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1、1,Chapter 3 Elasticity Theory,2,The contents of the chapter,1.What is elasticity?2.Elasticity of Demand 3.Elasticity of Supply,3,1.What is elasticity?,弹性elasticity：自变量变动一个百分比所引起的因变量变动的百分比。(注意：不是因变量变动量与自变量变动量之比。)e=（Y/Y）/（X/X）=（Y/X）（X/Y）弹性是一个具体的数值coefficient，与变量之间的度量无关。为什么用弹性：通过弹性，可以表示存在函数关系的变量与变量之间反应
2、的敏感程度并做出量化分析，从而能更好地认识变量之间的相互关系。,4,Elasticity is a measure of responsiveness.Two words are important here.The word measure means that elasticity results are reported as numbers,or elasticity coefficients.The word responsiveness means that there is a stimulus-reaction involved.Some change or stimulus
3、causes people to react by changing their behavior,and elasticity measures the extent to which people react.,5,2.Elasticity of Demand,Qd=f(P,I,Pi,Pe),6,2.1 Price elasticity of demand,The most common elasticity measurement is that of price elasticity of demand.It measures how much consumers respond in
4、 their buying decisions to a change in price.,7,The basic formula used to determine price elasticity is:,8,E.G.,If price increases by 10%and consumers respond by decreasing purchases by 20%,the equation computes the elasticity coefficient as-2.The result is negative because an increase in price(a po
5、sitive number)leads to a decrease in purchases(a negative number).Because the law of demand says it will always be negative,many economists ignore the negative sign.,9,弹性公式Elasticity formula,弧弹性公式arc elasticity formula:Q PaEd=-(a点到b点的弹性)P Qa Q PbEd=-(b点到a点的弹性)P Qb,10,弧弹性公式(中点公式)Q/（Qa+Qb）/2 Q Pa+Pb E
6、d=-或=-P/（Pa+Pb）/2 P Qa+Qb点弹性公式与计算 dQ/Q dQ P Ed=-或=-dP/P dP Q,11,E.G.,某杂志价格为2元时销售量为5万册，价格为3元时销售量为3万册，则需求价格弹性为多少？解：价格从2元上涨至3元，Ed=0.8 价格从3元下降至2元，Ed=2 利用中点公式计算则有Ed=1.25,12,需求函数：Qd=a-bP(a、b为常数，b0)，设P=1，求点弹性。,解：P=1，则Qd=a-b 1，另dQ/dP=-b dQ P 1 b Ed=-=b=dP Q a b a b,13,需求的价格弧弹性分类The classification of price e
7、lasticity of demand,Ed=0，需求完全无弹性Perfectly inelastic 0|Ed|1，需求缺乏弹性inelastic|Ed|=1，需求具有单位弹性unit elastic 1|Ed|，需求富有弹性elastic|Ed|=，需求有无限弹性或完全弹性 Perfectly elastic,14,o,Q,D 1,P,D 5,D 2,D 3,D 4,E,15,需求富有弹性的商品：电话,2001年7月1日，国家财政部、产业信息部联合发文取消了电话初装费，两个多月后，杭州的电话市场特别是城乡结合部及农村市场出现了空前的火爆场面。每天前往电信部门登记装电话的客户络绎不绝，最高一
8、天甚至超过以前一天登记数的10倍。萧山区甚至出现了一个月发展农村电话2.7万户的高峰，一个月新装电话农户就超过以往一年的数量。淳安县也出现了一天受理装机1485部的场面。,16,弹性与斜率elasticity and slope,对应于同一点，弹性与斜率的大小成反比(指绝对值)。斜率相等，弹性的大小取决于点的位置。直线型需求曲线上的点从左上方向右下方移动，弹性越来越小。,17,直线型需求曲线上的点弹性变化the changes of point elasticities along the linear demand curve,o,Q,P,D,A,B,C,线段AC：|Ed|1中点C：|Ed|
9、=1线段CB：|Ed|1点A：Ed点B：Ed 0,M,N,Ed=1/k.P/Q=MC/AM.OM/ON=OM/AM=CB/CAEd=1要求 CB=CA，所以，C为AB的中点,18,需求的价格弹性与收益Price Elasticity of Demand and Revenue,o,P,D,C,Q,P1,P2,P3,P4,Q1,Q2,Q3,Q4,A,B,E,F,19,Price Elasticity of Demand and Revenue,Total Revenue(TR)TR=PQd Qd=f(P)dTR/dP=Qd+PdQd/dP,20,Ed1,elastic，so dTR/dP0,P
10、TR Ed=1,unit elastic，dTR/dP=0,no affectEd=0，perfectly inelastic收入同比例于价格变化而变化。Ed=，perfectly elastic既定价格下收益可无限增加，厂商不会降价，涨价则会使收入减少为,21,影响需求价格弹性的因素The factors that affect the price elasticity of demand,商品的可替代性 Substitutability of goods商品用途的广泛性 Extensive use of goods商品对消费者的重要程度(preferrence)Importance of
