弹性及其应用 弹性 Elasticity Elasticity and Its ◆…是买者和卖者对市场环境变化作出反应的 Application 程度大小的一种度量方法 is a measure of how much buvers and sellers respond to changes in market conditions 第5章 Chapter 5 ◆…使我们能够更精确地分析供给和需求 llows us to analyze supply and demand with greater precision 需求的价格弹性 需求价格弹性的决定因素 Determinants of Price Elasticity of Demand Price Elasticity of Demand 给定百分之一的价格变化,需求量变化的百分 ◆必品还是膏修品 Necessities versus luxuries Price elasticity of demand is the percentage change in quantity demanded given a percent ◆相近普代品的可获得性 change in the price Availability of Close Substitut 杨扬的界定 ◆它衡量了一种物品的需求量对该物品价格变化 Definition ofthe Mark 出反应的程度大小 时闻范 It is a measure of how much the quantity Time Horizon 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 计算需求价格弹性 Determinants of Computing the Price Elasticity Price Elasticity of Demand of demand 那求倾向于更富有弹性 用需求量变动的百分数除以价格变动的百分数 Demand tends to be more elastic 就计算出了需求的价格弹性 ◆如果该商品是奢侈品 The price elasticity of demand is computed as the percentage change in the quantity demanded ◆时间间隔越长 divided by the percentage change in price. Pe巨分数ge ◆相近替代品的个数越多 Price Elasticity of Demand= Quantity Demanded the larger the number of close substitutes. 需求价格弹性 Percentage Change ◆市场界定得越狭隘 价格变化的百分数 the more narrowly defined the market
1 弹性及其应用 Elasticity and Its Application 第5章 Chapter 5 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. 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. 时间间隔越长 the longer the time period. 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. 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 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
计算需求价格弹性 运用中点公式计算需求价格弹性 Computing the Price Elasticity computing the Price Elasticity of Demand Using the Midpoint of demand Formula Percentage change in quatity demanded ◆如果你试图计算需求曲线上两点之 格弹性,你马上就会注意到一个恼 如果冰演淋蛋卷的价格从20美元上升到220美元,你所购买 从A点到B点的弹性,与从B点到A点 量从10个下障到8个,那么你的需求弹性可以计算如下: 不同的。 ao plei: the he prict of a bie e reases from S2. 00 to t you buy falls from 10 to 8 cones then your If you try calculate the price elasticity of elasticity of demand would he caleulated as demand between two points on a demand curve, you will quickly notice an annoying -20 percent problem: The elasticity from point A to point B seems different from the elasticity from point B 2.20-20×10010 percent 运用中点公式计算需求价格弹性 运用中点公式计算需求价格弹性 Computing the Price Elasticity of Computing the Price Elasticity of Demand Using the Midpoint Demand Using the Midpoint Formula Formula ◆例如,考虑下面的数字 For example, consider these numbers 当计算需求价格弹性时,中点公式更为可取,因 e Point A: Price=S4, Quantity=120 为无论变化的方向如何,它都能给出相同的答案 e Point B: Price=S6 Quantity=80 The midpoint formula is preferable when ◆弹性分别是 Elasticities are, calculating the price elasticity of demand because it gives the same answer regardless of the direction of ◆I(80-120)/120(6-4)/4|=(-33).5=-0.66 Price Elasticity of Demand=(Q-Q,)/(Q+Q)/2)1 ◆B→A: (P2-P1)/[(P2+P1)2] ◆l(120-8080/1(46)/6=5/(-33)=1.5 运用中点公式计算需求价格弹性 computing the Price Elasticity of 计算需求价格弹性 Demand Using the Midpoint Computing the Price Elasticity Formula of demand ◆在我们的例子中,A点和B点的中点是 Price Elasticity of Demand =(Qx-Qn/(Q 2+Q1/21 In our example, the mid point between point A 2-P1)[(P2+P1)2 and B is ◆中点 Midpoint:价格 Prices=S5,数量 Quantity=100 量从10个下降到个,运用中点公式,你的求弹性就可以计算如下 ◆无论方向,弹性均为1 S2.20 and the amount you buy falls from 10 to 8 cones, then your .A- in both directions equals I Elas elasticity of demand, using the midpoint formula, would be calculated ◆(80-120/100y(6-4)5=(-.2).2=1 (10+8)/2 ◆B→A: 22 percent=2.32 ◆(120-80/100(4-6)5}=,2/(-2)=1 (2.00+2.20)/2
