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