微观经济学2010 micro完全替代互补satia_第1页
微观经济学2010 micro完全替代互补satia_第2页
微观经济学2010 micro完全替代互补satia_第3页
微观经济学2010 micro完全替代互补satia_第4页
微观经济学2010 micro完全替代互补satia_第5页
已阅读5页,还剩26页未读 继续免费阅读

下载本文档

版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领

文档简介

Consumer

TherearethreestepsinvolvedintheConsumerTodescribehowandwhypeoplepreferonegoodtoanotherBudget Givenpreferencesandlimitedes,whatamountandtypeofgoodswillbeWhatcombinationofgoodswillconsumersbuytoizetheirsatisfaction?

BudgetDescribebudgetDescribechangesinbudget ernmentprogramsandbudgetNon-linearbudgetcommodity1,x2unitsofcommodity2andsoonvector(x1,x2,…,xn).

PhysicalConsumptionset:X={(x1,…,xn)|x10,…,xn0AconsumptionsetisthecollectionofallphysicallypossibleconsumptionbundlestotheconsumerBudgetCommoditypricesarep1,p2,…,Q:Whenisabundle(x1,…,xn)p1x1+…+pnxnwheremistheconsumer’s

BudgetThebundlesthatareonlyjustaffordableformtheconsumer’sbudgetconstraint.Thisistheset{(x1,…,xn)|x10,…,xnp1x1+…+pnxnmBudgetSetandConstraintfor

BudgetSetandConstraintfor m

+

=

m

+

=m m BudgetSetandConstraintfor

BudgetSetandConstraintfor m

+

=

m

+

=Just

NotaffordableJustaffordablem m BudgetSetandConstraintfor

BudgetSetandConstraintfor m

+

=

m

+

=NotaffordableJustaffordable

theofallaffordablem m BudgetSetandConstraintfor

Budget p1x1+p2x2=m

Slopeis-xmx2

=-

+

soslopeis-

m Budget Opp.costofanextraunitofcommodity1isp1/p2foregoneofcommodity

Budget Opp.costofanextraunitofcommodity1isp1/p2foregoneofcommodity Opp.costofanunitofcommodity2

p2/p1unitsforegoneofcommodity1.BudgetSets&Constraints; andPriceChangesdependuponpricesand happensaspricesor echange?

constraintchange em2budgetset Newaffordableconsumption

dothebudgetsetandbudgetconstraintchangeas emdecreases?budgetset

Originalnewbudgetconstraintsareparallel(same

budgetset dothebudgetsetandbudgetconstraintchangeas emdecreases?

BudgetConstraints- budgetset

thatarenolongerOldandnewareparallel.

Increasesin emshifttheconstraintoutwardinaparallelmanner,therebyenlargingthebudgetsetandimprovingDecreasesin emshifttheconstraintinwardinaparallelmanner,therebyshrinkingthebudgetsetandreducingBudgetConstraints-

Budget

PriceNooriginalchoiceislostandnewchoicesareaddedwhen worseoff. edecreasemay(typicallywill)

WhathappensifjustonepriceSupposep1Howdothebudgetsetandbudgetconstraintchangeasp1decreasesfromp1’top1”?

Howdothebudgetsetandbudgetconstraintchangeasp1decreasesfromp1’top1”? Newaffordable budgetset

budgetset

Budget

Price

choiceislostandnewchoicesareadded,soreducinone consumerworseoffSimilarly,increasingonepricepivotstheconstraintinwards,reduceschoiceandmay(typicallywill)maketheconsumerworseoff.

atarateof5%increasesallpricesby5%,frompto(1+0.05)p1.05p.AnadvaloremsalestaxleviedatarateofincreasesallpricesbytpfromptoAuniformsalestaxisapplieduniformlytoallAuniformsalestaxleviedatratetchanges

Auniformsalestaxleviedatratetchangesp1x1+p2x2=

p1x1+p2x2=p1x1+p2x2=Sales

Sales p1x1+p2x2= p1x1+p2x2=

e m t m (1t)

(1t)

1

1 (1t) (1t) Sales Auniformad salestaxleviedatrateisequivalentto

Foodstampsarecouponsthatcanbelegallyexchangedonlyforfood. (1t)

taxleviedat

1t

Howdoesacommodity-specificgiftsuchasafoodstam (1t) of“othergoods”ispG=$1“Othergoods”isacompositeItsimplifies ysistoa2-good

F+G=100: ThebudgetconstraintisF+G

GF+G=100:

GF+G=100:

Budgetsetafter40foodstampsissued.