11、goods to consumers商品的消费支出在消费总支出中所占的比重 The proportion of consumer spending in the consumer goods in total expenditure消费者调节需求量的时间 Time for consumer demand,22,需求收入弹性 Income elasticity of demand,It measures how the quantity demanded changes as consumer income changes.It is calculated as:Percentage chang
12、e in quantity demandedEi=Percentage change in income,23,formula：Q/Q Q I Ei=或=I/I I QClassify：Ey0,Normal,good;Ey1，Luxury,24,需求交叉弹性Cross-price elasticity of demand,Definition：It measures how the quantity demanded of one good changes as the price of another good changes.It is calculated as:Percentage c
13、hange in quantity of good x Exy=Percentage change in the price of good y,25,Formula：Qy/Qy Qy Px Exy=or=Px/Px Px QyClassification：Exy0，Substitute 替代品；Exy0，complement 互补品;Exy=0,irrelation 不相关,26,3.Price Elasticity of Supply,定义 Definition公式与计算 Formula and computation分类及影响因素 Classification and affect fa
14、ctors,27,定义Definition,It measures how much the quantity supplied responds to changes in the price.It is calculated as:Percentage change in quantity supplied Es=Percentage change in price,28,Computation:,The formula for arc price elasticity of supply Q PaEs=-(Es from a to b)P Qa Q PbEs=-(Es from b to
15、 a)P Qb,29,Middle point Es formula Q/（Qa+Qb）/2 Q Pa+Pb Es=or=P/（Pa+Pb）/2 P Qa+QbPoint Es formula dQ/Q dQ P Es=or=dP/P dP Q,30,E.G.for arc Es,Supply function is Qs=30+3P，the price changes from 6 to 8 or from 8 to 6,the Es will be?1.The price from 6 to 8,Es=3/82.The price from 8 to 6,Es=4/93.Using mid
16、dle point Es formula,Es=7/17,31,E.G.for point Es,Supply function is Qs=c+dP(c and d are constants，d0)，P=1，then the point Es will be?,P=1，Qs=c+d，dQ/dP=d dQ P 1 d Es=d=dP Q c+d c+d,32,Classification,Es=0，供给完全无弹性perfectly inelastic0Es1，供给缺乏弹性inelasticEs=1，供给具有单位弹性unit elastic1Es，供给富有弹性elasticEs=，供给有无限弹
17、性 perfectly elastic,33,Classification for Es,O,P,Q,S1 Es=0,S5 Es=,S3 Es=1,S2 Es1,S4 Es1,34,The factors affecting Es,Time for producer adjusting yeildMarginal costProduction cycle,35,4.The applications of elasticity theory,谷贱伤农 The lower price of food will reduce the revenue of farmers税负分担理论 The theo
18、ry of tax burden蛛网理论 Spider-web theory,36,谷贱伤农,Q,o,p,E1,P1,Q1,E2,P2,Q2,F,D,S1,S2,37,税负分担理论,o,Q,P,S0,E0,P0,Q0,D0,S1,E1,P1,Q1,P2,t,D0,E1,P1,Q1,P2,弹性不同税收的分担也不同,38,蛛网模型,基本假设：(1)本期的供给量取决于上期的价格；(2)本期的需求量取决于本期的价格。三种类型：收敛型蛛网、发散型蛛网、稳定型蛛网适用分析对象：有生产周期的产品。,39,蛛网模型（数学方法）,1.Qdt=Qst 2.Qdt=a-bPt(a,b0)3.Qst=-c+dPt-1
19、(c,d0)由1、2、3可得：bPt+dPt-1+=a+c将上式正规化，得Pt+1+（b/d）Pt=（a+c）/b,40,蛛网模型（数学方法）,解上差分方程：Pt=P0-(a+c)/(b+d)(-d/b)t+(a+c)/(b+d)P0表示初始价格在市场均衡时，Pe=Pt=Pt+1因此有：Pe=(a+c)/(b+d)，将Pe代入解中，Pt=（P0 Pe）(-d/b)t+Pe,41,蛛网模型（数学方法）,通过上式子，可以看出：1.当db时，震荡将为放大震荡2.当d=b时，震荡为单位震荡3.当d0)Qst=-c+dPt-1 Pt-1=c/d+(1/d)Qst(c,d0),42,收敛型蛛网（图示）,o
20、,Q,P,E,D,S,P*,Q*,P0,Q1,P1,Q2,P2,Q3,P3,Q4,43,发散型蛛网（图示）,o,Q,P,E,D,S,P*,Q*,P0,Q1,P1,Q2,P2,Q3,P3,Q4,44,稳定型蛛网（图示）,o,Q,P,D,S,E,P*,Q*,P0,Q1,P0,P1,Q2,P2,Q3,P3,Q4,45,三类蛛网模型的条件,收敛型蛛网的条件：供给弹性需求曲线斜率（绝对值）。发散型蛛网的条件：供给弹性需求弹性，或，供给曲线斜率需求曲线斜率（绝对值）。稳定型蛛网的条件：供给弹性=需求弹性，或，供给曲线斜率=需求曲线斜率（绝对值）。,46,思考题：,相对而言，为什么化妆品可以薄利多销而药品不可以？从经济学角度，你认为怎样可以减少迷幻商品(指烟、酒、毒品等)？,47,
