chapter-3-Preferences-西方经济英文版课件

Course:MicroeconomicsText:Varian’sIntermediateMicroeconomics

1Course:Microeconomics1Lastchapterwetalkaboutwhatisaffordableorfeasibletoconsumers.Thistimewetalkaboutpreferences:whattheconsumerlikemoreandwhattheylikeless.Asarationalagent,aconsumerchoosestheoptioninthebudgetsetthatishighestintheirpreferenceorder(i.e.onelikesthemost).2LastchapterwetalkaboutwhaPreferenceRelationsLetx,yareconsumptionbundles.denotesstrictpreferenceso

xymeansthatbundlexispreferredstrictlytobundley.~denotesindifference;x~ymeansxandyareequallypreferred.denotesweakpreference;

xymeansxispreferredatleastasmuchasisy.

~fpp~f3PreferenceRelationsLetx,yaPreferenceRelationsStrictpreference,weakpreferenceandindifferenceareallpreferencerelations.Particularly,theyareordinalrelations;i.e.theystateonlytheorderinwhichbundlesarepreferred.Ithasnoindicationofhowmuchtheylikeoneversustheother.4PreferenceRelationsStrictprePreferenceRelationsxyandyximplyx~y.xyand(notyx)implyxy.~f~f~f~fp5PreferenceRelationsxyanAssumptionsaboutPreferenceRelationsCompleteness:Foranytwobundlesxandyitisalwayspossibletomakethestatementthateither

xy

or

yx.Bundlesarealwayscomparable.Ifbotharetrue,thentheyareindifferenttotheindividual.~f~f6AssumptionsaboutPreferenceRAssumptionsaboutPreferenceRelationsReflexivity:Anybundlexisalwaysatleastaspreferredasitself;i.e.

xx.~f7AssumptionsaboutPreferenceRAssumptionsaboutPreferenceRelationsTransitivity:If

xisatleastaspreferredasy,and

yisatleastaspreferredasz,then

xisatleastaspreferredasz;i.e.

xyandyzxz.Itavoidscircularpreference,andensurethatthereexiststhebestbundle.~f~f~f8AssumptionsaboutPreferenceRIndifferenceCurvesTakeareferencebundlex’.Thesetofallbundlesequallypreferredtox’istheindifferencecurve(set)containingx’;thesetofallbundles{y:y~x’}.Weaklypreferredset:bundlesthatareweaklypreferredtox’.{y:yx’}.~f9IndifferenceCurvesTakearefeIndifferenceCurvesx2x1x”x”’x’~x”~x”’x’Theconsumerisindifferentbetweeneverypointontheindifferencecurve.10IndifferenceCurvesx2x1x”x”’x’IndifferenceCurvesx2x1z

x

yppxyzIfconsumerprefersmoretolessforeachgoods,allbundlesonthenortheastoftheindifferencecurvearestrictlypreferredtox,andallbundlessouthwestoftheindifferencecurvearelesspreferredtox.11IndifferenceCurvesx2x1zIndifferenceCurvesx2x1xAllbundlesinI1arestrictlypreferredtoallinI2.yzAllbundlesinI2arestrictlypreferredtoallinI3.I1I2I312IndifferenceCurvesx2x1xAllbuIndifferenceCurvesx2x1I(x’)xI(x)WP(x),thesetof

bundlesweaklypreferredtox.13IndifferenceCurvesx2x1I(x’)xIIndifferenceCurvesx2x1WP(x),thesetof

bundlesweaklypreferredtox.WP(x)

includes

I(x).xI(x)14IndifferenceCurvesx2x1WP(x),IndifferenceCurvesx2x1SP(x),thesetof

bundlesstrictlypreferredtox,

doesnot

includeI(x).xI(x)15IndifferenceCurvesx2x1SP(x),x2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.ButbecauseI1andI2representdistinctlevelofpreference,wesee

yz,acontradiction.p16x2x1xyzI1I2FromI1,x~y.p1Whenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesarenegativelysloped.Itisbecausewhenonehasmoreofonegood,onehastogetlessofanothertomakethisbundleindifferenttotheoriginalone.17WhenmoreofacommodityisalSlopesofIndifferenceCurvesBetterWorseGood2Good1Twogoods

anegativelyslopedindifferencecurve.18SlopesofIndifferenceCurvesBIflessofacommodityisalwayspreferredthenthecommodityisabad.e.g.rottenfruits;tobaccosmoke(ifyoudonotsmoke)Ifonegoodisgoodandtheotherisbad,thentheindifferencecurvewouldbeupwardsloping.19IflessofacommodityisalwaSlopesofIndifferenceCurvesBetterWorseGood2Bad1Onegoodandone

