高级微观经济学 黄有光 overview of inframargianlWord文档下载推荐.docx
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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
+
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)
(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
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