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1、AdvancedMicroeconomics(lecture1:productiontheoryI)YeJianliang(叶建亮)lecture1forChuKechenHonorsCollegeSummarytextbook:Varian,HalR.,1992,MicroeconomicsAnalysis,3rded.Mas-Colell,A.,M.Whinston,andJ.Green,1995,MicroeconomicsTheory.assignments:twiceaweek;Teamwork
2、;Deliverontheclass.examinations:Mid-term:bytheassignments;Final-term:80%ofthequestionscomingfromtheassignments.TheBasicFrameworkofMicroeconomicsTechnologyPreferenceChoice(production)Choice(purchase)SupplyDemandMarketEquilibriumlecture1forChuKechenHonorsCo
3、llegeTechnologyContain:“production(possibilities)set”(PS)and“productionfunction”;Propertiesofthe“PS”;Technicalrateofsubstitution;Returnstoscale.1.ProductionsetProductionplan(productionvector,orinput-outputvector):ProductionsetY:alltechnologicalfeasibley.R
4、estrictedproductionsetY(z):Someofyiinyarerestrictedonz.Short-runproductionset.1.ProductionsetInputrequirementset:Allyiinyarenegative,letthembe–x(thenxispositive),andtherestyjtobeq.So,and,andtheinputrequirementsetis:1.ProductionsetTransformationfunction:an
5、dsatisfiedifandonlyifyistechnologicallyefficient,theny2y11.ProductionsetProductionfunction:IfO=1,andI=n-1,then:means:Isoquant:Question1:calculatethePS,RS,TF,PF,IsoquantofCobb-DouglastechnologyandLeontieftechnology.2.PropertiesofPS.Yisnonempty:wehavesometh
6、ingtodo.Yisclose:Ycontainit’sboundary,Nofreelunch:Seethefig.Freedisposal:Seethefig.2.PropertiesofPS.Additive(freeentrance):Convexity:Seethefig.Proposition1:ifYisconvex,soisV(q).Proposition2:ifV(q)isconvex,f(x)isquasi-concave.3.TechnicalrateofsubstitutionM
7、arginalrateoftransformation(MRT)ofgoodjforgoodiatyandT(y)=0.T(y)=0,wegot:Seethefig.3.Technicalrateofsubstitutiononeproduction:themarginalratetechnicalofsubstitutionatx*.Asxchanges,wegottechnicalrateofsubstitution3.TechnicalrateofsubstitutionTheelasticityo
8、fsubstitution:thecurvatureoftheisoquant.Question2:calculatethe“TRS”andthe“elasticityofsubstitution”ofCobb-DouglastechnologyandCEStechnology.4.ReturnstoscaleNonincreasingreturnstoscale:Nondecreasingreturnstoscale:Con
