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Chapter_05

第五章弹性及其应用Elasticity and Its Application

弹性Elasticity . . .

……是买者和卖者对市场环境变化作出反应的程度大小的一种度量方法

…is a measure of how much buyers and sellers respond to changes in market conditions

……使我们能够更精确地分析供给和需求

…allows us to analyze supply and demand with greater precision.

3需求的价格弹性

Price Elasticity of Demand

给定百分之一的价格变化，需求量变化的百分

数就是需求的价格弹性。

Price elasticity of demand is the percentage change in quantity demanded given a percent change in the price.

它衡量了一种物品的需求量对该物品价格变化

作出反应的程度大小。

It is a measure of how much the quantity demanded of a good responds to a change in the price of that good.

需求价格弹性的决定因素

Determinants of

Price Elasticity of Demand

必需品还是奢侈品

Necessities versus Luxuries

相近替代品的可获得性

Availability of Close Substitutes

市场的界定

Definition of the Market

时间范围

Time Horizon

需求价格弹性的决定因素

Determinants of

Price Elasticity of Demand

需求倾向于更富有弹性：

Demand tends to be more elastic :

如果该商品是奢侈品

if the good is a luxury. 相近替代品的个数越多

the larger the number of close substitutes. 市场界定得越狭隘

the more narrowly defined the market. 时间间隔越长

the longer the time period.

计算需求价格弹性

Computing the Price Elasticity

of Demand

用需求量变动的百分数除以价格变动的百分数，就计算出了需求的价格弹性

The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in price.

需求价格弹性

Price Elasticity of Demand =

Percentage Change in Quantity Demanded

Percentage Change in Price

需求量变化的百分数

价格变化的百分数

7计算需求价格弹性

Computing the Price Elasticity

of Demand

price

in change Percentage demanded

quatity in change Percentage demand of elasticity Price =

例：如果冰淇淋蛋卷的价格从2.00美元上升到2.20美元，你所购买的数量从10个下降到8个，那么你的需求弹性可以计算如下：

Example: If the price of an ice cream cone increases from $2.00to $2.20 and the amount you buy falls from 10 to 8 cones then your elasticity of demand would be calculated as:

(810)

100

20102

(2.20 2.00)10100

2.00

percent percent ?×?==??×8

运用中点公式计算需求价格弹性Computing the Price Elasticity of Demand Using the Midpoint

Formula

计算需求曲线上两点之间的需求价格弹性时一个恼人的问题：从A 点到B 点的弹性，与从B 点到A 点的弹性是不同的。

If you try calculate the price elasticity of demand between two points on a demand curve, you will quickly notice an annoying problem: The

elasticity from point A to point B seems different from the elasticity from point B to point A.

例如，考虑下面的数字

For example, consider these numbers: Point A: Price=$4, Quantity=120 Point B: Price=$6, Quantity=80

弹性分别是Elasticities are, A →B:

[(80-120)/120]/[(6-4)/4] =(-.33)/.5=-0.66 B →A:

[(120-80)/80]/[(4-6)/6]=.5/(-.33)=-1.5

运用中点公式计算需求价格弹性Computing the Price Elasticity of Demand Using the Midpoint

Formula

当计算需求价格弹性时，中点公式更为可取，因为无论变化的方向如何，它都能给出相同的答案The midpoint formula is preferable when

calculating the price elasticity of demand because it gives the same answer regardless of the direction of the change.

)/2]

P )/[(P P (P )/2]Q )/[(Q Q (Q =

Demand of Elasticity Price 12121212+?+?10

运用中点公式计算需求价格弹性Computing the Price Elasticity of Demand Using the Midpoint

Formula

在我们的例子中，A 点和B 点的中点是

In our example, the midpoint between point A and B is,

价格Price=$5, 数量Quantity=100.

