微观经济学范里安第八版显示偏好.ppt

第七章,显示偏好,显示偏好分析,假设我们观察到了一个消费者在不同预算约束下的需求（作出的消费选择）。这会显示关于消费者偏好的一些信息。我们可以利用这些信息 ,显示偏好分析,检验消费者总是选择买得起的最受偏爱的消费束这一假说。 提示消费者的偏好关系.,偏好假设,偏好 在选择数据的收集期间内没有改变。 严格凸性. 单调性. 凸性和单调性表明最优的、负担得起的消费束是唯一的。,偏好假设,x2,x1,x1*,x2*,若偏好是凸的和单调的(性状良 好)。那么最优的、负担得起的 消费束是唯一的。,直接显示偏好,设消费束x*是消费束y 可以负担得起的情况下所选择的消费束。那么x* 是 y的直接显示偏好 (否则 y 将被选择).,直接显示偏好,x2,x1,x*,y,被选择的消费束 x*（需求束） 是消费束y和z的直接显示偏好,z,直接显示偏好,x 是 y 的直接显示偏好可以被写成 x y.,间接显示偏好,假设 x 是y的直接显示偏好，并且y是 z的直接显示偏好. 那么基于传递性, x 是 z的间接显示偏好. 可以被写成 x z x y and y z x z.,I,p,I,p,间接显示偏好,x2,x1,x*,z,选择 x*的时候 z 买不起.,选择 y* 的时候， x* 买不起。,间接显示偏好,x2,x1,x*,y*,z,选择 x* 的时候， z买不起。 选择 y* 的时候， x* 买不起。,间接显示偏好,x2,x1,x*,y*,z,选择 x* 的时候， z买不起。 选择 y* 的时候， x* 买不起。 所以 x* 和 z 不能直接比较,间接显示偏好,x2,x1,x*,y*,z,选择 x* 的时候， z买不起。 选择 y* 的时候， x* 买不起。 所以 x* 和 z 不能直接比较,间接显示偏好,x2,x1,x*,y*,z,但是 x*x* y*,选择 x* 的时候， z买不起。 选择 y* 的时候， x* 买不起。 所以 x* 和 z 不能直接比较,间接显示偏好,x2,x1,x*,y*,z,但是 x*x* y* 并且 y* z,选择 x* 的时候， z买不起。 选择 y* 的时候， x* 买不起。 所以 x* 和 z 不能直接比较,间接显示偏好,x2,x1,x*,y*,z,但是 x*x* y* 并且 y* z 所以 x* z.,I,p,显示偏好的两大公理,若要应用显示偏好来分析, 消费者选择必须合乎两个标准 显示偏好的弱公理和显示偏好的强公理,显示偏好的弱公理 (WARP),如果消费束x是消费束y的直接显示偏好，那么消费束y绝不可能是消费束x的直接显示偏好 x y not (y x).,显示偏好的弱公理 (WARP),违反 WARP 的消费者选择数据无法同经济理性相容. 运用经济理性分析所观察到的消费者选择的时候， WARP 是一个必要条件。,显示偏好的弱公理 (WARP),什么样的消费者选择数据违背了 WARP呢?,显示偏好的弱公理 (WARP),x2,x1,x,y,显示偏好的弱公理 (WARP),x2,x1,x,y,选择x 的时候，y 买得起 所以 x y.,显示偏好的弱公理 (WARP),x2,x1,x,y,选择x 的时候，y 买得起 所以 x y.,选择y 的时候，x买得起 所以y x.,显示偏好的弱公理 (WARP),x2,x1,x,y,这种情况是相互矛盾的.,选择x 的时候，y 买得起 所以 x y.,选择y 的时候，x买得起 所以y x.,检验数据是否违背了 WARP,某一消费者所出了如下选择: 在价格为 (p1,p2)=($2,$2) 时选择了 (x1,x2) = (10,1). 在价格为 (p1,p2)=($2,$1)时选择了 (x1,x2) = (5,5). 在价格为 (p1,p2)=($1,$2) 时选择了 (x1,x2) = (5,4). 这些数据是否违背了 WARP 呢?,检验数据是否违背了 WARP,检验数据是否违背了 WARP,红色数据是被选择的消费束的成本.,检验数据是否违背了 WARP,带圈的数据是负担得起，但未被选择的消费束。,检验数据是否违背了 WARP,Circles surround affordable bundles that were not chosen.,检验数据是否违背了 WARP,带圈的数据是负担得起，但未被选择的消费束。,检验数据是否违背了 WARP,检验数据是否违背了 WARP,检验数据是否违背了 WARP,(10,1) 是 (5,4)的直接 显示偏好,但 (5,4)同时 也是 (10,1)的直接显示 偏好。 所以，以上数据违背了 WARP。,检验数据是否违背了 WARP,(5,4) (10,1),(10,1) (5,4),x1,x2,显示偏好的强公理 (SARP),如果消费束 x 是消费束 y 的显示偏好 (直接的或者间接的) 并且 x y, 那么消费束 y 决不会是消费束 x的显示偏好 (直接的或者间接的) x y or x y,not ( y x or y x ).,I,p,显示偏好的强公理,什么样的数据满足显示偏好的弱公理(WARP) ，但却违背了显示偏好的强公理 (SARP)呢?,显示偏好的强公理,考虑以下数据: A: (p1,p2,p3) = (1,3,10) & (x1,x2,x3) = (3,1,4) B: (p1,p2,p3) = (4,3,6) & (x1,x2,x3) = (2,5,3) C: (p1,p2,p3) = (1,1,5) & (x1,x2,x3) = (4,4,3),显示偏好的强公理,A: ($1,$3,$10) (3,1,4).,B: ($4,$3,$6) (2,5,3).,C: ($1,$1,$5) (4,4,3).,显示偏好的强公理,显示偏好的强公理,情况 A的条件下, 消费束 A 是消费 束C的直接显示偏 好； A C.,显示偏好的强公理,情况 B的条件下, 消费束 B 是消费 束A的直接显示偏 好; B A.,显示偏好的强公理,情况 C的条件下, 消费束 C 是消费 束B的直接显示偏 好； C B.,显示偏好的强公理,显示偏好的强公理,数据没有违背 WARP.,显示偏好的强公理,数据没有违背 WARP 但是 .,我们有 A C, B A 并且 C B 所以, 基于传递性, A B, B C 并且 C A.,显示偏好的强公理,数据没有违背 WARP 但是 .,我们有 A C, B A 并且 C B 所以, 基于传递性, A B, B C 并且 C A.,I,I,I,显示偏好的强公理,I,I,I,B A 与A B相互矛盾,数据没有违背 WARP 但是 .,显示偏好的强公理,I,I,I,A C 与C A相互矛盾,数据没有违背 WARP 但是 .,显示偏好的强公理,I,I,I,数据没有违背 WARP 但是 .,C B 与B C相互矛盾,显示偏好的强公理,I,I,I,数据没有违背 WARP 但是却有3处违背了SARP.,显示偏好的强公理,观测到的消费者选择数据满足SARP是性状良好的偏好关系的充要条件，或者说这是理性的数据. 