微观张课件北京大学经济学院张元

1、Chapter 2Consumer Behavior and Demand Theory1学院 张元鹏Chapter 2 includes:n 2.1 Preference and Utilityn 2.2 Utilityization and Choicen 2.3 Comparative Static Analysis in Optimal Choicen 2.4 Income and Substitution Effectsn 2.5 Market Demand and Elasticity2学院 张元鹏Overview of Last Classn Budget Constraint(

2、预算约束)n Application of Budget Constraintn Utilityization (ConsumersOptimal Choice)n Types of Optimal Solution3学院 张元鹏2.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionization Mto Demandn 2.3.2 From P.C.C to Demand Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curve

3、n 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve4学院 张元鹏A Survey(概述)This section studies how people change their choices when conditions such as income or changes in the prices of goods affect the amount that people choose to consume.

4、This section then compares the new choices with those that were made before conditions changedThe main result of this approach is toconstruct an individuals demand curve5学院 张元鹏2.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionization Mto Demandn 2.3.2 From P.C.C to Demand Curven

5、 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve6学院 张元鹏2.3.1 From Utility Functionization Mto Demandn Defining Individual Demand Functionn An individual demand Function sho

6、ws the relationship between the price of a good and the quantity of that good purchased by an individual assuming that all other determinants of demand are held constant.= dqd(P, P , I ; preferences)xXYx7学院 张元鹏2.3.1From Utility Functionization Mto Demandn Max : U=U(X1,X2)n S.t. P1X1+P2X2=I8学院 张元鹏2.3

7、.1 From Utility Demand Functionization MtoL( x1, x2 , l ) = u( x1 , x2 ) - l p1x1Take first order necessary conditions for+ p2 x2um- I ¶u(x , x)- lp = 0121¶x¶u(x ,1x ) 12- lp2= 0¶x2p1x1 + p2 x2 - I = 0学院 张元鹏92.3.1 From Utility Functionization Mto DemandFrom 3 first-order conditio

8、ns, we can get three equations, and then solve them to get individual demand functions for two goods.x1*=x1(p1,p2,I) x2*=x2(p1,p2,I)xi*= xi(p1,p2 I) ( i=1,2) is called ordinary demand function(普通需求函数), is also called Marshallian Demand Function（马歇尔需求函数）10学院 张元鹏Cobb-Douglas Example： Ordinary Demandsn

9、 Given p1, p2 and I, how to calculate optimal ordinary demands (x1*,x2*)?n Assume Cobb-Douglas preferences:bU (x ,12= ¶U= axa-1 xbMU1¶ x121= ¶U= bxa xb-1MU¶ x212211学院 张元鹏Cobb-Douglas Example： Ordinary Demandsn So the MRS is¶U /¶ xaxa-1 xbdxaxMRS = 2 = -1 = -12 = -2 .bx&

10、#182;U /¶ xbxa xb-1dx12121n At (x1*,x2*), MRS = -p1/p2*soaxpbp-= -Þx2 =* 2 1 1 x1(1)bx *pap122n Also, at (x1*,x2*), the budget is exhausted, sop x* + p x*= I(2)学院 张元鹏112212Cobb-Douglas Example： Ordinary Demandsn Substitute for x2* from (1) into (2) to getbp1p x* + p= Ix*1121ap2n Solve for

11、x1* to getn Substitute x1* into (2) and solve for x2* to getbI=x*2(a + b) p13学院 张元鹏2Cobb-Douglas Example： Ordinary Demandsx2b2U (x ,1bI=x*2(a + b) p2x1=aIx*1(a +14学院 张元鹏Cobb-Douglas Example： Ordinary Demandsöa+bøæèaa)a+b1-a2U (x , x ) =a+b112p x*aIa= ap1 x1 =Þ=* 1 1 I (a + b

12、)(a + b)bIx*pba= 1- a.p2 x2 =*Þ= 1- 22 I (a + b)(a + b)(a + b)n Note that for Cobb-Douglas utility functionn 1.Demands are linear in incomen 2.Expenditure shares are constantn 3.Expenditure shares sum to one15学院 张元鹏2.3.2 From P.C.C to Demand Curven By the way of comparative static analysis, if

13、we let the price of a good change holding other factors constant, we get ordinary demand curven Example: the price of a good increasen Suppose p1 increases, from p1 to p1, and to p1n Hold p2 and I constant学院 张元鹏162.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionization Mto Dema

14、ndn 2.3.2 From P.C.C to Demand Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve17学院 张元鹏2.3.2 From P.C.C to Demand Curvethe price of a good Changesx2p1x1+ p2x2= Ip1=p1