无论方向，弹性均为1 Elasticity in both directions equals 1, A →B:

[(80-120)/100]/[(6-4)/5] =(-.2)/.2=-1 B →A:

[(120-80)/100]/[(4-6)/5]=.2/(-.2)=-111

计算需求价格弹性

Computing the Price Elasticity

of Demand

例：如果冰淇淋蛋卷的价格从2.00美元上升到2.20美元，而你购买的数量从10个下降到8个，运用中点公式，你的需求弹性就可以计算如下：Example: If the price of an ice cream cone increases from $2.00to $2.20 and the amount you buy falls from 10 to 8 cones, then your

elasticity of demand, using the midpoint formula,would be calculated as:

.25.9222

/)20.200.2()00.220.2(2

/)810()

810(==+?+?percent percent )/2]

P )/[(P P (P )/2]

Q )/[(Q Q (Q =

Demand of Elasticity Price 12121212+?+?12

弹性的范围

Ranges of Elasticity

缺乏弹性的需求Inelastic Demand

需求量的变化对价格变化的反应不强烈

Quantity demanded does not respond strongly to price changes.

需求价格弹性小于1 Price elasticity of demand is less than one.

富于弹性的需求Elastic Demand

需求量的变化对价格的变化反应强烈

Quantity demanded responds strongly to changes in price.

需求价格弹性大于1 Price elasticity of demand is greater than one.

计算需求价格弹性

Computing the Price Elasticity

of Demand

需求是富于价格弹性的

Demand is price elastic

$54

Demand

Quantity

100

Price

-3

percent

22-percent

67 5.00)/2

(4.005.00)

-(4.0050)/2

(10050)

-(100E D ==

++=

弹性的范围

Ranges of Elasticity

完全无弹性

Perfectly Inelastic

需求量对价格变化不作出反应

Quantity demanded does not respond to price changes.

完全（有）弹性

Perfectly Elastic

对价格的任何变化，需求量的变化无穷大

Quantity demanded changes infinitely with any change in price.

单位弹性

Unit Elastic

需求量变化和价格变化的百分数相同

Quantity demanded changes by the same percentage as the price.

完全无弹性的需求：弹性为零Perfectly Inelastic Demand

-Elasticity equals 0

数量Quantity 价格Price

4$5需求Demand

100

2. …没有引起需求量的任何变化

leaves the quantity demanded unchanged.

1. 价格上升An increase in price...

缺乏弹性的需求：弹性小于1

Inelastic Demand

-Elasticity is less than 1

数量Quantity

价格Price 4$51.价格上升22％A 22%increase in price...

需求Demand

100

902. …导致需求量下降11％

leads to a 11% decrease in quantity.

单位弹性的需求：弹性等于1Unit Elastic Demand

-Elasticity equals 1

数量Quantity

价格Price 4$51. 价格上升22％A 22%increase in price...

需求Demand

100

802. …导致需求量下降22％

leads to a 22% decrease in quantity.

富于弹性的需求：弹性大于1

Elastic Demand

-Elasticity is greater than 1

数量Quantity

价格Price 4$51. 价格上升22％A 22%increase in price...

需求Demand

100

502. …导致需求量下降67％

leads to a 67% decrease in quantity.

完全弹性的需求：弹性无穷大Perfectly Elastic Demand

-Elasticity equals infinity

数量Quantity

价格Price

需求Demand

1. 在4美元以上的任何价格，需求量都为零At any price

above $4, quantity demanded is zero.

2. 价格恰为4美元时，消费者愿意购买任何数量At exactly $4,consumers will buy any quantity.

3. 在价格低于4美元时，需求量为无穷大At a price below $4,

quantity demanded is infinite.

美国经济中部分物品的弹性Some Price Elasticities in the

U.S. Economy

富于弹性的需求Elastic demands

ê在外就餐Purchased meals 2.27ê金属Metals 1.52ê木制家具Furnitures, timber 1.25 ê汽车Motor Vehicles 1.14ê运输Transportation 1.03

缺乏弹性的需求Inelastic demands

ê水电气Gas, electricity, water .92ê石油Oil .91ê化学药品Chemicals .89

21美国经济中部分物品的弹性Some Price Elasticities in the

U.S. Economy

缺乏弹性的需求Inelastic demands (contd.)