对于性状良好的偏好关系来说，上述3组数据是非理性的。,重建无差异曲线,假设我们具有满足 SARP的消费者选择数据. 那么我们就可以充分接近地重建消费者的无差异曲线。 怎么做?,重建无差异曲线,观察值: A: (p1,p2) = ($1,$1) & (x1,x2) = (15,15) B: (p1,p2) = ($2,$1) & (x1,x2) = (10,20) C: (p1,p2) = ($1,$2) & (x1,x2) = (20,10) D: (p1,p2) = ($2,$5) & (x1,x2) = (30,12) E: (p1,p2) = ($5,$2) & (x1,x2) = (12,30). 穿过消费束 A = (15,15)的无差异曲线在什么地方呢?,重建无差异曲线,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20) C: (p1,p2)=(1,2); (x1,x2)=(20,10) D: (p1,p2)=(2,5); (x1,x2)=(30,12) E: (p1,p2)=(5,2); (x1,x2)=(12,30).,重建无差异曲线,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20) C: (p1,p2)=(1,2); (x1,x2)=(20,10) D: (p1,p2)=(2,5); (x1,x2)=(30,12) E: (p1,p2)=(5,2); (x1,x2)=(12,30).,Begin with bundles revealed to be less preferred than bundle A.,Recovering Indifference Curves,x2,x1,A,A: (p1,p2)=(1,1); (x1,x2)=(15,15).,Recovering Indifference Curves,x2,x1,A,A: (p1,p2)=(1,1); (x1,x2)=(15,15).,Recovering Indifference Curves,x2,x1,A,A: (p1,p2)=(1,1); (x1,x2)=(15,15).,A is directly revealed preferred to any bundle in,Recovering Indifference Curves,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20).,Recovering Indifference Curves,x2,x1,A,B,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20).,Recovering Indifference Curves,x2,x1,A,B,A is directly revealed preferred to B and ,Recovering Indifference Curves,x2,x1,B,B is directly revealed preferred to all bundles in,Recovering Indifference Curves,x2,x1,B,so, by transitivity, A is indirectly revealed preferred to all bundles in,Recovering Indifference Curves,x2,x1,B,so A is now revealed preferred to all bundles in the union.,A,Recovering Indifference Curves,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) C: (p1,p2)=(1,2); (x1,x2)=(20,10).,Recovering Indifference Curves,x2,x1,A,C,A: (p1,p2)=(1,1); (x1,x2)=(15,15) C: (p1,p2)=(1,2); (x1,x2)=(20,10).,Recovering Indifference Curves,x2,x1,A,C,A is directly revealed preferred to C and .,Recovering Indifference Curves,x2,x1,C,C is directly revealed preferred to all bundles in,Recovering Indifference Curves,x2,x1,C,so, by transitivity, A is indirectly revealed preferred to all bundles in,Recovering Indifference Curves,x2,x1,C,so A is now revealed preferred to all bundles in the union.,B,A,Recovering Indifference Curves,x2,x1,C,so A is now revealed preferred to all bundles in the union.,B,A,Therefore the indifference curve containing A must lie everywhere else above this shaded set.,Recovering Indifference Curves,Now, what about the bundles revealed as more preferred than A?,Recovering Indifference Curves,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20) C: (p1,p2)=(1,2); (x1,x2)=(20,10) D: (p1,p2)=(2,5); (x1,x2)=(30,12) E: (p1,p2)=(5,2); (x1,x2)=(12,30).,A,Recovering