2 计算需求价格弹性 Computing the Price Elasticity of Demand Percentage change in price Percentage change in quatity demanded 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，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 $2.00 to $2.20 and the amount you buy falls from 10 to 8 cones then your elasticity of demand would be calculated as: (8 10) 100 10 20 2 (2.20 2.00) 10 100 2.00 percent percent − × − = =− − × 运用中点公式计算需求价格弹性 Computing the Price Elasticity of Demand Using the Midpoint Formula 如果你试图计算需求曲线上两点之间的需求价 格弹性，你马上就会注意到一个恼人的问题： 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. 运用中点公式计算需求价格弹性 Computing the Price Elasticity of Demand Using the Midpoint Formula 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. (P P )/[(P P )/2] (Q Q )/[(Q Q )/2] Price Elasticity of Demand= 2 1 2 1 2 1 2 1 − + − + 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, 中点Midpoint: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)=-1 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 $2.00 to $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: 2.32 9.5 22 (2.00 2.20)/ 2 (2.20 2.00) (10 8)/ 2 (10 8) = = + − + − percent percent (P P )/[(P P )/2] (Q Q )/[(Q Q )/2] Price Elasticity of Demand = 2 1 2 1 2 1 2 1 − + − +
弹性的范围 计算需求价格弹性 Ranges of Elasticity Computing the Price Elasticity 峡乏弹性的求 Inelastic demand of demand ◆需求量的变化对价格变化的反应不强烈 Price Quantity demanded does not respond strongly to price (10050)/2 4.00-5.00Z ◆需求价格弹性小于1 (4.00+500/2 Price elasticity of demand is less than on 富于弹性的需求 Elastic demand 67 percent=-3 ◆需求量的变化对价格的变化反应强烈 Quantity demanded responds strongly to changes in 求是富干价格弹性的 ◆需求价格弹性大 0 50 100 Quantity Demand is price elastic Price elasticity of demand is greater than one. 弹性的范围 需求曲线的变化 Ranges of Elasticity A Variety of Demand Curves ◆完全无苹性 Perfectly Inelastic 需求量对价格变化不作出反应 ◆因为需求价格弹性衡量了需求量对价格 nded does not respond to price changes. 的反应程度,它就和需求曲线的斜率密 ◆完全(有)弹性 Perfectly Elastic 切相关。 对价格的任何变化,需求量的变化无穷大 Because the price elasticity of demand measures how much quantity demanded ◆单位弹性 Unit Elasti responds to the price, it is closely related 需求量变化和价格变化的百分数相同 to the slope of the demand curve. Quantity demanded changes by the same percentage as the price. ◆通过某一点的需求曲线越平坦,需求的 价格弹性就越大。 完全无弹性的需求:弹性为零 缺乏弹性的需求:弹性小于1 Perfectly Inelastic Demand Inelastic Demand Elasticity equals 0 Elasticity is less than 1 教量 Quantity 2.没有引起需求量的任何变化 2..导致需求量下降11% leads to a 11 decrease in quantity