Budgetsetafter40foodstampsissued.Thefamily’sbudgetsetisenlarged. (F-40)+G=100forF40G=100forF<40

(F-40)+G=100forF40G=100forF<40Whatiffoodstampscanbetradedona

F+G=100: Budgetconstraintafter40foodstampsissued.Budgetconstraintwithblackmarkettrading. F+G=100+0.5(40-F)for(F-40)+G=100forF

Budgetconstraintafter40foodstampsissued.Blackmarkettradingmakesthebudgetsetlargeragain. 、 username:

ShapesofBudgetQ:WhatmakesabudgetconstraintaA:Astraightlinehasaconstantslopeandp1x1+…+pnxn=msoifpricesareconstantsthenaconstraintisastraightline.ShapesofBudgetButwhatifpricesarenotE.g.bulkbuyingdiscounts,orpricepenaltiesforbuying“toomuch”.Thenconstraintswillbe

ShapesofBudgetConstraints-tyDiscountsSupposep2isconstantat$1butthatp1=$2for0x120andp1=$1fortyDiscountsSupposep2isconstantat$1butthatp1=$2for0x120andp1=$1forx1>20.Thentheconstraint’sslope2,for0x1

ShapesofBudgetConstraintswithatyDiscount m= Slope=-2/1=-(p1=2,Slope=-1/1=-p1/p21,forx1>

(p1=1,

ShapesofBudgetConstraintswithatyDiscount m= Slope=-2/1=-(p1=2,Slope=-1/1=-1(p1=1,p2=1)

BudgetConstraintswitha Theconstraint2x1+x2=mfor0x120

ShapesofBudgetConstraintswith ShapesofBudgetConstraintswith

ty

m=

ty

Budget

Budget Budget

Indifferencecurves(无差异曲线Marginalrateofsubstitution(边际替代率

RationalityinBehavioralAdecisionmakeralwayschoosesitsmostpreferredalternativefromitssetofSotomodelchoicewemustmodeldecision-makers’preferences. odifferentconsumptionstrictpreference(严格偏好)xismorepreferredthanyIndifference(无差异):x actlyaspreferredasweakpreference弱偏好)xisasatleastaspreferredasisy

AssumptionsaboutPreferencebundlesxandyitisalwayspossibletomakethecomparisonbetweenxandyReflexivity(反身性):AnybundlexisalwaysatleastaspreferredasitselfAssumptionsaboutPreference 传递性):xisatleastaspreferredasy,andyisatleastaspreferredasz,then

Indifference’Takeareferencebundlex.Thesetofallbundlesequallypreferredtox’istheindifferencecurvecontainingx’;thesetofallbundlesyx’.’Indifference Indifference

x’x”

y WP theset bundlespreferredto y

AllbundlesinI1arestrictlypreferredtoallinI2.zAllbundlesinI2 strictlypreferred allinWeaklyPreferredSet(弱偏好集 StrictlyPreferredSet(严格偏好集 WP theset bundles preferredto

IndifferenceCurvesCannot

SlopesofIndifferenceI I1xyz

Whenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesareneativelsloed.SlopesofIndifferenceanegativelyslopedindifferencecurve.

