《微觀經(jīng)濟(jì)學(xué)》清華大學(xué)-Tsinghua-Micro-Ch7-教學(xué)課件

ChapterSevenRevealedPreference顯現(xiàn)性偏好WhatIstheQuestionoftheChapter?Supposeweobserveacollectionofaconsumer’schoices,canwediscoverhis/herpreference?Isthispossibleatall?Ifso,underwhatconditionsisthispossible?(Thisisthereversequestionoffindingtheoptimalchoice)Digression:Sciencevs.Engineering

(對(duì)比科學(xué)家思維與工程師思維）

找問題與解問題的不同要對(duì)問題提問題務(wù)虛與務(wù)實(shí)的不同解釋世界與改造世界的不同旁觀者與參與者的不同MaintainedAssumptionsonPreferencesPreferencesdonotchangewhilethechoicedataaregathered.arestrictlyconvex.aremonotonic.AssumptionsonPreferencesx2x1x1*x2*Ifpreferencesareconvexand

monotonic(i.e.well-behaved)

thenthemostpreferred

affordablebundleisunique.DirectPreferenceRevelationSupposethatthebundlex*ischosenwhenthebundleyisaffordable.Thenx*isrevealeddirectlyaspreferredtoy(otherwiseywouldhavebeenchosen).DirectPreferenceRevelationx2x1x*yThechosenbundlex*is

revealeddirectlyaspreferred

tothebundlesyandz.zDirectPreferenceRevelationThatxisrevealeddirectlyaspreferredtoywillbewrittenas

x

y.DpIndirectPreferenceRevelationSupposexisrevealeddirectlypreferredtoy,andyisrevealeddirectlypreferredtoz.Then,wecallxisrevealedindirectlyaspreferredtoz.Writethisas

x

z

soxyandyzxz.DpDpIpIpzisnotaffordablewhenx*ischosen.

x*isnotaffordablewheny*ischosen.

Sox*andzcannotbecompared

directly.IndirectPreferenceRevelationx2x1x*y*zButx*x*

y*

andy*z

sox*z.DpDpIpTwoAxiomsofRevealedPreferenceToapplyrevealedpreferenceanalysis,choicesmustsatisfytwocriteria--theWeakandtheStrongAxiomsofRevealedPreference.TheWeakAxiomofRevealedPreference(WARP)Ifthebundlexisrevealeddirectlyaspreferredtothebundleythenitisneverthecasethatyisrevealeddirectlyaspreferredtox;i.e.

xynot(yx).DpDpTheWeakAxiomofRevealedPreference(WARP)ChoicedatawhichviolatetheWARPareinconsistentwitheconomicrationality.TheWARPisanecessaryconditionforapplyingeconomicrationalitytoexplainobservedchoices.TheWeakAxiomofRevealedPreference(WARP)WhatchoicedataviolatetheWARP?TheWeakAxiomofRevealedPreference(WARP)x2x1xyyischosenwhenxisavailable

soyx.xischosenwhenyisavailable

soxy.DpDpCheckingifDataViolatetheWARPAconsumermakesthefollowingchoices:Atprices(p1,p2)=($2,$2)thechoicewas(x1,x2)=(10,1).At(p1,p2)=($2,$1)thechoicewas(x1,x2)=(5,5).At(p1,p2)=($1,$2)thechoicewas(x1,x2)=(5,4).IstheWARPviolatedbythesedata?CheckingifDataViolatetheWARP(5,4)

(10,1)(10,1)

(5,4)x1x2DpDpTheStrongAxiomofRevealedPreference(SARP)Ifthebundlexisrevealed(directlyorindirectly)aspreferredtothebundleyandx1y,thenitisneverthecasethattheyisrevealed(directlyorindirectly)aspreferredtox;i.e.

xyorxynot(yxoryx).DpDpIpIpTheStrongAxiomofRevealedPreferenceWhatchoicedatawouldsatisfytheWARPbutviolatetheSARP?TheStrongAxiomofRevealedPreferenceConsiderthefollowingdata:

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)TheStrongAxiomofRevealedPreferenceA:($1,$3,$10)

(3,1,4).B:($4,$3,$6)

(2,5,3).C:($1,$1,$5)

(4,4,3).TheStrongAxiomofRevealedPreferenceInsituationA,

bundleAisdirectlyrevealed

preferredto

bundleC;AC.DpTheStrongAxiomofRevealedPreferenceTheStrongAxiomofRevealedPreferenceThedatadonotviolatetheWARPbut...Wehavethat

AC,BAandCB

so,bytransitivity,

AB,BCandCA.DpDpDpIpIpIpIIITheStrongAxiomofRevealedPreferenceThattheobservedchoicedatasatisfytheSARPisaconditionnecessaryandsufficientfortheretobeawell-behavedpreferencerelationthat“rationalizes”thedata.Soour3datacannotberationalizedbyawell-behavedpreferencerelation.RecoveringIndifferenceCurvesSupposewehavethechoicedatasatisfytheSARP.Thenwecandiscoverapproximatelywherearetheconsumer’sindifferencecurves.How?RecoveringIndifferenceCurvesSupposeweobserve:

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).WhereliestheindifferencecurvecontainingthebundleA=(15,15)?RecoveringIndifferenceCurvesThetableshowingdirectpreferencerevelationsis:RecoveringIndifferenceCurvesDirectrevelationsonly;theWARP

isnotviolatedbythedata.RecoveringIndifferenceCurvesBothdirectandindirectrevelations;neither