ê饮料Beverages .78ê烟草Tobacco .61ê食物Food .58ê住宅服务Housing service .55ê衣服Clothing .49ê书报杂志Books, magazines, newspapers .34ê肉类Meat .2

Sources : Ahson Mansur and John Whalley, “Numerical Specification of Applied General Equilibrium Models: Estimation, Calibration, and Data”, in Scarf and Shoven, eds., Applied General Equilibrium Analysis (New York: Cambridge University Press,1984), p. 109; Hendrik S. Houthakker and Lester D. Taylor, Consumer

Demand in the United States: Analysis and Projections (Cambridge: Harvard University Press, 1970).

弹性与总收益

Elasticity and Total Revenue

总收益是一个物品的买者支付的金额，

也是其卖者收取的金额。

Total revenue is the amount paid by buyers and received by sellers of a good. 用该物品的价格乘以出售量来计算。Computed as the price of the good times the quantity sold.

TR = P x Q

P x Q =$400

(总收益total revenue)

100

弹性与总收益

Elasticity and Total Revenue

弹性与总收益

Elasticity and Total Revenue

对于缺乏弹性的需求曲线，当价格上升时，需求量下降的比例小于价格上升的比例。从而总收益上升。With an inelastic demand curve, an increase in price leads to a decrease in quantity that is proportionately smaller. Thus, total revenue

increases .

弹性与总收益：缺乏弹性的需求Elasticity and Total Revenue:

Inelastic Demand

Revenue =$240

需求Demand

100

价格Price

价格从$1上升到$3 An increase in price from

$1 to $3...

…引起总收益从$100增加

到$240美元

leads to an increase in total revenue from$100 to $240

弹性与总收益

Elasticity and Total Revenue

对于富于弹性的需求曲线，当价格上升时，需求量下降的比例大于价格上升的比例。从而总收益下降。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.

弹性与总收益：富于弹性的需求Elasticity and Total Revenue:

Elastic Demand

50$5

收益Revenue =$200

价格从$4上升到$5 An increase in price from

$4 to $5...

…导致总收益从$200下降

到$100

leads to a decrease in total revenue from$200 to $100

案例研究：旅游景点门票定价

如果你是颐和园的负责人，你的财务经

理告诉你，由于资金缺乏，无法进行正常的景观维护，建议你考虑改变门票价格以增加总收益。

你将提高还是降低门票价格？

弹性与斜率

Elasticity vs. Slope

因为需求价格弹性衡量了需求量对价格的反

应程度，它就和需求曲线的斜率密切相关。Because the price elasticity of demand measures how much quantity demanded

responds to the price, it is closely related to the slope of the demand curve. 斜率=ΔQ/ΔP ，

弹性＝(ΔQ/Q)/(ΔP/P)=(ΔQ/ΔP)/(Q/P)

给定某一点，通过该点的需求曲线越平坦（斜率越大），在该点附近的需求价格弹性就越大。

计算线性需求曲线的弹性Computing the Elasticity of a

Linear Demand Curve

Price Quantity Total Revenue (Price x Quantity)Percent Change in Price Percent

Change in Quantity

Elasticity Description $014$0200%15%0.1Inelastic 1121267180.3Inelastic 2102040220.6Inelastic 382429291Unit elastic 46242240 1.8elastic 54201867 3.7elastic 62121520013elastic

线性需求曲线的斜率是不变的，但弹性不是不变的。The slope of a linear demand curve is constant, but its

elasticity is not.

31需求的收入弹性

Income Elasticity of Demand

需求收入弹性衡量一个物品的需求量对消费者

收入变化的反应程度大小。

Income elasticity of demand measures how much the quantity demanded of a good

responds to a change in consumers’income. 用需求量变化的百分数除以收入变化的百分数来计算。

It is computed as the percentage change in the quantity demanded divided by the percentage change in income.

