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 Elastici y of D mand Percen Ch ge in tity De nd Percen Ch ge Price 需求量变化的百分数 价格变化的百分数 2 计算需求价格弹性 Computing the Price Elasticity of Demand price inchange Percentage demandedquatity inchange Percentage demand of elasticityPrice = 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 20 10 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. )/2]P)/[(PP(P )/2]Q)/[(QQ(Q =Demand of Elasticity Price 1212 1212 +? +? 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: 32.2 5.9 22 2/)20.200.2( )00.220.2( 2/)810( )810( == + ? + ? percent percent )/2]P)/[(PP(P )/2]Q)/[(QQ(Q =Demand of Elasticity Price 1212 1212 +? +? 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 Quantity1000 Price 50 -3 percent 22- percent 67 5.00)/2(4.00 5.00)-(4.00 50)/2(100 50)-(100 E 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. 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 $51.价格 上升22％ A 22% increase in price... 需求Demand 10090 2. …导致需求量下降11％ leads to a 11% decrease in quantity. 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 $51. 价格 上升22％ A 22% increase in price... 需求 Demand 10080 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 10050 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 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 数量Quantity0 价格 Price $4 50 需求Demand 数量Quantity0 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？ 6 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 $0 14 $0 200% 15% 0.1 Inelastic 1 12 12 67 18 0.3 Inelastic 2 10 20 40 22 0.6 Inelastic 38 4 29 29 1 Unit elastic 46 2 22 40 1.8 elastic 5 4 20 18 67 3.7 elastic 6 2 12 15 200 13 elastic 70 0 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；对于劣等品来说，更高的 收入减少了对它的需求量 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 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 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. 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 7 中国：城镇居民消费支出构成 资料来源：《中国统计年鉴》 1992 2003 食品52.9 37.1 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2.6 11.1 娱乐教育文化服务8.8 14.4 居住6.0 10.7 杂项商品4.7 3.3 合计100.0 100.0 类别 年份 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... 110100 供给Supply 2. …导致供给量上升10％ leads to a 10% increase in quantity. 8 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... 125100 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 $4 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. 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 El Suppl Percent ge Change i antity upplie Per ge Change 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 ?农事的好消息会不会是农民的坏消息？ 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 hybrid that is more productive than existing varieties? 9 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. 小麦市场上供给增加 An Increase in Supply in the Market for Wheat $3 小麦的数量 Quantity of Wheat 1000 小麦的价格 Price of Wheat 需求Demand S 1 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. 小麦市场上供给增加 An Increase in Supply in the Market for Wheat $3 小麦的数量 Quantity of Wheat 1000 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 2 110 2. …引起价 格的大幅度 下降 Leads to a large fall in price... 计算弹性 Compute Elasticity -0.24 0.4 0.095- 2.00)/2(3.00 2.00-3.00 110)/2(100 110-100 =E D ≈= + + 计算弹性 Compute Elasticity -0.24 0.4 0.095- 2.00)/2(3.00 2.00-3.00 110)/2(100 110-100 =E D ≈= + + 需求是缺乏弹性的 Demand is inelastic 政策含义 Policy Implications ?随着农业的技术（或制度）进步，农 产品供给增加和农民数量减少具有某 种必然性 ?1948年美国有17％人口为农民， 1993年仅有2％。但农业产量为原 来的2倍多。 ?1952年中国84%劳动力在农业， 1999年为50%。农业产量增加了3 倍。 10 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.