高级微观经济学 黄有光 overview of inframargianl.docx

高级微观经济学 黄有光 overview of inframargianl.docx

《高级微观经济学 黄有光 overview of inframargianl.docx》由会员分享，可在线阅读，更多相关《高级微观经济学 黄有光 overview of inframargianl.docx（11页珍藏版）》请在冰豆网上搜索。

高级微观经济学黄有光overviewofinframargianl

Overviewoftheinframarginalanalysis

Whyeconomistsshiftedtheirattentionfromtheeconomicorganizationproblemtotheresourcesallocationproblem?

1）DavidRicardo'sconceptofcomparativeadvantage

∙Exogenouscomparativeadvantage

∙Endogenouscomparativeadvantage:

Smith’sconceptofeconomiesofthedivisionoflabour

Comparativeadvantagemayexistbetweenexanteidentical

viftheychoosedifferentlevelsofspecializationinproducingdifferentgoods

vifthereexistincreasingreturnstospecialization

2）Marshall'sneoclassicalframework

∙Thedichotomybetweenpureconsumersandfirms

∙Thereplacementoftheconceptofeconomiesofspecializationwiththeconceptofeconomiesofscale

∙Themarginalanalysisofdemandandsupply.

（Marshall’sneoclassicalframeworkcannotbeusedtoanalyseindividuals’decisionsinchoosinglevelsandpatternsofspecialization,sothatthestructureofdivisionbetweenpureconsumersandfirmsisexogenouslygiven）

Twotypesoftrade-offs:

Neoclassicaltrade-off---thetrade-offbetweentheproductionandconsumptionofalldifferentgoodsandservicesgiventhedegreeofscarcityofresources;（theproblemofallocationofscarceresource）

Classicaltrade-off---thetradeoffbetweentransactioncostsand

theeconomiesofspecializationfacilitatedbythedivisionoflabour（theproblemofeconomicorganization）

（a）Neoclassicalframework（b）Flowchartinneoclassicaleconomics

Figure1:

NeoclassicalAnalyticalFramework

NewClassicalEconomics（Yang-Ngframework）

Newclassicalgeneralequilibriummodelendogenizesindividual'slevelofspecializationandthelevelofdivisionoflabourforsocietyasawholewithinaframeworkwith:

1）consumer-producers

2）economiesofspecialization

3）transactioncosst

4）cornersolutions

（a）Autarky（b）Partialdivisionoflabor（c）Completedivisionoflabor

Fig.2:

NewClassicalAnalyticalFramework

Asimplemodelofinframarginalanalysis:

AneconomyhasMexanteidenticalindividualwhoarebothconsumerandproducers

TwoconsumptiongoodsXandY

Eachconsumer-producerhasthefollowingutilityfunction.

（1）

Eachconsumer-producer’sproductionfunctionsandendowmentconstraintare

（2a）

a>1

（2b）

.

Eachconsumer-producer’sbudgetconstraintis

（3）

piisthepriceofgoodi.Thelefthandsideof（3）isincomefromthemarketandtherighthandsideisexpenditure.Cornersolutionsareallowedandwehavethenon-negativityconstraints

（4）x,xs,xd,y,ys,yd,lx,ly0.

Eachconsumer-producermaximizesutilityin

（1）withrespecttox,xs,xd,y,ys,yd,lx,lysubjecttotheproductionconditionsgivenby

（2）,thebudgetconstraint（3）,andthenon-negativityconstraint（4）.Sincelxandlyarenotindependentofthevaluesoftheotherdecisionvariables,eachofthe6decisionvariablesx,xs,xd,y,ys,ydcantakeon0andpositivevalues.Whenadecisionvariabletakesonavalueof0,acornersolutionischosen.

Individualdecisionproblems

Thereare

solutionsinclude63cornersolutionsandoneinteriorsolutionforeachconsumerandproducer.

Usingthetheoremofspecializationnarrowsdownthesetofcandidatesfortheoptimumdecisions

TheoremofOptimalConfigurations:

Theoptimumdecisiondoesnotinvolvesellingmorethanonegoods,doesnotinvolvesellingandbuyingthesamegood,anddoesnotinvolvebuyingandproducingthesamegood.

（Implications:

interiorsolutioncanneverbeoptimal,themarninalanalysisforinteriorsolutiondoesnotworkforthenewclassicalframework）

Thistheorem,togetherwiththebudgetconstraintandtherequirementthatutilitybepositive,canbeusedtoreducethenumberofcandidatesfortheoptimumdecisionradicallyfrom64toonly3.

Thetheoremisintuitive.Sellingandbuyingthesamegoodinvolvesunnecessarytransactioncostsandthereforeisinefficient.Sellingtwogoodsisalsoinefficientsinceitpreventsthefullexploitationofeconomiesofspecialization.

Thelistofcandidatesfortheoptimumcornersolution

Table1:

ProfilesofZeroandPositiveValues

ofthe6DecisionVariables

+

+

+

+

+

+

0

+

+

0

+

+

0

+

0

0

+

+

+

0

0

0

+

+

+

0

0

0

0

+

0

0

0

0

0

+

Threeconfigurations

（i）Autarky,orconfigurationA,isdefinedby

ThedecisionproblemforconfigurationAis

（5a）

s.t.

.

Insertingallconstraintsintotheutilityfunction（5.5a）canbeconvertedtothefollowingnon-constrainedmaximizationproblem.

（5b）

totallydifferentiateuwithrespecttolx

（6）

thecornersolutionforconfigurationAis

（7）

Twoconfigurationsofspecialization:

（ii）ConfigurationB:

configurationwithspecializationis（x/y）,specializationinproducinggoodx,sellingxandbuyingy.

