《微观经济学》ppt课件Ch6Demand需求函数的静态比较分析.ppt

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1、Chapter SixDemand需求函数的静态比较分析需求函数的静态比较分析What Do We Do in This Chapter?u We conduct comparative 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.u Theoretically,nothing new.Own-Price ChangesuHow does

2、x1*(p1,p2,y)change as p1 changes,holding p2 and y constant?uSuppose only p1 increases,from p1 to p1 and then to p1.x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1p1p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1Fixed p2 and y.x1*(p1)x1*(p1)x1*(p1)p1x1*(p1)x1*(p1)x1*(p1)p1p1p1x1*Own-Price Ch

3、angesOrdinarydemand curvefor commodity 1p1 price offer curveFixed p2 and y.Own-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 offer curve against p1 is th

4、e ordinary demand curve for commodity 1.The Case of Cobb-Douglas Utility FunctionuTakeThen the ordinary demand functions for commodities 1 and 2 areOwn-Price ChangesandNotice that x2*does not vary with p1 so thep1 price offer curve is flat and the ordinarydemand curve for commodity 1 is a rectangula

5、r hyperbola.x1*(p1)x1*(p1)x1*(p1)Own-Price ChangesFixed p2 and y.x1*(p1)x1*(p1)x1*(p1)p1x1*Own-Price ChangesOrdinarydemand curvefor commodity 1 isFixed p2 and y.The Case of Perfect-Complements Utility FunctionuWhat does a p1 price-offer curve look like for a perfect-complements utility function?Then

6、 the ordinary demand functionsfor commodities 1 and 2 areThe Case of Perfect-Complements Utility FunctionOwn-Price ChangesWith p2 and y fixed,higher p1 causessmaller x1*and x2*.AsAsp1x1*Ordinarydemand curvefor commodity 1 isFixed p2 and y.Own-Price Changesx1x2p1p1p1y/p2The Case of Perfect-Substitute

7、s Utility FunctionThen the ordinary demand functionsfor commodities 1 and 2 areandFixed p2 and y.Own-Price Changesx2x1p1x1*Fixed p2 and y.p1p2=p1p1p1 price offer curveOrdinarydemand curvefor commodity 1Own-Price ChangesuUsually we ask“Given the price for commodity 1 what is the quantity demanded of

8、commodity 1?”uBut we could also ask the inverse question“At what price for commodity 1 would a given quantity of commodity 1 be demanded?”Own-Price ChangesuTaking quantity demanded as given and then asking what must be price describes the inverse demand function of a commodity.Inverse Demand Functio

9、nA Cobb-Douglas example:is the ordinary demand function andis the inverse demand function.Income ChangesuHow does the value of x1*(p1,p2,y)change as y changes,holding both p1 and p2 constant?Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curveThe Engel CurveuA plot of quantity demanded a

10、gainst income is called an Engel curve.Income ChangesFixed p1 and p2.y y yx1x1x1x2x2x2Incomeoffer curvex1*x2*yyx1x1x1x2x2x2yyyyyyEngelcurve;good 2Engelcurve;good 1Income Changes and Cobb-Douglas PreferencesuAn example of computing the equations of Engel curves;the Cobb-Douglas case.uThe ordinary dem

11、and equations areIncome Changes and Cobb-Douglas PreferencesRearranged to isolate y,these are:Engel curve for good 1Engel curve for good 2Income Changes and Cobb-Douglas Preferencesyyx1*x2*Engel curvefor good 1Engel curvefor good 2Income Changes and Perfectly-Complementary PreferencesuThe ordinary d

12、emand equations areIncome Changes and Perfectly-Complementary PreferencesRearranged to isolate y,these are:Engel curve for good 1Engel curve for good 2Income Changesx1*x2*yyx2x2x2yyyyyyx1x1x1Engelcurve;good 2Engelcurve;good 1Fixed p1 and p2.Income Changes and Perfectly-Substitutable PreferencesuAnot

13、her example of computing the equations of Engel curves;the perfectly-substitution case.uThe ordinary demand equations areIncome Changes and Perfectly-Substitutable PreferencesIncome Changes and Perfectly-Substitutable PreferencesSuppose p1 0.uThat is,the consumers MRS is the same anywhere on a strai

14、ght line drawn from the origin.(x1,x2)(y1,y2)(kx1,kx2)(ky1,ky2)p pp pIncome Effects-A Nonhomothetic ExampleuQuasilinear preferences are not homothetic.uFor example,Income Changes;Quasilinear Utilityx2x1x1x1*x2*yyx1Engelcurveforgood 2Engelcurveforgood 1Income EffectsuA good for which quantity demande

15、d rises with income is called normal.uTherefore a normal goods Engel curve is positively sloped.Income EffectsuA good for which quantity demanded falls as income increases is called income inferior.uTherefore an income inferior goods Engel curve is negatively sloped.Income Changes;Goods1&2 Normalx1x

16、1x1x2x2x2Incomeoffer curvex1*x2*yyx1x1x1x2x2x2yyyyyyEngelcurve;good 2Engelcurve;good 1Income Changes;Good 2 Is Normal,Good 1 Becomes Income Inferiorx2x1x1*x2*yyEngel curvefor good 2Engel curvefor good 1Ordinary GoodsuA good is called ordinary if the quantity demanded of it always increases as its ow

17、n price decreases.Ordinary GoodsFixed p2 and y.x1x2p1 price offer curvex1*Downward-sloping demand curve Good 1 isordinaryp1Giffen GoodsuIf,for some values of its own price,the quantity demanded of a good rises as its own-price increases then the good is called Giffen.Ordinary GoodsFixed p2 and y.x1x

18、2Ordinary GoodsFixed p2 and y.x1x2p1 price offer curvex1*Demand curve has a positively sloped part Good 1 isGiffenp1Cross-Price EffectsuIf an increase in p2increases demand for commodity 1 then commodity 1 is a gross substitute for commodity 2.reduces demand for commodity 1 then commodity 1 is a gro

19、ss complement for commodity 2.Cross-Price EffectsA perfect-complements example:soTherefore commodity 2 is a grosscomplement for commodity 1.Cross-Price Effectsp1x1*p1p1p1Increase the price ofgood 2 from p2 to p2and the demand curvefor good 1 shifts inwards-good 2 is acomplement for good 1.Cross-Pric

20、e EffectsA Cobb-Douglas example:soTherefore commodity 1 is neither a grosscomplement nor a gross substitute forcommodity 2.Summary1.Own Price Effect1.Price Offer curve;2.Ordinary demand curve;3.Inverse demand function;4.Ordinary goods vs.Giffen Goods.2.Income Effect1.Income offer curve;2.Engle curve;3.Normal goods vs.income inferior goods;4.Homothetic preferences.3.Cross Price Effect1.Gross substitutes;2.Gross complements.