彈性(elasticity)
彈性的定義
彈性的種類
需求彈性
供給彈性
所得彈性
交叉彈性
彈性與支出
彈性與市場干預之效果
彈性
 對“反應”的精確衡量
 … allows us to analyze supply and demand with
greater precision.
 … is a measure of how much buyers and sellers
respond to changes in market conditions
 衡量數量變動敏感的指標
 (price elasticity of demand，income elasticity)
需求的價格彈性
Price Elasticity of Demand
當價格變動百分之一時，需求量改
變的百分比
Percentage change in quantity demanded
Price elasticity of demand =
Percentage change in price
Price Elasticity of Demand
 The price falls to $19.50
and the quantity
demanded increases to
11 pizzas an hour.
The price falls by $1 and
the quantity demanded
increases by 2 pizzas an
hour.
Price Elasticity of Demand



The average price is
$20 and the average
quantity demanded is
10 pizzas an hour.
價格的弧彈性: 以平
均價格與需求量為
參考值
通常用於兩點差距
較大時
Price Elasticity of Demand


The percentage change
in quantity demanded,
%DQ, is calculated as
DQ/Qave, which is 2/10 =
1/5.
The percentage change
in price, %DP, is
calculated as DP/Pave,
which is $1/$20 = 1/20.




The percentage change in quantity demanded, %DQ, is
calculated as DQ/Qave, which is 2/10 = 1/5.
The percentage change in price, %DP, is calculated as
DP/Pave, which is $1/$20 = 1/20.
The price elasticity of demand is (1/5)/(1/20) = 20/5 = 4.
當價格變動百分之一時，需求量改變百分之四
The Midpoint Method: A Better
Way to Calculate Percentage
Changes and Elasticities
 The midpoint formula is preferable when
calculating the price elasticity of demand
because it gives the same answer regardless
of the direction of the price change.
Price elasticity of demand =
(Q2  Q1 ) /[(Q2  Q1 ) / 2]
( P2  P1 ) /[( P2  P1 ) / 2]
Price Elasticity of Demand
 弧彈性
 The Midpoint
Method
 ΔQ/(Q1+Q2)
 ΔP/(P1+P2)
Price Elasticity of Demand




By using the average price and average quantity, we get
the same elasticity value regardless of whether the price
rises or falls.
The ratio of two proportionate changes is the same as the
ratio of two percentage changes.
The measure is units-free because it is a ratio of two
percentage changes and the percentages cancel out.
Changing the units of measurement of price or quantity
leave the elasticity value the same.
Computing the Price Elasticity
of Demand
(100  50)
Price
ED 
$5
4
(4.00  5.00)
(100  50)/2
(4.00  5.00)/2
Demand
67 percent

 3
 22 percent
0
50
100 Quantity
Demand is price elastic.
Price Elasticity of Demand


The formula yields a negative value, because
price and quantity move in opposite directions.
But it is the magnitude, or absolute value, of the
measure that reveals how responsive the quantity
change has been to a price change.
價、量通常呈反方向變動，因此將彈性取絕
對值
彈性 Elasticity (ε)
 價格彈性 Price Elasticity


弧彈性 Arc Elasticity =
點彈性 Point Elasticity =
DQ
Q1  Q2
DP
P1  P2
Q P

P Q
彈性 Elasticity (ε)
 點彈性 Point Elasticity = Q  P
P Q

Q

即為需求線斜率的倒數(取絕對值)
P
 任一點 p q，需求線愈陡直，斜率愈大，
彈性愈小
彈性反映了需求的本質
 美國聯邦政府為安全考量強制父母為嬰兒
買票，有多少人會改搭汽車?
Price Elasticity of Demand
 Inelastic and Elastic Demand


Demand can be inelastic, unit elastic, or elastic,
and can range from zero to infinity.
If the quantity demanded doesn’t change when
the price changes, the price elasticity of demand
is zero and the good has a perfectly inelastic
demand. 完全無彈性
Price Elasticity of Demand


完全無彈性
a vertical demand
curve, elasticity =0
Price Elasticity of Demand
If the percentage change in the
quantity demanded equals the
percentage change in price, the
price elasticity of demand
equals 1 and the good has unit
elastic demand.
價格彈性=1
(Note that the demand curve is
not linear.)