计算收入弹性

Computing Income Elasticity

Income Elasticity of Demand

Percentage Change in Quantity Demanded Percentage Change

in Income

=需求的收入弹性＝

需求量变化的百分数/收入变化的百分数

收入弹性：物品的类型Income Elasticity

-Types of Goods - 正常品

Normal Goods

劣等品Inferior Goods

对于正常品来说，更高的收入增加了对它的需

求量（弹性为正）；对于劣等品来说，更高的收入减少了对它的需求量（弹性为负）。Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods .

收入弹性：物品的类型Income Elasticity

-Types of Goods -

某些物品被消费者看作必需品，它就倾向于缺乏收入弹性（弹性大于0但小于1）。

Goods consumers regard as necessities tend to be income inelastic

例如食物、燃油、衣服、公用事业、医疗服务

Examples include food, fuel, clothing, utilities, and medical services.

某些物品被消费者看作奢侈品，它就倾向于富于收入弹性（弹性大于1）。

Goods consumers regard as luxuries tend to be income elastic .

例如跑车、毛皮衣服、高档食品

Examples include sports cars, furs, and expensive foods.

35收入弹性的应用

随着一国的经济增长和人们收入水平提高，哪

种物品的支出额在收入中的比重增加，必需品还是奢侈品？奢侈品！

例子：中国，奢侈品成为消费“热点”

80年代：“三大件”——电视、冰箱、洗衣机 90年代：空调、汽车、电脑现在：住房、旅游

中国：城镇居民消费支出构成

资料来源：《中国统计年鉴》

19922003食品

52.937.1衣着14.1

9.8家庭设备用品及服务

8.4 6.3医疗保健 2.5

7.3交通通讯

2.611.1娱乐教育文化服务8.8

14.4居住

6.010.7杂项商品

4.7 3.3合计

100.0100.0

类别

年份

需求的交叉价格弹性

The Cross-Price Elasticity of

Demand

经济学家用需求的交叉价格弹性来衡量一种商

品的需求量随另一种商品价格改变的改变。Economists use the cross-price elasticity of demand to measure how the quantity

demanded of one good changes as the price of another good changes.

Cross-price elasticity

of demand

Percentage change in quantity

demanded of good 1Percentage change in the price of good 2

=需求交叉价格弹性

＝商品1需求量的百分比变化/商品2价格的百分比变化

需求的交叉价格弹性

The Cross-Price Elasticity of

Demand

交叉价格弹性是正数还是负数取决于这两种物

品是替代品还是互补品。

Whether the cross-price elasticity is a positive or negative number depends on whether the two goods are substitutes or complements.

对于替代品而言，越是相近的替代品，交叉价格弹性就越大。

供给的价格弹性

Price Elasticity of Supply

供给的价格弹性是价格变化百分之一导致的供

给量变化的百分数

Price elasticity of supply is the percentage change in quantity supplied resulting from a percent change in price.

它是对物品的供给量对该物品的价格变化作出反应的程度大小的一种度量方法

It is a measure of how much the quantity

supplied of a good responds to a change in the price of that good.

弹性的范围

Ranges of Elasticity

完全弹性

Perfectly Elastic

E S =∞

较富于弹性Relatively Elastic

E S > 1

单位弹性

Unit Elastic

E S = 1

弹性的范围

Ranges of Elasticity

较缺乏弹性Relatively Inelastic

E S < 1

完全无弹性

Perfectly Inelastic

E S = 0

完全无弹性的供给：弹性为零Perfectly Inelastic Supply

-Elasticity equals 0

数量Quantity 价格Price 4$5供给Supply

100

2. …没有引起供给量的改变

leaves the quantity supplied unchanged.

1. 价格上升An increase in price...

缺乏弹性的供给：弹性小于1

Inelastic Supply

-Elasticity is less than 1

数量Quantity

价格Price 4$51. 价格上升22％A 22%increase in price...

110

100供给Supply

2. …导致供给量上升10％

leads to a 10% increase in quantity.

单位弹性的供给：弹性等于1

Unit Elastic Supply

-Elasticity equals 1

数量Quantity

价格Price 4$51. 价格上升22％A 22%increase in price...