WARPnorSARPareviolatedbythedata.RecoveringIndifferenceCurvesSincethechoicessatisfytheSARP,thereisawell-behavedpreferencerelationthat“rationalizes”thechoices.RecoveringIndifferenceCurvesx2x1ABECDA:(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).Beginwithbundlesrevealed

tobelesspreferredthanbundleA.RecoveringIndifferenceCurvesx2x1AA:(p1,p2)=(1,1);(x1,x2)=(15,15).Aisdirectlyrevealedpreferred

toanybundleinRecoveringIndifferenceCurvesx2x1ABECDA:(p1,p2)=(1,1);(x1,x2)=(15,15)

B:(p1,p2)=(2,1);(x1,x2)=(10,20).RecoveringIndifferenceCurvesx2x1BBisdirectlyrevealedpreferred

toallbundlesinRecoveringIndifferenceCurvesx2x1Bso,bytransitivity,Aisindirectly

revealedpreferredtoallbundles

inRecoveringIndifferenceCurvesx2x1BsoAisnowrevealedpreferred

toallbundlesintheunion.ARecoveringIndifferenceCurvesx2x1Cso

A

isnowrevealedpreferred

toallbundlesintheunion.BAThereforetheindifference

curvecontainingAmustlie

everywhereelseabove

thisshadedset.RecoveringIndifferenceCurvesNow,whataboutthebundlesrevealedasmorepreferredthanA?RecoveringIndifferenceCurvesx2x1ABECDA:(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).ARecoveringIndifferenceCurvesx2x1DDisdirectlyrevealedpreferred

toA.

Well-behavedpreferencesare

convexARecoveringIndifferenceCurvesx2x1DDisdirectlyrevealedpreferred

toA.

Well-behavedpreferencesare

convexsoallbundlesonthe

linebetweenAandDare

preferredtoAalso.ARecoveringIndifferenceCurvesx2x1DDisdirectlyrevealedpreferred

toA.

Well-behavedpreferencesare

convexsoallbundlesonthe

linebetweenAandDare

preferredtoAalso.AAswell,...RecoveringIndifferenceCurvesx2x1Dallbundlescontainingthe

sameamountofcommodity2

andmoreofcommodity1than

DarepreferredtoDand

thereforearepreferredtoA

also.ARecoveringIndifferenceCurvesx2x1DAbundlesrevealedtobestrictlypreferredtoARecoveringIndifferenceCurvesx2x1ABECDA:(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).ARecoveringIndifferenceCurvesx2x1BCEDAllbundlesrevealed

tobepreferredtoAARecoveringIndifferenceCurvesNowwehaveupperandlowerboundsonwheretheindifferencecurvecontainingbundleAmaylie.RecoveringIndifferenceCurvesx2x1Allbundlesrevealed

tobepreferredtoAAAllbundlesrevealedtobelesspreferredtoARecoveringIndifferenceCurvesx2x1TheregioninwhichtheindifferencecurvecontainingbundleAmustlie.AIndexNumbersOvertime,manypriceschange.Areconsumersbetterorworseoff“overall”asaconsequence?Indexnumbersgiveapproximateanswerstosuchquestions.IndexNumbersTwobasictypesofindicespriceindices,andquantityindicesEachindexcomparesexpendituresinabaseperiodandinacurrentperiodbytakingtheratioofexpenditures.QuantityIndexNumbersAquantityindexisaprice-weightedaverageofquantitiesdemanded;i.e.

(p1,p2)canbebaseperiodprices(p1b,p2b)orcurrentperiodprices(p1t,p2t).QuantityIndexNumbersIf(p1,p2)=(p1b,p2b)thenwehavetheLaspeyresquantityindex;

QuantityIndexNumbersIf(p1,p2)=(p1t,p2t)thenwehavethePaaschequantityindex;

QuantityIndexNumbers

(studytherestofthechapteronyourown)Howcanquantityindicesbeusedtomakestatementsaboutchangesinwelfare?QuantityIndexNumbersIfthen

soconsumersoverallwerebetteroffinthebaseperiodthantheyarenowinthecurrentperiod.PriceIndexNumbersApriceindexisaquantity-weightedaverageofprices;i.e.

(x1,x2)canbethebaseperiodbundle(x1b,x2b)orelsethecurrentperiodbundle(x1t,x2t).PriceIndexNumbersIf(x1,x2)=(x1b,x2b)thenwehavetheLaspeyrespriceindex;

PriceIndexNumbersIf(x1,x2)=(x1t,x2t)thenwehavethePaaschepriceindex;

PriceIndexNumbersHowcanpriceindicesbeusedtomakestatementsaboutchangesinwelfare?Definetheexpenditureratio

PriceIndexNumbersIf

then

soconsumersoverallarebetteroffinthecurrentperiod.

FullIndexation?Changesinpriceindicesaresometimesusedtoadjustwageratesortransferpayments.Thisiscalled“indexation”.“Fullindexation”occurswhenthewagesorpaymentsareincreasedatthesamerateasthepriceindexbeingusedtomeasuretheaggregateinflationrate.SummaryTheKeytothischapteristheconceptofrevealedpreference:ifxischosenwhileyischoosable,thenxi