The Price Elasticity of Demand
Elastic Demand: Elasticity Is Greater Than 1
Price
$5
4
Demand
1. A 22%
increase
in price . . .
0
50
100
Quantity
2. . . . leads to a 67% decrease in quantity demanded.
Price Elasticity of Demand




Between the two previous cases, the percentage change
in the quantity demanded is smaller than the percentage
change in price so that the price elasticity of demand is
less than 1 and the good has inelastic demand.
價格彈性小於1
If the percentage change in the quantity demanded is
infinitely large when the price barely changes, the price
elasticity of demand is infinite and the good has
perfectly elastic demand.
彈性無窮大
Price Elasticity of Demand
Figure 4.3c illustrates
the case of perfectly
elastic demand—a
horizontal demand
curve.
彈性無窮大

Total Revenue and the Price
Elasticity of Demand
 Total revenue is the amount paid by buyers and
received by sellers of a good.
 Computed as the price of the good times the
quantity sold.
TR  P  Q
Price
Figure 2 Total Revenue
When the price is $4, consumers
will demand 100 units, and spend
$400 on this good.
$4
P × Q = $400
(revenue)
P
0
Demand
100
Q
Quantity
Elasticity and Total Revenue
along a Linear Demand Curve
 With an inelastic demand curve, an increase
in price leads to a decrease in quantity that is
proportionately smaller. Thus, total revenue
increases.
Price
Figure 3 How Total Revenue
Changes When Price Changes:
Inelastic Demand
Price
… leads to an Increase in
total revenue from $100 to
$240
An Increase in price from $1
to $3 …
$3
Revenue = $240
$1
Demand
Revenue = $100
0
100
Quantity
Demand
0
80
Quantity
Elasticity and Total Revenue along a
Linear Demand Curve
 With an elastic demand curve, an increase in
the price leads to a decrease in quantity
demanded that is proportionately larger. Thus,
total revenue decreases.
Price
Figure 3 How Total Revenue
Changes When Price Changes:
Elastic Demand
Price
… leads to an decrease in
total revenue from $200 to
$100
An Increase in price from $4
to $5 …
$5
$4
Demand
Demand
Revenue = $200
0
50
Revenue = $100
Quantity
0
20
Quantity
Note that with each price increase, the Law of Demand still holds – an
increase in price leads to a decrease in the quantity demanded. It is the
change in TR that varies!
Elasticity of a Linear Demand
Curve
Price Elasticity of Demand
 Elasticity Along a
Straight-Line
Demand Curve
 一條直線需求線上
每一點彈性不同
Figure 4 Elasticity of a Linear
Demand is elastic; When price increases from
Demand
$5, TR declines from
demand
is responsive$4
to toCurve
Price
changes in price.
$24 to $20.
Elasticity is > 1 in this range.
$7
6
5
4
Elasticity
is is<inelastic;
1 in this
range.
Demand
demand
is
3
not very responsive to changes
When price increases from
in price.
$2 to $3, TR increases from
$20 to $24.
2
1
0
2
4
6
8
10
12
14
Quantity
Price Elasticity of Demand
廠商的總收益(消費者的支出)和消費者的需
求彈性有關
彈性>1 p TR
 彈性 =1 p
TR 不變
 彈性<1 p
TR

Price Elasticity of Demand




The total revenue test is a method of estimating the price
elasticity of demand by observing the change in total
revenue that results from a price change (when all other
influences on the quantity sold remain the same).
If a price cut increases total revenue, demand is elastic.
If a price cut decreases total revenue, demand is inelastic.
If a price cut leaves total revenue unchanged, demand is unit
elastic.
Price Elasticity of Demand

At $12.50, demand is
unit elastic and total
revenue stops increasing.
As the price falls from
$12.50 to zero, demand
is inelastic, and total
revenue decreases.
Price Elasticity of Demand
In part b (shown here),
as the quantity
increases from zero to
25, demand is elastic,
and total revenue
increases.
At 25, demand is unit
elastic, and total revenue is
at its maximum.

As the quantity increases
from 25 to 50, demand is
inelastic, and total
revenue decreases.
General form
 Demand: P=a+ bQ
 TR=(a+ bQ)Q=aQ+ bQ2
 MR=a+2bQ
Expenditure and Elasticity



If your demand is elastic, a 1 percent price cut increases the
quantity you buy by more than 1 percent and your
expenditure on the item increases.
If your demand is inelastic, a 1 percent price cut increases
the quantity you buy by less than 1 percent and your
expenditure on the item decreases.
If your demand is unit elastic, a 1 percent price cut increases
the quantity you buy by 1 percent and your expenditure on
the item does not change.
Price Elasticity of Demand
Demand tends to be more elastic:
the larger the number of close substitutes.
 if the good is a luxury/佔所得的比重.
 the more narrowly defined the market