Indifference Curves,x2,x1,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) D: (p1,p2)=(2,5); (x1,x2)=(30,12).,A,Recovering Indifference Curves,x2,x1,D,D is directly revealed preferred to A.,A,Recovering Indifference Curves,x2,x1,D,D is directly revealed preferred to A. Well-behaved preferences are convex,A,Recovering Indifference Curves,x2,x1,D,D is directly revealed preferred to A. Well-behaved preferences are convex so all bundles on the line between A and D are preferred to A also.,A,Recovering Indifference Curves,x2,x1,D,D is directly revealed preferred to A. Well-behaved preferences are convex so all bundles on the line between A and D are preferred to A also.,A,As well, .,Recovering Indifference Curves,x2,x1,D,all bundles containing the same amount of commodity 2 and more of commodity 1 than D are preferred to D and therefore are preferred to A also.,A,Recovering Indifference Curves,x2,x1,D,A,bundles revealed to be strictly preferred to A,Recovering Indifference Curves,x2,x1,A,B,E,C,D,A: (p1,p2)=(1,1); (x1,x2)=(15,15) B: (p1,p2)=(2,1); (x1,x2)=(10,20) C: (p1,p2)=(1,2); (x1,x2)=(20,10) D: (p1,p2)=(2,5); (x1,x2)=(30,12) E: (p1,p2)=(5,2); (x1,x2)=(12,30).,A,Recovering Indifference Curves,x2,x1,A,E,A: (p1,p2)=(1,1); (x1,x2)=(15,15) E: (p1,p2)=(5,2); (x1,x2)=(12,30).,Recovering Indifference Curves,x2,x1,A,E,E is directly revealed preferred to A.,Recovering Indifference Curves,x2,x1,A,E,E is directly revealed preferred to A. Well-behaved preferences are convex,Recovering Indifference Curves,x2,x1,A,E,E is directly revealed preferred to A. Well-behaved preferences are convex so all bundles on the line between A and E are preferred to A also.,Recovering Indifference Curves,x2,x1,A,E,E is directly revealed preferred to A. Well-behaved preferences are convex so all bundles on the line between A and E are preferred to A also.,As well, .,Recovering Indifference Curves,x2,x1,A,E,all bundles containing the same amount of commodity 1 and more of commodity 2 than E are preferred to E and therefore are preferred to A also.,Recovering Indifference Curves,x2,x1,A,E,More bundles revealed to be strictly preferred to A,Recovering Indifference Curves,x2,x1,A,B,C,E,D,Bundles revealed earlier as preferred to A,Recovering Indifference Curves,x2,x1,B,C,E,D,All bundles revealed to be preferred to A,A,Recovering Indifference Curves,Now we have upper and lower bounds on where the indifference curve containing bundle A may lie.,Recovering Indifference Curves,x2,x1,All bundles revealed to be preferred to A,A,All bundles revealed to be less preferred to A,Recovering Indifference Curves,x2,x1,All bundles revealed to be preferred to A,A,All bundles revealed to be less preferred to A,Recovering Indifference Curves,x2,x1,The region in which the indifference curve containing bundle A must