badapositivelyslopedindifferencecurve.Ifyouwantmoreofthegood,youalsohavetogetmoreofthebadsothatyouareindifferentbetweenthem.20SlopesofIndifferenceCurvesBIfonejustdonotcareaboutwhetherorhowmuchtohaveacommodity,thisiscalledaneutralgood.E.g.:goodsthatyoudon’tuseanddonotcareabouttheirexistence.Ifonecommodityisneutral,theotherisgood,theindifferencecurvewouldbevertical/horizontal.21Ifonejustdonotcareabout2222ExtremeCasesofIndifferenceCurves;PerfectSubstitutesIfaconsumeralwaysregardsunitsofcommodities1and2asequivalent,thenthecommoditiesareperfectsubstitutes.Onlythetotalamount(oraweightedsum)ofthetwocommoditiesinbundlesdeterminestheirpreferencerank-order.Example:orangejuiceoftwodifferentbrands.Apartmentindifferentlocations.23ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectSubstitutesx2x1881515Slopesareconstantat-1.I2I1BundlesinI2allhaveatotal

of15unitsandarestrictlypreferredtoallbundlesin

I1,whichhaveatotalof

only8unitsinthem.24ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsIfaconsumeralwaysconsumescommodities1and2infixedproportion(e.g.one-to-one),thenthecommoditiesareperfectcomplements.Onlythenumberofpairsofunitsofthetwocommoditiesdeterminesthepreferencerank-orderofbundles.E.g.:leftshoes/rightshoes;computerandmonitor.25ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I145o5959Eachof(5,5),(5,9)and(9,5)contains

5pairssoeachisequallypreferred.

26ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I2I145o5959Sinceeachof(5,5),(5,9)and(9,5)contains5pairs,eachislesspreferredthanthebundle(9,9)

whichcontains9pairs.

27ExtremeCasesofIndifferenceAbundlestrictlypreferredtoanyothersisasatiationpointorablisspoint.Thesatiationpointisthebestbundle.Moreofanythingarenotbetter.Whatdoindifferencecurveslooklikeforpreferencesexhibitingsatiation?28AbundlestrictlypreferredtoIndifferenceCurvesExhibitingSatiationx2x1Satiation

(bliss)

point29IndifferenceCurvesExhibitingIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

point30IndifferenceCurvesExhibitingIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

point31IndifferenceCurvesExhibitingIndifferenceCurvesforDiscreteCommoditiesAcommodityisinfinitelydivisibleifitcanbeacquiredinanyquantity;e.g.waterorcheese.Acommodityisdiscreteifitcomesinunitlumpsof1,2,3,…andsoon;e.g.aircraft,shipsandrefrigerators.32IndifferenceCurvesforDiscreIndifferenceCurvesforDiscreteCommoditiesSupposecommodity2isaninfinitelydivisiblegood(gasoline)whilecommodity1isadiscretegood(aircraft).Whatdoindifference“curves”looklike?33IndifferenceCurvesforDiscreGasolineAircraft01234Indifference“curves”

arecollectionsof

discretepoints.34GasolineAircraft01234IndiffereWell-BehavedPreferencesTypicalassumptionsofpreferencesApreferencerelationis“well-behaved”ifitismonotonicandconvex.Monotonicity:Moreofanycommodityisalwayspreferred(i.e.nosatiationandeverycommodityisagood).ThisimpliesanegativelyslopedIC.35Well-BehavedPreferencesTypicaWell-BehavedPreferencesConvexity:Mixturesofbundlesare(atleastweakly)preferredtothebundlesthemselves.E.g.,the50-50mixtureofthebundlesxandyis

z=(0.5)x+(0.5)y.

