清华大学中级微观经济学讲义18课件

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1、http://www.sem.tsinghua.edu.cn/ChapterEighteenTechnologyWhereAreWeintheCourse?Wehavestudiedconsumerbehavior;Wenowstudyproducerbehavior;Wewillthencombinethesetwotostudymarketequilibrium.ThreeStepstoStudyofProducerBehavior1st:Weworkonproducer’s“budgetset”,whichisthetechnologyset;2nd:Westud

2、yproducer’s“utilityfunction”,whichishisprofitfunction;3rd:Weexamineproducer’schoice,whichishisoptimalproductionplan.TechnologiesAtechnologyisaprocessbywhichinputsareconvertedtoanoutput.Usuallyseveraltechnologieswillproducethesameproduct.Howdowecomparetechnologies?ProductionFunctionsLetyd

3、enotetheoutputlevel.Aninputbundleisavectoroftheinputlevels;(x1,x2,…,xn).Thetechnology’sproductionfunctionstatesthemaximumamountofoutputpossiblefromaninputbundle.ProductionFunctionsy=f(x)istheproductionfunction.x’xInputLevelOutputLevely’y’=f(x’)isthemaximaloutputlevelobtainablefromx’input

4、units.Oneinput,oneoutputTechnologySetsAproductionplanisaninputbundleandanoutputlevel;(x1,…,xn,y).AproductionplanisfeasibleifThecollectionofallfeasibleproductionplansisthetechnologyset.TechnologySetsy=f(x)istheproductionfunction.x’xInputLevelOutputLevely’y”y’=f(x’)isthemaximaloutputlevelo

5、btainablefromx’inputunits.Oneinput,oneoutputy”=f(x’)isanoutputlevelthatisfeasiblefromx’inputunits.TechnologySetsThetechnologysetisTechnologySetsx’xInputLevelOutputLevely’Oneinput,oneoutputy”ThetechnologysetTechnicallyinefficientplansTechnicallyefficientplansTechnologieswithMultipleIn

6、putsWhatdoesatechnologylooklikewhenthereismorethanoneinput?Thetwoinputcase:Inputlevelsarex1andx2.Outputlevelisy.SupposetheproductionfunctionisTechnologieswithMultipleInputsTheyoutputunitisoquantisthesetofallinputbundlesthatyieldatmostthesameoutputlevely.Thecompletecollectionofisoquantsis

7、theisoquantmap.IsoquantswithTwoVariableInputsyº8yº4x1x2yº6yº2Cobb-DouglasTechnologiesACobb-DouglasproductionfunctionisoftheformE.g.x2x1Allisoquantsarehyperbolic,asymptotingto,butnevertouchinganyaxis.Cobb-DouglasTechnologiesFixed-ProportionsTechnologiesAfixed-proportions