lie.,A,Index Numbers,Over time, many prices change. Are consumers better or worse off “overall” as a consequence? Index numbers give approximate answers to such questions.,Index Numbers,Two basic types of indices price indices, and quantity indices Each index compares expenditures in a base period and in a current period by taking the ratio of expenditures.,Quantity Index Numbers,A quantity index is a price-weighted average of quantities demanded; i.e. (p1,p2) can be base period prices (p1b,p2b) or current period prices (p1t,p2t).,Quantity Index Numbers,If (p1,p2) = (p1b,p2b) then we have the Laspeyres quantity index;,Quantity Index Numbers,If (p1,p2) = (p1t,p2t) then we have the Paasche quantity index;,Quantity Index Numbers,How can quantity indices be used to make statements about changes in welfare?,Quantity Index Numbers,If then so consumers overall were better off in the base period than they are now in the current period.,Quantity Index Numbers,If then so consumers overall are better off in the current period than in the base period.,Price Index Numbers,A price index is a quantity-weighted average of prices; i.e. (x1,x2) can be the base period bundle (x1b,x2b) or else the current period bundle (x1t,x2t).,Price Index Numbers,If (x1,x2) = (x1b,x2b) then we have the Laspeyres price index;,Price Index Numbers,If (x1,x2) = (x1t,x2t) then we have the Paasche price index;,Price Index Numbers,How can price indices be used to make statements about changes in welfare? Define the expenditure ratio,Price Index Numbers,If then so consumers overall are better off in the current period.,Price Index Numbers,But, if then so consumers overall were better off in the base period.,Full Indexation?,Changes in price indices are sometimes used to adjust wage rates or transfer payments. This is called “indexation”. “Full indexation” occurs when the wages or payments are increased at the same rate as the price index being used to measure the aggregate inflation rate.,Full Indexation?,Since prices do not all increase at the same rate, relative prices change along with the “general price level”. A common proposal is to index fully Social Security payments, with the intention of preserving for the elderly the “purchasing power” of these payments.,Full Indexation?,The usual price index proposed for indexation is the Paasche quantity index (the Consumers Price Index). What will be the consequence?,Full Indexation?,Notice that this index uses current period prices to weight both base and current period consumptions.,Full Indexation?,x2,x1,x2b,x1b,Base period budget constraint,Base period choice,Full Indexation?,x2,x1,x2b,x1b,Base period budget constraint,Base period choice,Current period budget constraint before indexation,Full Indexation?,x2,x1,x2b,x1b,Base period budget constraint,Base period choice,Cu