125

100供给Supply

2. …导致供给量上升22％

leads to a 22% increase in quantity.

富于弹性的供给：弹性大于1

Elastic Supply

-Elasticity is greater than 1

数量Quantity

价格Price 4$51. 价格上升22％A 22%

increase in price...

200100供给Supply

2. …导致供给量上升67％

leads to a 67% increase in quantity.

完全弹性的供给：弹性无穷大Perfectly Elastic Supply

-Elasticity equals infinity

数量Quantity

价格Price

供给Supply

1. 只要价格高于$4，供给量无穷大At any price

above $4, quantity supplied is infinite.

2. 价格恰好为$4，生产者愿意供给任一数量At exactly $4,producers will

supply any quantity.

3. 价格低于$4，供给量为零At a price below $4,

quantity supplied is zero.

供给弹性的决定因素Determinants of Elasticity of Supply

卖者改变其生产物品的数量的能力

Ability of sellers to change the amount of the good they produce.

海滩边的土地是无弹性的

Beach-front land is inelastic.

书籍、汽车或者制成品是富于弹性的

Books, cars, or manufactured goods are elastic.

时间间隔Time period.

在长期，供给更有弹性

Supply is more elastic in the long run.

供给弹性的决定因素Determinants of Elasticity of Supply

数量Quantity

价格Price 3

410020050052512

15弹性很大。Elasticity is large (greater than 1).

弹性很小。Elasticity is small (less than 1).

价格弹性沿着供给曲线改变，因为企业往往具有一个生产的最大能力。The price elasticity can vary over the supply curve because firms often have a maximum capacity

for production.

计算供给价格弹性

Computing the Price Elasticity

of Supply

用供给量变化的百分数除以价格变化的百分

数，就算出来了供给的价格弹性。

The price elasticity of supply is computed as the percentage change in the quantity supplied divided by the percentage change in

price.

Elasticity of Supply =

Percentage Change in Quantity Supplied

Percentage Change in Price

供给价格弹性

供给量变化的百分数

价格变化的百分数

弹性的应用

Application of Elasticity

考察是供给还是需求曲线移动。

Examine whether the supply or demand curve shifts.

确定曲线移动的方向。

Determine the direction of the shift of the curve.

用供求图说明市场均衡如何变化。

Use the supply-and-demand diagram to see how the market equilibrium changes.

农业的好消息能是农民的坏消息吗？Can Good News for Farming Be

Bad News for Farmers?

当大学里的农学家们发现了一个比现有品种更高

产的新小麦杂交品种时，小麦种植者和小麦市场上会发生什么？

What happens to wheat farmers and the market for wheat when university agronomists discover a new wheat hybridthat is more productive than existing varieties?

3. …而销售量却只能以更小的比例增加。结果，收益从$300下降到$220。

and a proportionately smaller increase in quantity sold. As a result, revenue falls from $300 to $220.

农业的好消息能是农民的坏消息吗？Can Good News for Farming Be

Bad News for Farmers?$3

小麦的数量

Quantity of Wheat

100

Price of

Wheat

1. 当需求缺乏弹性时，供给增加When demand is inelastic,an increase in supply...

需求Demand

S 1

S 2

2110

2. …引起价格的大幅度下降

Leads to a large fall in price...

农业的好消息能是农民的坏消息吗？Can Good News for Farming Be

Bad News for Farmers?

-0.240.4

0.095

- 2.00)/2

(3.002.00

-3.00110)/2(100110-100=

E D ≈=

++计算弹性Compute Elasticity

需求是缺乏弹性的Demand is inelastic

农业的好消息能是农民的坏消息吗？Can Good News for Farming Be Bad

News for Farmers?

在人类史上，农业技术进步提高了单个农民生产的食物数量。Over the human history, advances in farm technology increased the amount of food that each farmer produce.

由于食物需求缺乏弹性，食物供给的增加导致了农业收益下降，这又鼓励了人们离开农业。

This increase in food supply, together with inelastic food

demand, caused farm revenues to fall, which in turn encouraged people to leave farming.