15、x118学院 张元鹏2.3.2 From P.C.C to Demand Curvethe price of a good Increasex2p1x1+ p2x2= Ip1= p1p1= p1x119学院 张元鹏2.3.2 From P.C.C to Demand Curvep1x1+ p2x2= Ix2p1= p1p1= p1p1= p1x120学院 张元鹏2.3.2 From P.C.C to Demand Curvex2p1= p1x1x1*(p1)21学院 张元鹏From P.C.C to Demand Curvep1x2p= p 11p1x1*x1*(p1)xx1*(p1)22学院

16、 张元鹏2.3.2 From P.C.C to Demand Curvep1x2p1= p1p1x1*x1*(p1)x1*(p1)x1*(p1)23学院 张元鹏2.3.2 From P.C.C to Demand Curvep1x2p1p1x1*x1*(p1)x1*(p1)x1*(p1)x1*(p1)24学院 张元鹏2.3.2 From P.C.C to Demand Curvep1x2p1= p1p1p1x1*x1*(p1)x1*(p1)x1*(p1)xx1*(p1)x1*(p1)25学院 张元鹏2.3.2From P.C.C to Demand Curvep1p1x2p1p1x1*x1*(

17、p1)x1*(p1)x1*(p1)x1*(p1) x *(p )x1*(p1)1126学院 张元鹏2.3.2 From P.C.C to Demand Curvep1p1x2demand curvep1p1x1*x1*(p1)x1*(p1)x1*(p1)x1*(p1) x *(p ) x1*(p1)1127学院 张元鹏2.3.2 From P.C.C to Demand Curvep1p1x2demand curvep1p1x1*x1*(p1)x1*(p1)x1*(p1) x *(p ) x1*(p1)1128学院 张元鹏x1*(p1)2.3.2 From P.C.C to Demand Cu

18、rvep1p1demand curvex2p1p1P.C.Cx1*x1*(p1)x1*(p1)x1*(p1) x *(p ) x1*(p1)1129学院 张元鹏x1*(p1)Summary: the price of a good Changesn Price consumption curve（P.C.C）:n contains all utility-izing bundles traced out as p1changes holding p2 and I constantn (在收入和其他商品价格不变条件下，某一商品价格变化所引起的消费者效用最大化的消费组合的点的轨迹)n Ordina

19、ry demand curve for commodity 1:n Plot of x1-coordinate of p1- price offer curve for each value of p1n Reflects optimal consumption of x1 at each p130学院 张元鹏Example: Cobb-Douglas Utilityn Assume Cobb-Douglas Utility functionbU (x ,12n Ordinary demand functions areaIbIx*( p , p , I ) =x*( p , p , I )

20、=,112212a + b pa + b p12n x2* is constant (flat) not f(p1)n x1* demand is rectangular hyperbola(直角双曲线) (px=k)学院 张元鹏31Example: Cobb-Douglas Utility=aIx *x1+ b )pa(21bI=x *2+ ba()p2P.C.Cx1*(p1)x1*(p1)x1学院 张元鹏x1*(p1)32Example: Cobb-Douglas Utilityp1demand curvex2aI=x *1+ ba()p1x1*x1*(p1) x *(p ) x1*(p1

21、)11x33学院 张元鹏P.C.C2.3.3 Judging edfrom P.C.Cn 1. Defining edDqe= - q = - Dq · pDpdDpqpæp öDqdqpor = lim ç-Dp®0è·÷ = -·Dpq ødpq34学院 张元鹏2.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionization Mto Demandn 2.3.2 From P.C.C to Demand

22、 Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve35学院 张元鹏2.3.3 Judging ed from P.C.Cn 2. ed and Consumer's ExpenditureTE = p ´ q,( p)dTE = d p ´ q( p) =

23、·(1- e)ddpdpèe< 1 Þ dTE > 0 Û p ­ (¯) Þ TE ­ (¯)ddpe> 1 Þ dTE < 0 Û p ­ (¯) Þ TE ¯ (­)ddpe= 1 Þ dTE = 0 Û p ­ (¯) Þ TEddp36学院 张元鹏2.3.3 Judging ed from P.C.Cn 3. Judging edfrom P.C.C37

24、学院 张元鹏2.3.3 Judging edfrom P.C.C（p 1¯Þ）¯Û商x品的 < 1（ep 2¯Þ）­Û商x品的 > 1eTETEdd38学院 张元鹏2.3.3 Judging edfrom P.C.C（p4）¯Þ¯Û商x 品的 <e0（p 3）¯ÞÛ商x品的= 1eqTEdd39学院 张元鹏402.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utili