個別廠商

vs. 產業.
the longer the time period
替代的可能性
The closeness of substitutes +
The closer the substitute for a good or service, the
more elastic is the demand for it.
Necessities, such as food or housing, generally have
inelastic demand.必須品
Luxuries, such as exotic vacations, generally have
elastic demand.奢侈品

佔所得的比率

The greater the proportion of income consumers
spend on a good, the larger is its elasticity of
demand. +
距價格改變的時間

The more time consumers have to adjust to a
price change, or the longer that a good can be
stored without losing its value, the more elastic is
the demand for that good. +
Price Elasticity of Demand

Figure 4.6 shows
how the elasticity of
demand for food
varies with the
proportion of income
spent on food in
different countries.
所得彈性(Income elasticity)
 當所得改變百分之一，財貨需求量變動的
百分比


The income elasticity of demand measures how
the quantity demanded of a good responds to a
change in income, other things being equal.
The formula for calculating the income elasticity
of demand is:
Percentage change in quantity demanded
Percentage change in income
More Elasticities of Demand





If the income elasticity of demand is greater than 1,
demand is income elastic and the good is a luxury good .
奢侈財
Examples include sports cars, furs, and expensive foods
If the income elasticity of demand is greater than zero but
less than 1, demand is income inelastic and the good is a
normal good .正常財.
Examples include food, fuel, clothing, utilities, and
medical services
If the income elasticity of demand is less than zero
(negative), the good is an inferior good.劣等財
More Elasticities of Demand

Figure 4.8 shows
estimates of the
income elasticity for
food in different
countries. A higher
average income is
associated with a
lower income
elasticity of demand
for food.
Cross Elasticity of Demand
交叉彈性



The cross elasticity of demand is a measure of the
responsiveness of demand for a good to a change in the
price of a substitute替代財or a complement互補財, other
things remaining the same.
當一貨價格變動百分之一，其他財貨需求量(供給量)變動的百分
比
The formula for calculating the cross elasticity is:
Percentage change in quantity demanded
Percentage change in price of substitute or complement
交叉彈性

The cross elasticity of demand for a substitute is
positive.
 替代財(substitutes)：當一物價格下降，另
一物需求量下降，則兩者互為代替品，
 例：咖啡vs茶；糖vs代糖
交叉彈性



The cross elasticity of demand for a complement
is negative.
互補財(complements)：當一物價格下降，另
一物需求量上升，則兩者互為互補品
例：咖啡vs奶精
More Elasticities of Demand

Figure 4.7 shows the
increase in the quantity of
pizza demanded when the
price of a burger (a
substitute for pizza) rises.
The figure also shows the
decrease in the quantity of
pizza demanded when the
price of a soft drink (a
complement of pizza) rises.
為什麼考慮彈性？
 改變價格時，顧客如何反應？（價位該定
在何處）
 改變價格時，對手如何反應？（改變那一
個市場）
 改變價格時，自己的收益如何改變？
 收益改變後，情況可維持多久？
彈性大小與均衡變動
 比較靜態分析(Comparative static analysis)：
探討市場均衡如何因其他條件改變而變動
的研究




需求彈性小
當供給增加 Q*變動小
需求彈性大
當供給增加 Q*變動大
P*變動大
P*變動小
彈性的差異影響均衡價、量
的變化
Price Elasticity of Supply
 供給的價格彈性
(Price elasticity of
supply)：當價格變動
百分之一，供給量變
動的百分比
 In Figure 4.9a, a
change in demand
brings a small increase
in the quantity
supplied and a large
rise in price.
Price Elasticity of Supply

In Figure 4.9b, a
change in demand
brings a large
increase in the
quantity supplied
and a small rise in
price.
Price Elasticity of Supply

The contrast between
the two outcomes in
Figure 4.9 highlights
the need for a
measure of the
responsiveness of the
quantity supplied to
a price change.
供給的價格彈性
Elasticity of Supply

The elasticity of supply measures the responsiveness of
the quantity supplied to a change in the price of a good
when all other influences on selling plans remain the
same.
Percentage change
in quantity supplied
Price elasticity of supply =
Percentage change in price
Elasticity of Supply