SlopesofIndifferenceIflessofacommodityisalwayspreferredGoodSlopesofIndifferenceOnegoodandone positivelysloped

Perfectsubstitutes(完全替代Perfectcomplements(完全互补Satiation餍足BadExtremeCasesofIndifference

ExtremeCasesofIndifferenceCurves:PerfectSlopesareconstantat-BundlesinI2allhaveatotalof15units

o9

Eachof(5,5),and(9,5)contains5pairssoeachisequally l-BehavedConvexity:l-BehavedConvexity:Mixturesofbundlesare(atleastweakly)preferredtothebundlesthemselves.E.g.,the50-50mixtureofthebundlesxandyiszisatleastaspreferredasxor Well-BehavedPreferences--

Well-BehavedPreferences-- x

z=+ isstrictly

z=(tx1+(1-t)y1,tx2+(1- 2

1

tobothxandy.

ispreferredtoxandyfr <1.y Well-BehavedPreferences--

Preferencesarestrictly whenallmixtures

weaklyconvexif are preferredtobundlesxandy.y

leastonemixturezisequallypreferredx toa Non-Convex MoreNon-ConvexThemixture islesspreferredhnx

Themixture islesspreferredhnx MarginalRateofMarginalRateofdx2=’therateatwhichtheconsumerisonlyjustwillingtoexchangecommodity2forasmallamountofcommodity1.MarginalwillingnesstoMRSatx’lim-

2

=-dx2/dx1atMarginalRateof MRS&Ind.CurveClothing

AMRS=-B1

C

MRS= MRS esmoreasx1increases 64

D1-1-

MRS=EG

MRS=

MRSisnotalwaysincreasing

x1

U(x1,x2)2 2

MRS=

dUdU(x1,x2)

dx1

dx2= MRS=

MRSdx2

/_/

u

UtilityFunctionand’Aconsumerspreferencescanberepresentedbyautilityfunction’The“perfectsubstitutes”preferencecanbereresentedbUx The“perfectcomplements”preferences:U(x,y)=min{x,y}Istheutilitfunctionreresentationuniue

UtilityFunctionandTheutilityrepresentationisnotApositivemonotonictransformationofautilityfunctionrepresentsthesamereferenceastheoriinalutilitfunctionAslongastheutilityfunctionsgivethesameorderingoftheconsumptionbundles,Theutilityisordinal,ratherthanConsumerConsumerComputingordinaryV(x1,x2)

f[u(x1,x2

f'(u)MRSv/x1

f'(u)u/f'(u)u/

u/TheprincipalbehavioralpostulateisthattoTheavailablechoicesconstitutethechoiceset.Howisthemostpreferredbundleinthe

RationalConstrainedMorepreferredRationalConstrained preferred

RationalConstrainedThemostpreferredaffordablebundleisDEMAND(orDEMAND)atthegiven

Ordinarydemandswillbedenotedbyx1*(p1,p2,m)andx2*(p1,p2,m).* *RationalConstrained RationalConstrainedWhen

*>0and

*>0the

(x1*,x2*)is bundleisIfbuying(x1*,x2*)costs$mthenthebudgeti

(x1*,x2*)exhauststhe* *RationalConstrained (x1*,x2*)is(x1*,x2*)exhauststhebudget;p1x1*+p2x2*=m.

RationalConstrained (x1*,x2*)isinteriorTheslopeofthecurveat(x1*,x2*)equalstheslopeofthebudget ** **RationalConstrained(x1*,x2*)satisfiestwo(a)thebudget p1x1*+p2x2*=btanenc:thesloeofthebud

MeaningoftheTangency onsumptionbundle(x1,Theconsumeriswillingtogiveup2unitofx2constraint,-p/p,andtheslopeof

exchangeforanadditionalunitof◦ Themarketallowshertogiveuponly1unitofindifferencecurvecontaining(x1*,x2*)

toobtainanadditionalequalat

(x1,x2)isnotoptimalShecanbebetteroffincreasingherconsumptionofSolvefor2simultaneousBudgetTheconditionsmaybeobtainedby theLagrangianmultipliermethod, constrainedoptimizationin locate(x1*,x2*)forgivenp1,p2andm?

SupposethattheconsumerhasCobb-U(x,x)

温馨提示

  • 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
  • 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
  • 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
  • 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
  • 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
  • 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
  • 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。

评论

0/150

提交评论