zisatleastaspreferredasxory.36Well-BehavedPreferencesConvexWell-BehavedPreferences--Convexity.x2y2x2+y22x1y1x1+y12xyz=

x+y2Is(weakly)preferredtobothxandy.37Well-BehavedPreferences--CoWell-BehavedPreferences--Convexity.x2y2x1y1xyz=(tx1+(1-t)y1,tx2+(1-t)y2)ispreferredtoxandyforall0<t<1.38Well-BehavedPreferences--CoWell-BehavedPreferences--Convexity.x2y2x1y1xyPreferencesarestrictlyconvex

whenallmixturesz

arestrictly

preferredtotheir

component

bundlesxandy.z39Well-BehavedPreferences--Cox2y2x1y1zBetterThemixturez

islesspreferredthanxory.Onelikesboth,butdoeswanttoconsumetogether.40x2y2x1y1zBetterThemixturez

ix2y2x1y1zBetterThemixturez

islesspreferredthanxory.41x2y2x1y1zBetterThemixturez

iItrepresentsamorebalancedpreferenceratherthanapreferencethatinducesaspecialization.Itisnaturaltoconsumethegoodsinvolvedinpositiveamount.Italsoimpliesadiminishingmarginalrateofsubstitution.42ItrepresentsamorebalancedSlopesofIndifferenceCurvesThenegativeoftheslopeofanindifferencecurveisitsmarginalrateofsubstitution(MRS).Note:thisisslightlydifferentfromthetextbook,butmydefinitionismorepopular.Thisrepresentsthemaximumamountofx2oneiswillingtogiveupperunitofx1ataspecificconsumptionbundle.43SlopesofIndifferenceCurvesTMarginalRateofSubstitutionx2x1x’MRSatx’isthe(negative)slopeofthe

indifferencecurveatx’44MarginalRateofSubstitutionxMarginalRateofSubstitutionx2x1

MRSatx’is

lim-{Dx2/Dx1}

Dx10

=-dx2/dx1atx’Dx2Dx1x’45MarginalRateofSubstitutionxMarginalRateofSubstitutionx2x1dx2dx1-dx2=MRS´dx1so,atx’,MRSistherateatwhichtheconsumerisonlyjustwillingtoexchangecommodity2forasmallamountofcommodity1.x’46MarginalRateofSubstitutionxMRS&Ind.CurvePropertiesBetterWorseGood2Good1Twogoods

anegativelyslopedindifferencecurveMRS>0.47MRS&Ind.CurvePropertiesBetMRS&Ind.CurvePropertiesBetterWorseGood2Bad1Onegoodandone

badapositivelyslopedindifferencecurveMRS<0.Becauseinsteadofgivingup,youhavetoobtainmoregood2foryoutobewillingtoacceptmoregood1.48MRS&Ind.CurvePropertiesBetMRS&Ind.CurvePropertiesGood2Good1MRS=5MRS=0.5MRSalwaysdecreaseswithx1

ifandonlyifpreferencesarestrictly

convex.Wecallitadiminishingmarginalrateofsubstitution.49MRS&Ind.CurvePropertiesGooMRS&Ind.CurvePropertiesx1x2MRS=0.5MRS=5MRSincreases

asx1increases

non-convexpreferences

50MRS&Ind.CurvePropertiesx1xMRS&Ind.CurvePropertiesx2x1MRS

=0.5MRS=2MRSisnotalwaysdecreasingasx1increasesnon-convexpreferences.MRS=1.551MRS&Ind.CurvePropertiesx2xInthischapter,wetalkabouthowwecanspecifyconsumer’spreferencetowardsdifferentconsumptionbundles.Wecanuseindifferentcurvetodepictdifferentkindsofpreferences.Themarginalrateofsubstitutionistheslopeofindifferencecurve.Itrepresentsthewillingnesstosubstituteonegoodforanotherone.52Inthischapter,wetalkaboutWehavetalkedaboutpreferenceandindifferencecurveinthischapter.Toputpreferenceinamoremathematicallyconvenientway,weintroducetheutilityfunctioninthecomingchapter.Thenwecanputtogetherpreference/utilityandbudgetconstrainttoanalyzeconsumerchoices.53WehavetalkedaboutpreferencCourse:MicroeconomicsText:Varian’sIntermediateMicroeconomics

54Course:Microeconomics1Lastchapterwetalkaboutwhatisaffordableorfeasibletoconsumers.Thistimewetalkaboutpreferences:whattheconsumerlikemoreandwhattheylikeless.Asarationalagent,aconsumerchoosestheoptioninthebudgetsetthatishighestintheirpreferenceorder(i.e.onelikesthemost).55LastchapterwetalkaboutwhaPreferenceRelationsLetx,yareconsumptionbundles.denotesstrictpreferenceso

xymeansthatbundlexispreferredstrictlytobundley.~denotesindifference;x~ymeansxandyareequallypreferred.denotesweakpreference;

xymeansxispreferredatleastasmuchasisy.

