范里安現(xiàn)代觀點(diǎn)中級(jí)微觀經(jīng)濟(jì)學(xué)PowerPoint 演示文稿

1、1Chapter SixDemand2Properties of Demand FunctionsuComparative statics analysis of ordinary demand functions - the study of how ordinary demands x1*(p1,p2,y) and x2*(p1,p2,y) change as prices p1, p2 and income y change.3Own-Price ChangesuHow does x1*(p1,p2,y) change as p1 changes, holding p2 and y co

2、nstant?uSuppose only p1 increases, from p1 to p1 and then to p1.4 x1x2p1 = p1Fixed p2 and y.p1x1 + p2x2 = yOwn-Price Changes5Own-Price Changesx1x2p1= p1p1 = p1Fixed p2 and y.p1x1 + p2x2 = y6Own-Price Changesx1x2p1= p1p1=p1Fixed p2 and y.p1 = p1p1x1 + p2x2 = y7x2x1p1 = p1Own-Price ChangesFixed p2 and

3、 y.8x2x1x1*(p1)Own-Price Changesp1 = p1Fixed p2 and y.9x2x1x1*(p1)p1x1*(p1)p1x1*Own-Price ChangesFixed p2 and y.p1 = p110 x2x1x1*(p1)p1x1*(p1)p1p1 = p1x1*Own-Price ChangesFixed p2 and y.11x2x1x1*(p1)x1*(p1)p1x1*(p1)p1p1 = p1x1*Own-Price ChangesFixed p2 and y.12x2x1x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)p1p1x

4、1*Own-Price ChangesFixed p2 and y.13x2x1x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)p1p1p1 = p1x1*Own-Price ChangesFixed p2 and y.14x2x1x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)p1p1p1 = p1x1*Own-Price ChangesFixed p2 and y.15x2x1x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1p1p1x1*Own-Price ChangesFixed p2 and y.16x2

5、x1x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1p1p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1Fixed p2 and y.17x2x1x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1p1p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1Fixed p2 and y.18x2x1x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1

6、p1p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1p1 price offer curveFixed p2 and y.19Own-Price ChangesuThe curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and y constant, is the p1- price offer curve.uThe plot of the x1-coordinate of the p1- price off

7、er curve against p1 is the ordinary demand curve for commodity 1.20Own-Price ChangesuWhat does a p1 price-offer curve look like for Cobb-Douglas preferences?21Own-Price ChangesuWhat does a p1 price-offer curve look like for Cobb-Douglas preferences?uTakeThen the ordinary demand functions for commodi

8、ties 1 and 2 areU xxx xa b(,).1212 22Own-Price Changesxp pyaabyp1121*(, ) xp pybabyp2122*(, ). andNotice that x2* does not vary with p1 so thep1 price offer curve is23Own-Price Changesxp pyaabyp1121*(, ) xp pybabyp2122*(, ). andNotice that x2* does not vary with p1 so thep1 price offer curve is flat

9、 24Own-Price Changesxp pyaabyp1121*(, ) xp pybabyp2122*(, ). andNotice that x2* does not vary with p1 so thep1 price offer curve is flat and the ordinarydemand curve for commodity 1 is a25Own-Price Changesxp pyaabyp1121*(, ) xp pybabyp2122*(, ). andNotice that x2* does not vary with p1 so thep1 pric

10、e offer curve is flat and the ordinarydemand curve for commodity 1 is a rectangular hyperbola.26x1*(p1)x1*(p1)x1*(p1)x2x1Own-Price ChangesFixed p2 and y.xbyab p22*() xayab p11*() 27x1*(p1)x1*(p1)x1*(p1)x2x1p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1 isFixed p2 and y.xbyab p22*() xayab

11、p11*() xayab p11*() 28Own-Price ChangesuWhat does a p1 price-offer curve look like for a perfect-complements utility function?29Own-Price ChangesuWhat does a p1 price-offer curve look like for a perfect-complements utility function? U xxxx(,)min,.1212 Then the ordinary demand functionsfor commoditie

12、s 1 and 2 are30Own-Price Changesxp pyxp pyypp11221212*(, )(, ). 31Own-Price Changesxp pyxp pyypp11221212*(, )(, ). With p2 and y fixed, higher p1 causessmaller x1* and x2*.32Own-Price Changesxp pyxp pyypp11221212*(, )(, ). With p2 and y fixed, higher p1 causessmaller x1* and x2*.pxxyp11220 ,.*As33Ow

