清华大学中级微观经济学讲义（清华李稻葵）

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

2、hichisthetechnologyset;2nd:Westudyproducer’s“utilityfunction”,whichishisprofitfunction;3rd:Weexamineproducer’schoice,whichishisoptimalproductionplan.TechnologiesAtechnologyisaprocessbywhichinputsareconvertedtoanoutput.Usuallyseveraltechnologieswillproduce

3、thesameproduct.Howdowecomparetechnologies?ProductionFunctionsLetydenotetheoutputlevel.Aninputbundleisavectoroftheinputlevels;(x1,x2,…,xn).Thetechnology’sproductionfunctionstatesthemaximumamountofoutputpossiblefromaninputbundle.ProductionFunctionsy=f(x)ist

4、heproductionfunction.x’xInputLevelOutputLevely’y’=f(x’)isthemaximaloutputlevelobtainablefromx’inputunits.Oneinput,oneoutputTechnologySetsAproductionplanisaninputbundleandanoutputlevel;(x1,…,xn,y).AproductionplanisfeasibleifThecollectionofallfeasibleproduc

5、tionplansisthetechnologyset.TechnologySetsy=f(x)istheproductionfunction.x’xInputLevelOutputLevely’y”y’=f(x’)isthemaximaloutputlevelobtainablefromx’inputunits.Oneinput,oneoutputy”=f(x’)isanoutputlevelthatisfeasiblefromx’inputunits.TechnologySetsThetechnolo

6、gysetisTechnologySetsx’xInputLevelOutputLevely’Oneinput,oneoutputy”ThetechnologysetTechnicallyinefficientplansTechnicallyefficientplansTechnologieswithMultipleInputsWhatdoesatechnologylooklikewhenthereismorethanoneinput?Thetwoinputcase:Inputlevelsarex

7、1andx2.Outputlevelisy.SupposetheproductionfunctionisTechnologieswithMultipleInputsTheyoutputunitisoquantisthesetofallinputbundlesthatyieldatmostthesameoutputlevely.Thecompletecollectionofisoquantsistheisoquantmap.IsoquantswithTwoVariableInputsyº8yº4x1x2yº

8、6yº2Cobb-DouglasTechnologiesACobb-DouglasproductionfunctionisoftheformE.g.x2x1Allisoquantsarehyperbolic,asymptotingto,butnevertouchinganyaxis.Cobb-DouglasTechnologiesFixed-ProportionsTechnologiesAfixed-proportions