北大中级微观经济PPT课件

1 ChapterTwenty CostMinimization 2 CostMinimization Afirmisacost minimizerifitproducesanygivenoutputlevely 0atsmallestpossibletotalcost c y willdenotethefirm ssmallestpossibletotalcostforproducingyunitsofoutput c y isthefirm stotalcostfunction 3 CostMinimization Whenthefirmfacesgiveninputpricesw w1 w2 wn thetotalcostfunctionwillbewrittenasc w1 wn y 4 TheCost MinimizationProblem Considerafirmusingtwoinputstomakeoneoutput Thefirm sproductionfunctionisy f x1 x2 Taketheoutputlevely 0asgiven Taketheinputpricesw1andw2asgiven Thenthecostofaninputbundle x1 x2 isw1x1 w2x2 5 TheCost MinimizationProblem Forgivenw1 w2andy thefirm scost minimizationproblemistosolve subjectto 6 TheCost MinimizationProblem Thelevelsx1 w1 w2 y andx1 w1 w2 y intheleast costlyinputbundlearethefirm sconditionaldemandsforinputs1and2 Thefirm stotal smallestpossible costforproducingyoutputunitsistherefore 7 ConditionalInputDemands Forgivenw1 w2andy howarethelevelsofinputs1and2intheleastcostlyinputbundlelocated Andhowisthefirm stotalcostfunctioncomputed 8 Iso costLines Acurvewhichcontainsalloftheinputbundleswhichcostthesameamountisaniso costcurve E g givenw1andw2 the 100iso costlinehastheequation 9 Iso costLines Ingeneral givenw1andw2 theequationofthe ciso costlineiswhichrearrangestoTheslopeis w1 w2 10 Iso costLines c w1x1 w2x2 c w1x1 w2x2 c c x1 x2 11 Iso costLines c w1x1 w2x2 c w1x1 w2x2 c c x1 x2 Slopes w1 w2 12 They OutputUnitIsoquant x1 x2 Allinputbundlesyieldingy unitsofoutput Whichisthecheapest f x1 x2 y 13 TheCost MinimizationProblem x1 x2 Allinputbundlesyieldingy unitsofoutput Whichisthecheapest f x1 x2 y 14 TheCost MinimizationProblem x1 x2 Allinputbundlesyieldingy unitsofoutput Whichisthecheapest f x1 x2 y 15 TheCost MinimizationProblem x1 x2 Allinputbundlesyieldingy unitsofoutput Whichisthecheapest f x1 x2 y 16 TheCost MinimizationProblem x1 x2 Allinputbundlesyieldingy unitsofoutput Whichisthecheapest f x1 x2 y x1 x2 17 TheCost MinimizationProblem x1 x2 f x1 x2 y x1 x2 Ataninteriorcost mininputbundle a 18 TheCost MinimizationProblem x1 x2 f x1 x2 y x1 x2 Ataninteriorcost mininputbundle a and b slopeofisocost slopeofisoquant 19 TheCost MinimizationProblem x1 x2 f x1 x2 y x1 x2 Ataninteriorcost mininputbundle a and b slopeofisocost slopeofisoquant i e 20 ACobb DouglasExampleofCostMinimization AfirmhasaCobb Douglastechnology itsproductionfunctionbeingThefirmfacesgiveninputpricesw1andw2 Whatarethefirm sconditionalinputdemandfunctions 21 ACobb DouglasExampleofCostMinimization Attheinputbundle x1 x2 whichminimizesthecostofproducingyoutputunits a b and 22 ACobb DouglasExampleofCostMinimization a b 23 ACobb DouglasExampleofCostMinimization a b From b 24 ACobb DouglasExampleofCostMinimization a b From b Nowsubstituteinto a toget 25 ACobb DouglasExampleofCostMinimization a b From b Nowsubstituteinto a toget 26 ACobb DouglasExampleofCostMinimization a b From b Nowsubstituteinto a toget So isthefirm sconditionaldemandforinput1 27 ACobb DouglasExampleofCostMinimization isthefirm sconditionaldemandforinput2 Since and 28 ACobb DouglasExampleofCostMinimization Sotheanswertothequestion Whichinputbundleyieldingyoutputunitsischeapestwheninputpricesarew1andw2 is 29 Fixedw1andw2 ConditionalInputDemandCurves 30 Fixedw1andw2 ConditionalInputDemandCurves 31 Fixedw1andw2 ConditionalInputDemandCurves 32 Fixedw1andw2 ConditionalInputDemandCurves 33 Fixedw1andw2 ConditionalInputDemandCurves outputexpansionpath 34 Fixedw1andw2 ConditionalInputDemandCurves outputexpansionpath Cond demandforinput2 Cond demandforinput1 35 ACobb DouglasExampleofCostMinimization Fortheproductionfunctiontheanswertothequestion Whichinputbundleyieldingyoutputunitsischeapestwheninputpricesarew1andw2 is 36 ACobb DouglasExampleofCostMinimization Sothefirm stotalcostfunctionis 37 ACobb DouglasExampleofCostMinimization Sothefirm stotalcostfunctionis 38 ACobb DouglasExampleofCostMinimization Sothefirm