一消费者选择理论回顾First consumer choice theory review.docx

一消费者选择理论回顾First consumer choice theory review.docx

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一消费者选择理论回顾Firstconsumerchoicetheoryreview

一、消费者选择理论回顾（First,consumerchoicetheoryreview）

First,consumerchoicetheoryreview

1.1basicstructure

1.2consumerpreferences

Consumptionbundle

Bundlesofconsumption（set）

Atotaloftwocommodities,X,Y,areassumedtobepositivecommodities（goods,not,bads）

Axiom（axioms）orhypothesis

（1）nonsatisfaction（non-satiation）

Themoretheamountofgoodsyouget,thebetter.

So,inanyonecommoditygroup,theentireX-Yspaceisdividedintofiveparts:

themutualexclusionpointofa（better-thanset）intheset,toset（worse-thanset）,andtheothertwosets.Ifthereisanodifferenceset,thenitmustbelocatedinthetwosets（I,IV）andincludeapoints.

Notethatbetterthansetanddifferencesetcontainallboundaries,butnotapoints.

（2）completeness

Canbecomparedtoanytwocommoditygroups（22comparisons）

AB,AB,ora~b

IfXandYareinfinitelydivisible,andconsumerscancompareanytwocommoditygroups,thereisacontinuoussetofindifferencesets（indifferenceset）,andthesetmustbeadownwardslopingline.as

Atthepointabove,atanypointoftheindifferencecurve,theslopeisnegative.Theslopeabsolutevalueisthemarginalrateofsubstitution（marginalrateofsubstitution）.

Accordingtocompleteness,theX-Yspacecanbedividedintothreemutuallyexclusivesets,namely,nodifferenceset,betterset（locatedattheupperrightofthenondifferentialset）anddifferenceset（locatedintheleftloweroftheindifferenceset）.

（3）convexity（convexity）.Convexityisstrictlydivided（strong）andlax（weak）.

Strictconvexity:

diminishingmarginalrateofsubstitution;

Nonstrictconvexity:

marginalsubstitutionratedoesnotincrease;

（4）differentiabilityorsmoothness（differentiabilityorsmoothness）

（==marginalrateofsubstitution）

（5）transitivity（transitivity）

Ifa~bandb~c,thenc~a

Transitivitydoesnotallowanyintersectionoftwodifferentindifferencecurves

1.3indifferencecurves

Importantproperties:

Noncrossing

Notnecessarilyparallel

Everycurveabovetherightmeanshigherutility

-otherthings

Completesubstitute

Perfectcomplement

1.4utilityfunctionU（X,Y）:

Anumericalrepresentationofaperson'spreference

Ordinalutilityfunctionandcardinalutilityfunction

MathematicalderivationandrepresentationofsubstitutionrateofEditors

=+=0

=<0

Sufficientconditionsfordiminishingmarginalrateofsubstitution

=

Intheupperform,theslopeoftheindifferencecurveisnegative.Thenif

<0,<0,>0,

>0

Thatis,thereisnodifferencecurveconvexorigin;themarginalsubstitutionratedecreases.

1.5budgetconstraint

LetconsumershaveincomeI,allforpurchasing/consumingXandYtwocommodities（goods）,andXandYrespectively.be

I=X+Y

=+=0,=

（）theslopeofthebudgetconstraintline:

Anothermethodtodeducetheslopeofthebudgetconstraintline:

I=+

Y=,=

Acomparisonbetweenmarginalsubstitutionrateandslopeofbudgetconstraintline:

Theformerisbasedontheconsumer'spersonalpreferences,theunitXvalueofhowmanyunitsofY;thelatterisbasedonthemarketprice,aunitofXinthemarketforhowmanyunitsofY

Thebudgetconstraintlinemovesparalleltotheright/leftsidewiththeincrease/decreaseoftherevenueI.

1.6consumerequilibrium

GiventheincomeI,price,andconsumerpreferences,thecurvebetweenanondifferencecurveandthebudgetconstraintlineistheequilibriumpoint（Figuree）.Atthispoint,theutilityoftheconsumerismaximized（givenincome）,

He/shehasreachedthehighestindifferencecurve.Atthispoint

=

（question:

whatifconsumerutilityismaximized?