13、n-Price Changesxp pyxp pyypp11221212*(, )(, ). With p2 and y fixed, higher p1 causessmaller x1* and x2*.pxxyp11220 ,.*Aspxx1120 ,.*As34Fixed p2 and y.Own-Price Changesx1x235p1x1*Fixed p2 and y.xypp212* xypp112* Own-Price Changesx1x2p1xypp112* p1 = p1 y/p236p1x1*Fixed p2 and y.xypp212* xypp112* Own-P

14、rice Changesx1x2p1p1p1 = p1xypp112* y/p237p1x1*Fixed p2 and y.xypp212* xypp112* Own-Price Changesx1x2p1p1p1xypp112* p1 = p1y/p238p1x1*Ordinarydemand curvefor commodity 1 isFixed p2 and y.xypp212* xypp112* xypp112*. Own-Price Changesx1x2p1p1p1yp2y/p239Own-Price ChangesuWhat does a p1 price-offer curv

15、e look like for a perfect-substitutes utility function?U xxxx(,).1212 Then the ordinary demand functionsfor commodities 1 and 2 are40Own-Price Changesxp pyif ppy pif pp112121120*(, ),/, xppyif ppy pif pp212122120*(, ),/,. and41Fixed p2 and y.Own-Price Changesx2x1Fixed p2 and y.x20* xyp11* p1 = p1 p2

16、42Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.x20* xyp11* p1p1 = p1 p2xyp11* 43Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.p1p1 = p1 = p244Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.p1p1 = p1 = p245Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.x20* xyp1

17、1* p1p1 = p1 = p2 x10* xyp22* 46Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.x20* xyp12* p1p1 = p1 = p2 x10* xyp22* 012 xyp* p2 = p147Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.xyp22* x10* p1p1x10* p2 = p148Fixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.p1p2 = p1p1xy

18、p11* 012 xyp*yp2p1 price offer curveOrdinarydemand curvefor commodity 149Own-Price ChangesuUsually we ask “Given the price for commodity 1 what is the quantity demanded of commodity 1?”uBut we could also ask the inverse question “At what price for commodity 1 would a given quantity of commodity 1 be

19、 demanded?”50Own-Price Changesp1x1*p1Given p1, what quantity isdemanded of commodity 1?51Own-Price Changesp1x1*p1Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.x152Own-Price Changesp1x1*x1Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.The inverse question is:G

20、iven x1 units are demanded, what is the price of commodity 1?53Own-Price Changesp1x1*p1x1Given p1, what quantity isdemanded of commodity 1?Answer: x1 units.The inverse question is:Given x1 units are demanded, what is the price of commodity 1? Answer: p154Own-Price ChangesuTaking quantity demanded as

21、 given and then asking what must be price describes the inverse demand function of a commodity.55Own-Price ChangesA Cobb-Douglas example:xayab p11*() is the ordinary demand function andpayab x11 ()*is the inverse demand function.56Own-Price ChangesA perfect-complements example:xypp112* is the ordina

22、ry demand function andpyxp112 *is the inverse demand function.57Income ChangesuHow does the value of x1*(p1,p2,y) change as y changes, holding both p1 and p2 constant?58x2x1Income ChangesFixed p1 and p2.y y y59x2x1Income ChangesFixed p1 and p2.y y y60 x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x

23、2x261x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curve62Income ChangesuA plot of quantity demanded against income is called an Engel curve.63x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curve64x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex1

24、*yx1x1x1yyy65x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex1*yx1x1x1yyyEngelcurve;good 166x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex2*yx2x2x2yyy67x2x1Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex2*yx2x2x2yyyEngelcurve;good 268x2x1

25、Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex1*x2*yyx1x1x1x2x2x2yyyyyyEngelcurve;good 2Engelcurve;good 169Income Changes and Cobb-Douglas PreferencesuAn example of computing the equations of Engel curves; the Cobb-Douglas case.uThe ordinary demand equations areU xxx xa b(,).1212

26、xayab pxbyab p1122*();(). 70Income Changes and Cobb-Douglas Preferencesxayab pxbyab p1122*();(). Rearranged to isolate y, these are:yab paxyab pbx ()()*1122Engel curve for good 1Engel curve for good 271Income Changes and Cobb-Douglas Preferencesyyx1*x2*yab pax ()*11Engel curvefor good 1yab pbx ()*22