Figure 4.10 on the next slide shows three cases
of the elasticity of supply.
Supply is perfectly inelastic if the supply curve is
vertical and the elasticity of supply is 0.
Supply is unit elastic if the supply curve is linear
and passes through the origin. (Note that slope is
irrelevant.)
Supply is perfectly elastic if the supply curve is
horizontal and the elasticity of supply is infinite.
Elasticity of Supply
“Perfectly inelastic” (one extreme)
0%
% change in Q
Price elasticity
=
=
of supply
% change in P
P
S curve:
vertical
S
P2
Sellers’
price sensitivity:
0
Elasticity:
0
10%
=0
P1
P rises
by 10%
Q1
Q changes
by 0%
Q
“Inelastic”
< 10%
% change in Q
Price elasticity
<1
=
=
of supply
10%
% change in P
P
S curve:
relatively steep
S
P2
Sellers’
price sensitivity:
relatively low
Elasticity:
<1
P1
P rises
by 10%
Q1 Q2
Q rises less
than 10%
Q
“Unit elastic”
% change in Q
Price elasticity
=
=
of supply
% change in P
10%
=1
P
S curve:
intermediate slope
S
P2
Sellers’
price sensitivity:
intermediate
Elasticity:
=1
10%
P1
P rises
by 10%
Q1
Q2
Q rises
by 10%
Q
“Elastic”
> 10%
% change in Q
Price elasticity
>1
=
=
of supply
10%
% change in P
P
S curve:
relatively flat
S
P2
Sellers’
price sensitivity:
relatively high
Elasticity:
>1
P1
P rises
by 10%
Q1
Q2
Q rises more
than 10%
Q
“Perfectly elastic” (the other
extreme)
any %
% change in Q
Price elasticity
= infinity
=
=
of supply
0%
% change in P
P
S curve:
horizontal
Sellers’
price sensitivity:
extreme
Elasticit
y:infinity
S
P2 = P1
P changes
by 0%
Q1
Q2
Q changes
by any %
Q
Elasticity of Supply
 The Factors That Influence the Elasticity of Supply






The elasticity of supply depends on
Resource substitution possibilities +
The easier it is to substitute among the resources used to
produce a good or service, the greater is its elasticity of
supply.生產要素、生產過程變通、替代的可能
紅茶與綠茶
The time frame for supply decisions
The more time that passes after a price change, the
greater is the elasticity of supply.時間的長短+
Elasticity of Supply





The time frame for supply decisions
The more time that passes after a price change,
the greater is the elasticity of supply.
Momentary supply is perfectly inelastic. The
quantity supplied immediately following a price
change is constant.
Short-run supply is somewhat elastic.
Long-run supply is the most elastic.
 The supply schedule
for chocolate chip
cookies is as given in
the table above. As the
price rises, the
elasticity of supply
decreases.
 P 1.5
P=2.5
 3/2
5/4
Price
(dollars)
Quantity
supplied
1
10
2
30
3
50
4
70
變動緣起
分析對象
商品本身價格
需求量
供給量
需求價格彈性
供給價格彈性
其他商品價格
需求交叉彈性
供給交叉彈性
所得改變
需求所得彈性
供給所得彈性
彈性大小與均衡變動
 比較靜態分析(Comparative static analysis)：
探討市場均衡如何因其他條件改變而變動
的研究




需求彈性小 當供給增加
Q*變動小 P*變動大
需求彈性大 當供給增加
Q*變動大 P*變動小
 所以需求或供給彈性大，均衡改變多反
應在價格Q
 需求或供給彈性小，均衡改變多反應在
價格P
Can Good News for Farming
Be Bad News for Farmers?
 Examine whether the supply or demand
curve shifts.
 Determine the direction of the shift of the
curve.
 Use the supply-and-demand diagram to see
how the market equilibrium changes.
Figure 7 An Increase in Supply
in the Market for Wheat
Price of
Wheat
2. . . . leads
to a large fall
in price . . .
1. When demand is inelastic,
an increase in supply . . .
S1
S2
$3
2
Demand
0
100
110
Quantity of
Wheat
3. . . . and a proportionately smaller
increase in quantity sold. As a result,
revenue falls from $300 to $220.
Compute the Price Elasticity of
Demand When There Is a
Change in Supply
100  110
(100  110) / 2
ED 
3.00  2.00
(3.00  2.00) / 2
0.095

 0.24
0.4
Demand is inelastic.
Why Did OPEC Fail to Keep
the Price of Oil High?
 Supply and Demand can behave differently
in the short run and the long run


In the short run, both supply and demand for oil
are relatively inelastic
But in the long run, both are elastic
Production outside of OPEC
 More conservation by consumers

Does Drug Interdiction Increase
or Decrease Drug-Related
Crime?
 Drug interdiction impacts sellers rather than
buyers.


Demand is unchanged.
Equilibrium price rises although quantity falls.
 Drug education impacts the buyers rather
than sellers.


