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1、7.生产技术与利润最大化27.1技术（Technologies）7.1.1什么叫技术？技术是投入转换为产出的过程E.g.labor,acomputer,aprojector,electricity,andsoftwarearebeingcombinedtoproducethislecture.Usuallyseveraltechnologieswillproducethesameproduct.ablackboardandchalkcanbeusedinsteadofacomputerandaprojector.Whichtechnologyis“best”?How
2、dowecomparetechnologies?37.1.2ProductionFunctionsydenotestheoutputlevel.Thetechnology’sproductionfunctionstatesthemaximumamountofoutputpossiblefromaninputbundle.4ProductionFunctions -Oneinput,oneoutputy=f(x)x1InputLevelxOutputLevely1y1=f(x1)isthemaximaloutputlevelobtainablefromx1inputu
3、nits.5TechnologieswithMultipleInputsSupposetheproductionfunctionis(x1,x2)=(1,8)(x1,x2)=(8,8)6TechnologieswithMultipleInputsOutput,yx1x2(8,1)(8,8)7IsoquantswithTwoVariableInputsyº8yº4x1x28用产量面表示生产函数LOKTPK1L1L2K2AA’BB’CC’DD’Q1Q2E1F1G1E2F2G2E1’E2’G1’G2’9IsoquantswithTwoVariableInputsOutpu
4、t,yx1x2yº8yº410Cobb-DouglasTechnologiesACobb-Douglasproductionfunctionisoftheform11Fixed-ProportionsTechnologiesAfixed-proportionsproductionfunctionisoftheform12Fixed-ProportionsTechnologiesx2x1min{x1,2x2}=144814247min{x1,2x2}=8min{x1,2x2}=4x1=2x213Perfect-SubstitutesTechnologiesAperfe
5、ct-substitutesproductionfunctionisoftheform14Perfect-SubstitutionTechnologies93186248x1x2x1+3x2=9x1+3x2=18x1+3x2=2415有限种投入比的技术1234567812345678R1X2:X1=8:1R2X2:X1=3:1R3X2:X1=1:1R4X2:X1=1:4现有6单位x1和3单位x22单位x1和2单位x2用于R3，生产产品50单位；4单位x1和1单位x2用于R4，生产产品50单位产量100单位的等产量线167.1.3Marginal(Physical)P
6、roductsThemarginalproductofinputiistherate-of-changeoftheoutputlevelasthelevelofinputichanges,holdingallotherinputlevelsfixed.Thatis,17Marginal(Physical)Products187.1.4Returns-to-ScaleMarginalproductsdescribethechangeinoutputlevelasasingleinputlevelchanges.Returns-to-scaledescribeshowt
7、heoutputlevelchangesasallinputlevelschangeindirectproportion(e.g.allinputlevelsdoubled,orhalved).19Constantreturns-to-scaleIf,foranyinputbundle(x1,…,xn),thenthetechnologydescribedbythe productionfunctionfexhibitsconstant returns-to-scale.E.g.(k=2)doublingallinputlevels doublestheoutp
