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1、ChapterEighteenTechnologyWhereAreWeintheCourse?Wehavestudiedconsumerbehavior;Wenowstudyproducerbehavior;Wewillthencombinethesetwotostudymarketequilibrium.ThreeStepstoStudyofProducerBehavior1st:Weworkonproducer’s“budgetset”,whichisthetechnologyset;2nd:Westudyproducer’s“utilityfunc
2、tion”,whichishisprofitfunction;3rd:Weexamineproducer’schoice,whichishisoptimalproductionplan.TechnologiesAtechnologyisaprocessbywhichinputsareconvertedtoanoutput.Usuallyseveraltechnologieswillproducethesameproduct.Howdowecomparetechnologies?ProductionFunctionsLetydenotetheoutputl
3、evel.Aninputbundleisavectoroftheinputlevels;(x1,x2,…,xn).Thetechnology’sproductionfunctionstatesthemaximumamountofoutputpossiblefromaninputbundle.ProductionFunctionsy=f(x)istheproductionfunction.x’xInputLevelOutputLevely’y’=f(x’)isthemaximaloutputlevelobtainablefromx’inputunits.O
4、neinput,oneoutputTechnologySetsAproductionplanisaninputbundleandanoutputlevel;(x1,…,xn,y).AproductionplanisfeasibleifThecollectionofallfeasibleproductionplansisthetechnologyset.TechnologySetsy=f(x)istheproductionfunction.x’xInputLevelOutputLevely’y”y’=f(x’)isthemaximaloutputlevel
5、obtainablefromx’inputunits.Oneinput,oneoutputy”=f(x’)isanoutputlevelthatisfeasiblefromx’inputunits.TechnologySetsThetechnologysetisTechnologySetsx’xInputLevelOutputLevely’Oneinput,oneoutputy”Thetechnology setTechnically inefficient plansTechnically efficientplansTechnologieswithM
6、ultipleInputsWhatdoesatechnologylooklikewhenthereismorethanoneinput?Thetwoinputcase:Inputlevelsarex1andx2.Outputlevelisy.SupposetheproductionfunctionisTechnologieswithMultipleInputsTheyoutputunitisoquantisthesetofallinputbundlesthatyieldatmostthesameoutputlevely.Thecompletecollec
7、tionofisoquantsistheisoquantmap.IsoquantswithTwoVariableInputsyo8yo4x1x2yo6yo2Cobb-DouglasTechnologiesACobb-DouglasproductionfunctionisoftheformE.g.x2x1Allisoquantsarehyperbolic, asymptotingto,butnever touchinganyaxis.Cobb-DouglasTechnologiesFixed-ProportionsTechnologiesAfixed-pr
8、oportionsproductionfunctionisoftheformE.