27、Engel curvefor good 272Income Changes and Perfectly-Complementary PreferencesuAnother example of computing the equations of Engel curves; the perfectly-complementary case.uThe ordinary demand equations arexxypp1212*. U xxxx(,)min,.1212 73Income Changes and Perfectly-Complementary PreferencesRearrang

28、ed to isolate y, these are:yppxyppx ()()*121122Engel curve for good 1xxypp1212*. Engel curve for good 274Fixed p1 and p2.Income Changesx1x275Income Changesx1x2y y yFixed p1 and p2.76Income Changesx1x2y y yFixed p1 and p2.77Income Changesx1x2y y yx1x1x2x2x2x1Fixed p1 and p2.78Income Changesx1x2y y yx

29、1x1x2x2x2x1x1*yyyyEngelcurve;good 1x1x1x1Fixed p1 and p2.79Income Changesx1x2y y yx1x1x2x2x2x1x2*yx2x2x2yyyEngelcurve;good 2Fixed p1 and p2.80Income Changesx1x2y y yx1x1x2x2x2x1x1*x2*yyx2x2x2yyyyyyEngelcurve;good 2Engelcurve;good 1x1x1x1Fixed p1 and p2.81Income Changesx1*x2*yyx2x2x2yyyyyyx1x1x1yppx

30、()*122yppx ()*121Engelcurve;good 2Engelcurve;good 1Fixed p1 and p2.82Income Changes and Perfectly-Substitutable PreferencesuAnother example of computing the equations of Engel curves; the perfectly-substitution case.uThe ordinary demand equations areU xxxx(,).1212 83Income Changes and Perfectly-Subs

31、titutable Preferencesxp pyif ppy pif pp112121120*(, ),/, xppyif ppy pif pp212122120*(, ),/,. 84Income Changes and Perfectly-Substitutable Preferencesxp pyif ppy pif pp112121120*(, ),/, xppyif ppy pif pp212122120*(, ),/,. Suppose p1 p2. Then85Income Changes and Perfectly-Substitutable Preferencesxp p

32、yif ppy pif pp112121120*(, ),/, xppyif ppy pif pp212122120*(, ),/,. Suppose p1 p2. Thenxyp11* x20* and86Income Changes and Perfectly-Substitutable Preferencesxp pyif ppy pif pp112121120*(, ),/, xppyif ppy pif pp212122120*(, ),/,. Suppose p1 0.uThat is, the consumers MRS is the same anywhere on a str

33、aight line drawn from the origin.(x1,x2) (y1,y2) (kx1,kx2) (ky1,ky2)p pp p90Income Effects - A Nonhomothetic ExampleuQuasilinear preferences are not homothetic.uFor example,U xxf xx(,)().1212 U xxxx(,).1212 91Quasi-linear Indifference Curvesx2x1Each curve is a vertically shifted copy of the others.E

34、ach curve intersectsboth axes.92Income Changes; Quasilinear Utilityx2x1x193Income Changes; Quasilinear Utilityx2x1x1x1*yx1Engelcurveforgood 194Income Changes; Quasilinear Utilityx2x1x1x2*yEngelcurveforgood 295Income Changes; Quasilinear Utilityx2x1x1x1*x2*yyx1Engelcurveforgood 2Engelcurveforgood 196

35、Income EffectsuA good for which quantity demanded rises with income is called normal.uTherefore a normal goods Engel curve is positively sloped.97Income EffectsuA good for which quantity demanded falls as income increases is called income inferior.uTherefore an income inferior goods Engel curve is n

36、egatively sloped.98x2x1Income Changes; Goods1 & 2 Normalx1x1x1x2x2x2Incomeoffer curvex1*x2*yyx1x1x1x2x2x2yyyyyyEngelcurve;good 2Engelcurve;good 199Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1100Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1101Income

37、Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1102Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1103Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1104Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1Incomeoffer curve105Income

38、 Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1x1*yEngel curvefor good 1106Income Changes; Good 2 Is Normal, Good 1 Becomes Income Inferiorx2x1x1*x2*yyEngel curvefor good 2Engel curvefor good 1107Ordinary GoodsuA good is called ordinary if the quantity demanded of it always increases as its own price decreases.108Ordinary GoodsFixed p2 and y.x1x2109Ordinary GoodsFixed p2 and y.x1x2p1 price offer curve1