25、ty Functionization Mto Demandn 2.3.2 From P.C.C to Demand Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve41学院 张元鹏2.3.4 From I.C.C to Engle Curven Change income I, ho

26、lding prices constantn Income consumption curve(I.C.C)（收入消费线）:在商品价格不变条件下，由于消费者收入水平变化所引起的消费者最优消费组合的轨 迹。n Engle curve: graph of quantity demanded and income42学院 张元鹏2.3.4 From I.C.C to Engle CurveIncome changes, holding prices constantx2I < I < Ix1学院 张元鹏432.3.4 From I.C.C to Engle Curvex2x144学院 张

27、元鹏2.3.4 From I.C.C to Engle Curvex2x2 x2x2x1x1学院 张元鹏x1x1452.3.4 From I.C.C to Engle Curvex2Income consumption curvex2 x2x2x1x1学院 张元鹏x1x1462.3.4 From I.C.C to Engle CurveIEngel Curvex2II II.C.Cx1*xxx2 x2x211x 1x1x1x1x147学院 张元鹏2.3.4 From I.C.C to Engle Curvex1Engel CurveII Ix2I.C.Cx1 x1 x1x2Engel Curv

28、ex2 x2x2I IIx1x1x1x x2x2x1248学院 张元鹏Example: Cobb-Douglas Utilityn Cobb-Douglas Engel curves:U(x1, x2) = x1an Ordinary demands:x2bx* =aI;=bI.x*12(a + b)p1(a + b)p249学院 张元鹏Example: Cobb-Douglas Utilityn Rearranging to solve for I:n Engel curve for good 1:+(ab)p*1=Ix1an Engel curve for good 2:+(ab)p*2=

29、Ix2b50学院 张元鹏Example: Cobb-Douglas Utility+(ab)p(ab)pI*I=1*=2IxIx12abx1*x2*51学院 张元鹏2.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionization Mto Demandn 2.3.2 From P.C.C to Demand Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel

30、Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve52学院 张元鹏2.3.5 Homothetic(同位性) andEngel CurvesEngel curves are straight lines if consumers preferences are homothetic (all examples thus far)A consumers preferences are homothetic if and only if, for every k>0,(x1,x2

31、) < (y1,y2)Û(kx1,kx2)<(ky1,ky2)n That is, the consumers MRS is the same anywhere on a straight line drawn from the originn Often assumed in dynamic optimization problems53学院 张元鹏2.3.5 Homothetic(同位性) andEngel CurvesIncome Effects: Nonhomothetic Examplen Quasilinear preferences are not homo

32、theticU(x1, x2) = f(x1) + x2n For example,1 + x 2 .U54学院 张元鹏2.3.5 Homothetic(同位性) andEngel Curvesx2Quasi-linear Indifference CurvesEach curve is vertically shifted copy of otherEach curve intersects both axes.x155学院 张元鹏2.3.5 Homothetic(同位性) and CurvesEngelx2Income Changes: Quasi-linear Utilityx1x156

33、学院 张元鹏Income Changes: Quasi-linear UtilityEngel CurveIx2x1*x1x1x157学院 张元鹏Income Changes: Quasi-linear UtilityEngel CurveIx2x2*x1x158学院 张元鹏Income Changes: Quasi-linear Utilityx1 Engel CurveIx2x1*x1Ix2EngelCurvex1x2*x159学院 张元鹏2.3 Comparative Analysis in Optimal Choicen 2.3.1 From Utility Functionizati

34、on Mto Demandn 2.3.2 From P.C.C to Demand Curven 2.3.3 Judging ed from P.C.Cn 2.3.4 From I.C.C to Engle Curven 2.3.5 Homothetic(同位性) andEngel Curvesn 2.3.6 Judging Types of Goods from I.C.Cn 2.3.7 Judging eI from Engle Curve60学院 张元鹏2.3.6 Judging Types of Goods from I.C.Cn Normal good(正常品):n quantity

35、 demanded rises with incomen Engel curve is positively slopedn Inferior good（低档品）:n quantity demanded falls with incomen Engel curve is negatively sloped61学院 张元鹏1.Income Changes: x1, x2Normal Goodsx1Engel CurveII Ix2I.C.Cx1 x1 x1x2 x2x2x2Engel CurveI IIx1x1x1x2 x2学院 张元鹏x2x1622.Income Changes: x2Normal, x1Inferiorx2x163学院 张元鹏2.Income Changes: x2No