Demand is shifted.
Equilibrium price and quantity are lowered.
Figure 9 Policies to Reduce the
Use
of
Illegal
Drugs
Drug Education
Drug Interdiction
Price of Drugs
Price of Drugs
The demand for illegal
drugs is inelastic.
In each case, the change
D1price
in
S2
S1
S1
is the same.
D1
D2
Quantity of Drugs
Quantity of Drugs
Interdiction shifts the supply, while education shifts the demand.
The changes in quantities (and TR) are
remarkable. But in one market the price goes up.
And in the other it goes down.
實例分析1
以價制量
 1960年代煙酒進口公賣，但因需求彈性小，
抑制的消費量有限
P
D2
D1
Q2 Q1
Q
實例分析2
穀賤傷農
 稻米盛產則價格下降，因需求彈性小，
需求數量增加不多，農民總收入減少
D
P
P
S1
S1
S2
S2
Q
Q
實例分析3
物以稀為貴
 需求固定時，供給量減少，則價格上漲
P
P2
D
S2
S1
P1
Q
實例分析4
 租稅與轉嫁: 繳稅者未必是真正承擔稅負
的人
 租稅轉嫁：tax shift，需求彈性愈小，消費
者擔愈重，轉嫁愈嚴重
Taxes

The tax revenue
takes part of the
consumer surplus
and producer
surplus.


The decreased
quantity creates a
deadweight loss.
無謂的損失
P
D1
S2
tax
S1
P2
P1
需求彈性小
消費者承擔的稅負
較多
Q2
Q1
Q
P
D1
S2
D2
tax
S1
P2
P1
需求彈性小
消費者承擔的稅負
較多
Q2’ Q2 Q1
Q
政府對價量的直接管制
 數量管制：供需彈性愈小，供需價格差距
愈大黑市運作或其他機制會產生
 價格管制
Stabilizing Farm Revenues
 An Agricultural Market



The supply of farm products is heavily
influenced by natural forces (weather, insects,
etc.) beyond the control of farmers.
Consumer demand for farm products is inelastic.
These two characteristics combine to make the
market for farm products and farm revenues
volatile.
Stabilizing Farm Revenues



Figure 6.11(a) shows the
market for wheat.
Once the crop is planted,
supply is perfectly inelastic
along the momentary
supply curve MS0.
The price is $4 a bushel
and farm total revenue is
$80 billion.
Stabilizing Farm Revenues
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A poor harvest decreases supply.
Farmers lose $20 billion
of total revenue on the
decreased quantity sold.
But they gain $30
billion from the
higher price.
Because demand is
inelastic, total revenue
increases—to $90 billion.
Stabilizing Farm Revenues
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Now a bumper harvest
increases supply.
Farmers lose $40 billion of
total revenue on the original
quantity because the price
falls.
They gain only $10 billion
from the increased quantity.
Because demand is inelastic,
total revenue decreases—to
$50 billion.
Stabilizing Farm Revenues
 Speculative Markets in Inventories
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Speculative markets have developed for the inventories
of those farm products that can be stored over long
periods of time.耐久的農作因此產生投機市場
Inventory holders speculate by:
Buying for inventory when the expected future price
exceeds the current price.
Selling from inventory when the current price exceeds
the expected future price.
Stabilizing Farm Revenues
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Figure 6.12 shows how
inventory speculation
changes the outcome.
Supply is now perfectly
elastic at the price
expected by inventory
holders—supply curve S.
A poor harvest decreases
production but inventories
are sold off.
Stabilizing Farm Revenues
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A bumper crop increases
production, but some of
the extra output goes into
inventory.
The price is stabilized at
the inventory speculators’
expected price.
投機市場以存貨調節市
場價格與交易量
Stabilizing Farm Revenues
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In reality, speculation decreases but does not
completely eliminate price fluctuations.
減少價格波動
While speculation does not stabilize farmers’
revenues, it changes the effects of bumper
harvests and crop failures.
Farmers’ total revenues now increase with
bumper crops and decrease with crop failures.
 Price elasticity of demand measures how
much the quantity demanded responds to
changes in the price.
 Price elasticity of demand is calculated as the
percentage change in quantity demanded
divided by the percentage change in price.
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If a demand curve is elastic, total revenue falls
when the price rises.
If it is inelastic, total revenue rises as the price
rises.
 The income elasticity of demand measures
how much the quantity demanded responds
to changes in consumers’ income.
 The cross-price elasticity of demand
measures how much the quantity demanded
of one good responds to the price of another
good.
 The price elasticity of supply measures how
much the quantity supplied responds to
changes in the price.
 In most markets, supply is more elastic in the
long run than in the short run.
 The price elasticity of supply is calculated as
the percentage change in quantity supplied
divided by the percentage change in price.
 The tools of supply and demand can be
applied in many different types of markets.