3 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 $5 4 Demand 0 100 Quantity Price 50 -3 -22percent 67percent (4.00 5.00)/2 (4.00-5.00) (100 50)/2 (100-50) ED = = + + = 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. 需求曲线的变化 A Variety of Demand Curves 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. 通过某一点的需求曲线越平坦，需求的 价格弹性就越大。 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 1.价格 $5 上升22％ A 22% increase in price... 需求 Demand 90 100 2. …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1 富于弹性的需求:弹性大于1 Unit Elastic Demand Elastic Demand Elasticity equals 1 Elasticity is greater than 1 价格 量 Quantity 量 Quantity 2.导致需求 2.导致求量下降67% leads to a 67% decrease in quantity 完全弹性的需求:弹性无穷大 美国经济中部分物品的弹性 Perfectly Elastic Demand Some Price Elasticities in the Elasticity equals infinity U.S. Economy Price 富于弹性的需求 Elastie demands 7在外就餐 Purchased meals 2.27 7金属 Metals 1.52 7木制家具 Furnitures, timber 求 Demand 刁汽车 Motor vehicles 运输 Transportation 着管产天向爱量 m缺乏弹性的需求 Inelastic demands buy any quantity 石油Oil 3在价低于元时,求量为无射大 7化学药品 Chemicals quantity demanded is infinite. 美国经济中部分物品的弹性 Some price elasticities in the 弹性与总收益 U.S. Economy Elasticity and Total Revenue 缺乏弹性的需求 Inelastic demands( contd.) ◆总收益是一个物品的买者支付的金额, 饮料Be 也是其卖者收取的金额 烟草 Tobacco Total revenue is the amount paid by buyers and received by sellers of a good. 7住宅服务 Housing service ◆用该物品的价格乘以出售量来计算 7衣服 Clothing .49 Computed as the price of the good times 7书报杂志 Books,, Magazines,. newspapers.34 the quantity sold TR=PX Q
4 单位弹性的需求：弹性等于1 Unit Elastic Demand - Elasticity equals 1 数量 Quantity 价格 Price 4 1. 价格 $5 上升22％ A 22% increase in price... 需求 Demand 80 100 2. …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 $5 1. 价格 上升22％ A 22% increase in price... 需求 Demand 50 100 2. …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 $4 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 2.27 Ê金属 Metals 1.52 Ê木制家具 Furnitures, timber 1.25 Ê汽车 Motor Vehicles 1.14 Ê运输 Transportation 1.03 缺乏弹性的需求 Inelastic demands Ê水电气 Gas, electricity, water .92 Ê石油 Oil .91 Ê化学药品 Chemicals .89 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 .78 Ê烟草 Tobacco .61 Ê食物 Food .58 Ê住宅服务 Housing service .55 Ê衣服 Clothing .49 Ê书报杂志 Books, magazines, newspapers .34 Ê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
弹性与总收益 弹性与总收益 Elasticity and Total Revenue 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 PxQ=5400 With an inelastic demand curve, 总收益 total revenue 需求 Demand 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 弹性与总收益 Inelastic Demand Elasticity and Total Revenue 价格 对于富于弹性的需求曲线,当价格 价格从S1上升到 到S240美元 上升时,需求量下降的比例大于价 SI to S3 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 需求 is proportionately larger. Thus, total revenue decreases 弹性与总收益:富于弹性的需求 Elasticity and Total revenue 案例研究:旅游景点门票定价 Elastic Demand 导敦总收益从5200下降 ◆如果你是颐和园的负责人,你的财务经 从4上升到 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 以增加总收益。你将提高还是降低门 票价格? 求 Demand t Reven Revenue=5100 ◆如果你是北京市一家电影院的经理,同 样的情况下,你的考虑又如何?
5 $4 需求 Demand 数量 Quantity P 0 价格 Price P x Q = $400 (总收益total revenue) 100 Q 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 $3 数量 Quantity 0 价格 Price 80 Revenue = $240 需求 Demand $1 需求 Demand 数量 Quantity 0 收益Revenue = $100 100 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 需求Demand 0 数量 Quantity 价格 Price $4 50 需求Demand 0 数量 Quantity Price Revenue = $100 $5 20 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？ 如果你是北京市一家电影院的经理，同 样的情况下，你的考虑又如何？