证据Evidences ：

美国的农民数量从1950年到2004年下降了70％，但农业产量为原来的2倍多。

Despite the 70 percent drop in the number of farmers, U.S. farms produced more than twice the output of crops and livestock in 2004 as they did in 1950.

中国的农业（第一产业）劳动力数量从1991年（开始下降）到2004年下降了10％，农业产量增加了60％。

为什么欧佩克不能保持高油价？Why Did OPEC Fail to Keep the

Price of Oil High?

在上世纪70年代，石油输出国组织（OPEC ）决定提高世界石油价格以提高其收入。

In the 1970s members of the Organization of Petroleum Exporting Countries (OPEC) decided to raise the world price of oil in order to increase their incomes.

这些国家通过共同减少他们供给的石油来实现这一目标。

These countries accomplished this goal by jointly reducing the amount of oil they supplied.

但是，欧佩克发现维持高油价是困难的。

Yet OPEC found it difficult to maintain a high price.

56为什么欧佩克不能保持高油价？Why Did OPEC Fail to Keep the

Price of Oil High?

Demand 需求

S 1

S 2

1、在短期中，当供给和需求缺乏弹性时，供给移动……

In the short run, when supply and demand are inelastic, a shift in supply……

P 1

P 22、……导致价格大幅上涨……leads to a large increase

in price.Demand 需求

S 1

S 2

1、在长期中，当供给和需求富有弹性时，供给移动……

In the long run, when supply and demand are elastic, a shift in supply……

P 1

22、……导致价格小幅上涨……leads

to a small increase in price.石油数量

Quantity of Oil

石油价格Price of Oil

石油数量

Quantity of Oil

石油价格Price of Oil

短期石油市场

长期石油市场

57禁毒增加还是减少了与毒品相关的犯罪？Does Drug Interdiction Increase or Decrease Drug-related Crime?

Demand 需求

S 1S 2

1、禁毒减少了毒品供给……Drug interdiction reduces the supply of drugs……

P 1

P 22、……提高了价格……which raises the price.

毒品数量

Quantity of Drugs

毒品价格

Price of Drugs

Q 1

Q 23、……减少了销售量and reduces the quantity sold.

D 1

Supply 供给

1、禁毒教育减少了毒品需求……Drug education reduces the demand of drugs……

P 1P 2

2、……降低了价格……which raises the price.

毒品数量

Quantity of Drugs

毒品价格

Price of Drugs

Q 1

Q 23、……减少了销售量

and reduces the quantity sold.

D 2

禁毒

禁毒教育

禁毒增加还是减少了与毒品相关的犯罪？Does Drug Interdiction Increase or Decrease Drug-related Crime?

由于毒品的需求缺乏弹性，禁毒带来的价格提高的比例大于毒品使用减少的比例，因而增加了吸毒者为毒品支出的总货币量。

Since the demand for drugs is inelastic, drug

interdiction raises the price of drugs proportionately more than it reduces drug use, thus raises the total amount of money that drug users pay for drugs.

这样禁毒可能增加了与毒品相关的犯罪。

Thus, drug interdiction could increase drug-related crime.

相反的，禁毒教育既减少了毒品使用，又减少了与毒品相关的犯罪。

In contrast, drug education can reduce both drug use

and drug-related crime.

总结Summary

需求价格弹性衡量了需求量对价格变化作出反应的程度。

Price elasticity of demand measures how much the quantity demanded responds to changes in the price. 如果需求曲线富于弹性，价格上升会导致总收益下降If a demand curve is elastic, total revenue falls when the price rises.

如果需求曲线缺乏弹性，价格上升会导致总收益上升If it is inelastic, total revenue rises as the price rises.

总结Summary

供给价格弹性衡量了供给量对价格变化作出

反应的程度。

The price elasticity of supply measures how much the quantity supplied responds to changes in the price.

在大多数市场上，供给在长期比在短期更富于弹性。

In most markets, supply is more elastic in the long run than in the short run.