~fpp~f56PreferenceRelationsLetx,yaPreferenceRelationsStrictpreference,weakpreferenceandindifferenceareallpreferencerelations.Particularly,theyareordinalrelations;i.e.theystateonlytheorderinwhichbundlesarepreferred.Ithasnoindicationofhowmuchtheylikeoneversustheother.57PreferenceRelationsStrictprePreferenceRelationsxyandyximplyx~y.xyand(notyx)implyxy.~f~f~f~fp58PreferenceRelationsxyanAssumptionsaboutPreferenceRelationsCompleteness:Foranytwobundlesxandyitisalwayspossibletomakethestatementthateither

xy

or

yx.Bundlesarealwayscomparable.Ifbotharetrue,thentheyareindifferenttotheindividual.~f~f59AssumptionsaboutPreferenceRAssumptionsaboutPreferenceRelationsReflexivity:Anybundlexisalwaysatleastaspreferredasitself;i.e.

xx.~f60AssumptionsaboutPreferenceRAssumptionsaboutPreferenceRelationsTransitivity:If

xisatleastaspreferredasy,and

yisatleastaspreferredasz,then

xisatleastaspreferredasz;i.e.

xyandyzxz.Itavoidscircularpreference,andensurethatthereexiststhebestbundle.~f~f~f61AssumptionsaboutPreferenceRIndifferenceCurvesTakeareferencebundlex’.Thesetofallbundlesequallypreferredtox’istheindifferencecurve(set)containingx’;thesetofallbundles{y:y~x’}.Weaklypreferredset:bundlesthatareweaklypreferredtox’.{y:yx’}.~f62IndifferenceCurvesTakearefeIndifferenceCurvesx2x1x”x”’x’~x”~x”’x’Theconsumerisindifferentbetweeneverypointontheindifferencecurve.63IndifferenceCurvesx2x1x”x”’x’IndifferenceCurvesx2x1z

x

yppxyzIfconsumerprefersmoretolessforeachgoods,allbundlesonthenortheastoftheindifferencecurvearestrictlypreferredtox,andallbundlessouthwestoftheindifferencecurvearelesspreferredtox.64IndifferenceCurvesx2x1zIndifferenceCurvesx2x1xAllbundlesinI1arestrictlypreferredtoallinI2.yzAllbundlesinI2arestrictlypreferredtoallinI3.I1I2I365IndifferenceCurvesx2x1xAllbuIndifferenceCurvesx2x1I(x’)xI(x)WP(x),thesetof

bundlesweaklypreferredtox.66IndifferenceCurvesx2x1I(x’)xIIndifferenceCurvesx2x1WP(x),thesetof

bundlesweaklypreferredtox.WP(x)

includes

I(x).xI(x)67IndifferenceCurvesx2x1WP(x),IndifferenceCurvesx2x1SP(x),thesetof

bundlesstrictlypreferredtox,

doesnot

includeI(x).xI(x)68IndifferenceCurvesx2x1SP(x),x2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.ButbecauseI1andI2representdistinctlevelofpreference,wesee

yz,acontradiction.p69x2x1xyzI1I2FromI1,x~y.p1Whenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesarenegativelysloped.Itisbecausewhenonehasmoreofonegood,onehastogetlessofanothertomakethisbundleindifferenttotheoriginalone.70WhenmoreofacommodityisalSlopesofIndifferenceCurvesBetterWorseGood2Good1Twogoods

anegativelyslopedindifferencecurve.71SlopesofIndifferenceCurvesBIflessofacommodityisalwayspreferredthenthecommodityisabad.e.g.rottenfruits;tobaccosmoke(ifyoudonotsmoke)Ifonegoodisgoodandtheotherisbad,thentheindifferencecurvewouldbeupwardsloping.72IflessofacommodityisalwaSlopesofIndifferenceCurvesBetterWorseGood2Bad1Onegoodandone

badapositivelyslopedindifferencecurve.Ifyouwantmoreofthegood,youalsohavetogetmoreofthebadsothatyouareindifferentbetweenthem.73SlopesofIndifferenceCurvesBIfonejustdonotcareaboutwhetherorhowmuchtohaveacommodity,thisiscalledaneutralgood.E.g.:goodsthatyoudon’tuseanddonotcareabouttheirexistence.Ifonecommodityisneutral,theotherisgood,theindifferencecurvewouldbevertical/horizontal.74Ifonejustdonotcareabout7522ExtremeCasesofIndifferenceCurves;PerfectSubstitutesIfaconsumeralwaysregardsunitsofcommodities1and2asequivalent,thenthecommoditiesareperfectsubstitutes.Onlythetotalamount(oraweightedsum)ofthetwocommoditiesinbundlesdeterminestheirpreferencerank-order.Example:orangejuiceoftwodifferentbrands.Apartmentindifferentlocations.76ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectSubstitutesx2x1881515Slopesareconstantat-1.I2I1BundlesinI2allhaveatotal