Two.Theapplicationandextensionofconsumerdemandtheory

WhenYisabad

2.1negativecommodities（bads）

Positivegoods（goods）canprovideutilityforpeople.Negativecommodities（bads）onlybringnegativeeffectstopeople（disutility）.Microeconomicstextbooksusuallyassumethattwocommodities,XandY,arepositivecommodities.However,whenwetakeintoaccountenvironmentalpollutionandotherissues,thatassumptiondoesnotapply.Pollutantsareanegativecommodityforpeople.WeconsiderthecasethatXisapositivecommodityandYisanegativecommodity.

2.2consumerpreferences

Wecanderivetherelatedindifferencegraphbyapplyingthesameaxiomofconsumerpreferenceasthepreviousone.

（1）nonsatisfaction（non-satiation）:

Notethatwhenacommodityiscommodity（good）,doesnotmeettheconsumerslovemeansmoregoodsquantity;butwhenacommodityisnegativewhenthegoods（bad）,consumerslovethelessnumberofgoods.Inthisway,theX-Yspacecanbedividedintofivemutuallyexclusivesets:

pointa,betterset,differenceset,andtheothertwosets（II,IIIregion）,withpointaasreference.Ifthereisanodifferenceset,itmustbelocatedinthesetwosetsandincludethepointa（thefollowing）

Attention:

betterthansetanddifferenceset,includingallofitsboundaries（butnotapoints）.

（2）completeness（completeness）

IfXandYareinfinitelydivisible,andconsumerscancompareanytwocommoditygroups,thereisacontinuoussetofindifferencesetsthatmustbeanupwardline.

Below,atanypointintheindifferencecurve,themarginalrateofsubstitutionis:

aunitincreaseinYconsumptionmustincreasetheconsumptionofX（constantutilitytoenableconsumerstomakeconsumersgetthecorrespondingcompensation）（Note:

strictlyspeaking,itshouldbecalledmarginalcompensationrate）.Accordingtocompleteness,thewholeX-Yspacecanbedividedintothreemutuallyexclusivesets:

nodifferenceset,betterset（atthelowerrightofthenondifferenceset）anddifferenceset（leftupperoftheindifferenceset）

（3）concavity（concavity）:

strictandlax.Strictlyguaranteeddecreasing;notstrictlyguaranteedwithoutincreasing.

（4）differentiability/smoothness（differentiability/smoothness）

（==marginalrateofsubstitution）

（5）transitivity（transitivity）

Ensurethatnotwocurvesintersectwithoutdifference

2.3indifferencecurves

2.4othercircumstances

（1）Y:

good;X:

bad

Accordingtothesameprinciple,whenYisapositivecommodityandXisanegativeproduct,wecandeducethefollowingindifferencegraph.

（2）whenbothXandYarenegativecommodities:

（3）wecanillustrateallfourpossiblescenarioswithagraph:

2.5sufficientconditionsfordiminishing

=>0

=

Sincethesymbolsherearedifficulttomakeageneralassumption,weset=0（i.e.,notconsidered）.that

=

Here,theslopeoftheindifferencecurveispositive.

If<0（becauseYisanegativecommodity）,>0.Suppose<0,and<0（meanYmarginalnegativeutilityincrease）,then

<0

（studentscanusethesamestepsandapplythesameassumptionswhenXisanegativecommodityandYisapositivecommodity

>0

2.6budgetconstraintline

LetIbetheincomeandthepriceofXandYrespectively.be

I=X+Y

Available:

=

However,sinceYisanegativecommodity,itisdifficulttoassumethatanypersonwillpayapositivepriceforconsumingaunitofsuchacommodity.Onthecontrary,themarketpriceshouldbenegative,thatis,peoplewillbecompensatedfortheconsumptionofaunitofsuchgoods（<0）.Inotherwords

=>0

ThepointaisthetotalamountofXthatcanbepurchasedwhenIisfullyusedinX.

2.7consumerequilibrium

Epointistheequilibriumpointofconsumers,atwhichpoint,theutilityofconsumersismaximizedatthispoint,

=

One

LecturesonEnvironmentalEconomics