight-line demand curve.
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Example 4.11.
What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd?
0
161412108642
Price ($/sq yd)
(sq yds/wk) 4 6 8 10 12
Reduction in expenditure from sale at a lower price
Increase in expenditure from additional sales
F
E
G
14 16Quantity
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.
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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.
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Elasticity and Total Expenditure
If demand is... A price increase will... A price reduction will...
elastic
inelastic
reduce totalexpenditure
increase totalexpenditure
increase totalexpenditure
reduce totalexpenditure
P Q P Qx = P Q P Qx =
P PQx =QP Q PQx =
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A demand curve with constant elasticity
Q
P
Unitary elastic: PxQ=k
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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 P/P = 1%, Q/Q = -0.2%. Elasticity = (Q/Q)/(P/P) = -0.2. (inelastic)So answer a is correct. A fare increase will increase total revenue.
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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 goodSubstitute Goods
When the cross-price elasticity of demand is positive
Complement GoodsWhen the cross-price elasticity of demand is
negative
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Income Elasticity of Demand
The percentage by which quantity demanded changes in response to a 1 percent change in incomeNormal Goods
Income elasticity is positive
Inferior GoodsIncome elasticity is
negative
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The Price Elasticity of Supply
Price Elasticity of SupplyThe percentage change in the quantity
supplied that occurs in response to a 1 percent change in price
PP
QQ supply of elasticity Price
slope
1
Q
P supply of elasticity Price
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Example 4.14. A Supply Curve for Which Price Elasticity Declines as Quantity Rises
2
8A
22128 A
3
10B
3
521310 B
Quantity
Pri
ce
0
4
S
8
2
Observations:1. Elasticity >02. Elasticity >1 for linear supply
curve that has a positive Y-intercept.
3. Elasticity decreases as quantity increases.
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Example 4.15. A Supply Curve for Which Price Elasticity is unity
S
15
5B
P
Q
12
4A
Quantity
Pri
ce
0
The price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin.
1515155 B
14/1212/4 A
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A challenge
Construct an example of supply curve so that price elasticity increases as quantity rises.
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A Perfectly Inelastic Supply Curve
Quantity of land in Central
(1,000s of acres)
Pri
ce (
$/ac
re)
0
S
Elasticity = 0 at everypoint along a verticalsupply curve
What is the price elasticity of supply of land within Central?
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A Perfectly Elastic Supply Curve
Quantity of lemonade
(cups/day)
Pri
ce (
cen
ts/c
up
)
0
14 S
If MC is constant, then theprice elasticity of supply at every pointalong a horizontal supply curve is infinite
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Determinants of Supply Elasticity
1. Flexibility of inputs2. Mobility of inputs3. Ability to produce substitute inputs4. Time
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Example 4:16. Why are gasoline prices so much more volatile than car prices?
Differences in marketsDemand for gasoline is more inelasticGasoline market has larger and more frequent
supply shifts
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Greater Volatility in Gasoline Prices than in Car Prices
Quantity(millions of gallons/day)
Pri
ce (
$/g
allo
n)
0 6
1.69
S’
D
1.02
7.2
S
Gasoline
40
Greater Volatility in Gasoline Prices than in Car Prices
Pri
ce (
$1,0
00s/
car)
D
17
S’
11Quantity
(1,000s of cars/day)Cars
16.4
12
S
Cars
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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.
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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.
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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.
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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.
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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.
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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
Q
D S
Pe
Price Ceiling
Trading Loci
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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
Q
D S
Price Ceiling
Because supply is upward sloping,↑P → ↑ TR
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P
Q
D S
Pe
Price Ceiling
Relative inelastic
Relative elastic
Hence, the increase in rents that occur AFTER abolishing rent control is smaller when(B) The own price elasticity of demand is elastic.
Example 4.19.
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End