of15unitsandarestrictlypreferredtoallbundlesin

I1,whichhaveatotalof

only8unitsinthem.77ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsIfaconsumeralwaysconsumescommodities1and2infixedproportion(e.g.one-to-one),thenthecommoditiesareperfectcomplements.Onlythenumberofpairsofunitsofthetwocommoditiesdeterminesthepreferencerank-orderofbundles.E.g.:leftshoes/rightshoes;computerandmonitor.78ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I145o5959Eachof(5,5),(5,9)and(9,5)contains

5pairssoeachisequallypreferred.

79ExtremeCasesofIndifferenceExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I2I145o5959Sinceeachof(5,5),(5,9)and(9,5)contains5pairs,eachislesspreferredthanthebundle(9,9)

whichcontains9pairs.

80ExtremeCasesofIndifferenceAbundlestrictlypreferredtoanyothersisasatiationpointorablisspoint.Thesatiationpointisthebestbundle.Moreofanythingarenotbetter.Whatdoindifferencecurveslooklikeforpreferencesexhibitingsatiation?81AbundlestrictlypreferredtoIndifferenceCurvesExhibitingSatiationx2x1Satiation

(bliss)

point82IndifferenceCurvesExhibitingIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

point83IndifferenceCurvesExhibitingIndifferenceCurvesExhibitingSatiationx2x1BetterBetterBetterSatiation

(bliss)

point84IndifferenceCurvesExhibitingIndifferenceCurvesforDiscreteCommoditiesAcommodityisinfinitelydivisibleifitcanbeacquiredinanyquantity;e.g.waterorcheese.Acommodityisdiscreteifitcomesinunitlumpsof1,2,3,…andsoon;e.g.aircraft,shipsandrefrigerators.85IndifferenceCurvesforDiscreIndifferenceCurvesforDiscreteCommoditiesSupposecommodity2isaninfinitelydivisiblegood(gasoline)whilecommodity1isadiscretegood(aircraft).Whatdoindifference“curves”looklike?86IndifferenceCurvesforDiscreGasolineAircraft01234Indifference“curves”

arecollectionsof

discretepoints.87GasolineAircraft01234IndiffereWell-BehavedPreferencesTypicalassumptionsofpreferencesApreferencerelationis“well-behaved”ifitismonotonicandconvex.Monotonicity:Moreofanycommodityisalwayspreferred(i.e.nosatiationandeverycommodityisagood).ThisimpliesanegativelyslopedIC.88Well-BehavedPreferencesTypicaWell-BehavedPreferencesConvexity:Mixturesofbundlesare(atleastweakly)preferredtothebundlesthemselves.E.g.,the50-50mixtureofthebundlesxandyis

z=(0.5)x+(0.5)y.

zisatleastaspreferredasxory.89Well-BehavedPreferencesConvexWell-BehavedPreferences--Convexity.x2y2x2+y22x1y1x1+y12xyz=

x+y2Is(weakly)preferredtobothxandy.90Well-BehavedPreferences--CoWell-BehavedPreferences--Convexity.x2y2x1y1xyz=(tx1+(1-t)y1,tx2+(1-t)y2)ispreferredtoxandyforall0<t<1.91Well-BehavedPreferences--CoWell-BehavedPreferences--Convexity.x2y2x1y1xyPreferencesarestrictlyconvex

whenallmixturesz

arestrictly

preferredtotheir

component

bundlesxandy.z92Well-BehavedPreferences--Cox2y2x1y1zBetterThemixturez

islesspreferredthanxory.Onelikesboth,butdoeswanttoconsumetogether.93x2y2x1y1zBetterThemixturez

ix2y2x1y1zBetterThemixturez

islesspreferredthanxory.94x2y2x1y1zBetterThemixturez

iItrepresentsamorebalancedpreferenceratherthanapreferencethatinducesaspecialization.Itisnaturaltoconsumethegoodsinvolvedinpositiveamount.Italsoimpliesadiminishingmarginalrateofsubstitution.95ItrepresentsamorebalancedSlopesofIndifferenceCurvesThenegativeoftheslopeofanindifferencecurveisitsmarginalrateofsubstitution(MRS