Itisdefinedbyx,xs,yd,lx>0,xd=ys=y=ly=0.Thisdefinition,togetherwith

（1）-（4）,canbeusedtospecifythedecisionproblemforthisconfiguration.

（8）

s.t.

（productionconditions）

（budgetconstraint）

Pluggingtheconstraintsintotheutilityfunctiontoeliminate

x,and

yieldsthenonconstrainedmaximizationproblem

（9）

Thecornersolutionforconfiguration（x/y）is

（10）xs=0.5,yd=pxxs/py=px/2py,ux=kpx/4py.

（iii）ConfigurationC:

configurationwithspecializationis（y/x）,inwhichtheindividualsellsgoodyandbuysgoodx,isdefinedbyy,ys,sd,ly>0,yd=xs=x=lx=0.Thedecisionproblemforthisconfigurationis:

（11）

s.t.

（productioncondition）

（budgetconstraint）

Followingtheprocedureusedinsolvingforthecornersolutionforconfiguration（x/y）,thecornerdemandandsupplyfunctionsandcornerindirectutilityfunctionforconfiguration（y/x）issolvedasfollows:

（12）ys=0.5,xd=py/2px,uy=kpy/4px.

Table2:

ThreeCornerSolutions

Configuration

Cornerdemand

Cornersupply

Self-providedquantities

Levelof

specialization

Indirectutility

function

A

0

0

x=y=0.5

lx=ly=0.5

uA=2-2a

（x/y）

yd=px/2py

xs=0.5

x=0.5

lx=1,

ly=0

ux=kpx/4py

（y/x）

xd=py/2px

ys=0.5

y=0.5

lx=0,

ly=1

uy=kpy/4px

StructuresandCornerequilibria

Therearetwoorganizationstructures:

StructureA（Autarky）

StructureD（Divisionoflabour）:

AcombinationofconfigurationsBandC.

Letthenumber（measure）ofindividualschoosing（x/y）beMxandthenumberchoosing（y/x）beMy.

Thereisacornerequilibriumforeachstructure.

Themarketclearingandutilityequalizationconditionsareestablishedbyfreechoicebetweenconfigurationsandutilitymaximizationbehavior.

InstructureD,thecornerequilibriumrelativepriceoftradedgoodsis:

or

themarketdemandforgoodxis

XdMyxd=Mypy/2px,

themarketsupplyofgoodxis

XsMxxs=Mx/2

Themarketclearingconditionforgoodxis

Xd=Mypy/2px=Xs=Mx/2,orpx/py=My/Mx

ThecornerequilibriuminstructureDis

px/py=1,Mx=My=M/2.

x=y=xs=ys=xd=yd=½,uD=k/4

Table3:

TwoCornerEquilibria

Structure

Relativeprice

Numberof

Specialists

Quantitiesof

goods

Percapita

realincome

A

dy/dx=1

x=y=0.5a

2-2a

D

px/py=1

Mx=My=M/2

x=y=xs=ys=xd=yd=½,

k/4

Generalequilibriumanditscomparativestatics

Proposition1:

Thecornerequilibriumthatgeneratesmaximumpercapitarealincomeisthefullequilibrium

Proposition2:

Equilibriumisthedivisionoflabourif

andisautarkyif

Proposition3:

Asufficientimprovementintransactionefficiencygeneratestheconcurrenceofprogressinlabourproductivityandtheincreasesinthelevelofspecialization,inthelevelofdivisionoflabour,thedegreeofmarketintegration,thedegreeofinterdependence,andthedegreeofcommercialisation.

（a）StructureA,autarky（b）StructureD,divisionoflabor

Figure2:

AutarkyandDivisionofLabor

Twotypesofcomparativestatics:

1）inframarginalcomparativestaticsofgeneralequilibriumacrossthestructures

explaintherelationshipbetweeneconomicgrowthandeconomicorganization

2）marginalcomparativestaticsofcornerequilibriumwithineachgivenstructure.

vNewclassicaltheoryanalysesboththeadjustmentswithinagivenstructureofeconomicorganizationandchangesineconomicorgainization.

WelfareimplicationsofEquilibrium

Thefirstwelfaretheorem:

Inanewclassicalmodelwithexanteidenticalconsumer-producers,eachcornerequilibriumislocallyParetooptimalforthegivenstructureandthegeneralequilibriumisgloballyParetooptimal.

Implication:

cornerequilibriumisallocationallyefficient,thegeneralequilibriumisbothorganizationallyefficientandallocationallyefficient.

ConsiderstructureD:

LetXi={xi,xis,yid}bethedecisionofindividualichoosingconfiguration（x/y）

Yj={yj,yjs,xjd}bethedecisionofindividualjchoosingconfiguration（y/x）.

thecornerequilibriumvaluesofXiandYiasXi*andYi*,respectively,andthecornerequilibriumpriceofgoodxintermsofgoodyasp.

SupposethatthecornerequilibriuminstructureDisnotlocallyParetooptimal.ThenthereexistsanallocationXi,YiinstructureDsuchthat

（2a）ui（Xi）ui（Xi*）foralli,andui（Xi）>ui（Xi*）forsomei

（2b）uj（Yj）uj（Yj*）forallj.

Thisimpliesthatabenevolentcentralplannercanincreaseatleastoneindividual’sutilitywithoutreducingallothers’utilitiesbyshiftingthedecisionsfrom{Xi*,Yi*}to{Xi,Yi}.Thatis,thecornerequilibriumdecisions{Xi*,Yi*}arenotlocallyParetooptimal.

Sinceutilityisastrictlyincreasingf