stotalcostfunctionis 39 ACobb DouglasExampleofCostMinimization Sothefirm stotalcostfunctionis 40 APerfectComplementsExampleofCostMinimization Thefirm sproductionfunctionisInputpricesw1andw2aregiven Whatarethefirm sconditionaldemandsforinputs1and2 Whatisthefirm stotalcostfunction 41 APerfectComplementsExampleofCostMinimization x1 x2 min 4x1 x2 y 4x1 x2 42 APerfectComplementsExampleofCostMinimization x1 x2 4x1 x2 min 4x1 x2 y 43 APerfectComplementsExampleofCostMinimization x1 x2 4x1 x2 min 4x1 x2 y Whereistheleastcostlyinputbundleyieldingy outputunits 44 APerfectComplementsExampleofCostMinimization x1 x2 x1 y 4 x2 y 4x1 x2 min 4x1 x2 y Whereistheleastcostlyinputbundleyieldingy outputunits 45 APerfectComplementsExampleofCostMinimization Thefirm sproductionfunctionis andtheconditionalinputdemandsare and 46 APerfectComplementsExampleofCostMinimization Thefirm sproductionfunctionis andtheconditionalinputdemandsare and Sothefirm stotalcostfunctionis 47 APerfectComplementsExampleofCostMinimization Thefirm sproductionfunctionis andtheconditionalinputdemandsare and Sothefirm stotalcostfunctionis 48 AverageTotalProductionCosts Forpositiveoutputlevelsy afirm saveragetotalcostofproducingyunitsis 49 Returns to ScaleandAv TotalCosts Thereturns to scalepropertiesofafirm stechnologydeterminehowaverageproductioncostschangewiththefirm soutputlevel Supposeourcost minimizingfirmispresentlyproducingy outputunits Howdoesthefirm saveragecostofproductionchangeifitinsteadproduces2y unitsofoutput 50 ConstantReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsconstantreturns to scalethendoublingitsoutputlevelfromy to2y requiresdoublingallinputlevels 51 ConstantReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsconstantreturns to scalethendoublingitsoutputlevelfromy to2y requiresdoublingallinputlevels Totalproductioncostdoubles 52 ConstantReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsconstantreturns to scalethendoublingitsoutputlevelfromy to2y requiresdoublingallinputlevels Totalproductioncostdoubles Averageproductioncostdoesnotchange 53 DecreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsdecreasingreturns to scalethendoublingitsoutputlevelfromy to2y requiresmorethandoublingallinputlevels 54 DecreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsdecreasingreturns to scalethendoublingitsoutputlevelfromy to2y requiresmorethandoublingallinputlevels Totalproductioncostmorethandoubles 55 DecreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsdecreasingreturns to scalethendoublingitsoutputlevelfromy to2y requiresmorethandoublingallinputlevels Totalproductioncostmorethandoubles Averageproductioncostincreases 56 IncreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsincreasingreturns to scalethendoublingitsoutputlevelfromy to2y requireslessthandoublingallinputlevels 57 IncreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsincreasingreturns to scalethendoublingitsoutputlevelfromy to2y requireslessthandoublingallinputlevels Totalproductioncostlessthandoubles 58 IncreasingReturns to ScaleandAverageTotalCosts Ifafirm stechnologyexhibitsincreasingreturns to scalethendoublingitsoutputlevelfromy to2y requireslessthandoublingallinputlevels Totalproductioncostlessthandoubles Averageproductioncostdecreases 59 Returns to ScaleandAv TotalCosts y outputunit constantr t s decreasingr t s increasingr t s AC y 60 Returns to ScaleandTotalCosts Whatdoesthisimplyfortheshapesoftotalcostfunctions 61 Returns to ScaleandTotalCosts y y 2y c y c 2y Slope c 2y 2y AC 2y Slope c y y AC y Av costincreaseswithyifthefirm stechnologyexhibitsdecreasingr t s 62 Returns to ScaleandTotalCosts y c y y 2y c y c 2y Slope c 2y 2y AC 2y Slope c y y AC y Av costincreaseswithyifthefirm stechnologyexhibitsdecreasingr t s 63 Returns to ScaleandTotalCosts y y 2y c y c 2y Slope c 2y 2y AC 2y Slope c y y AC y Av costdecreaseswithyifthefirm stechnologyexhibitsincreasingr t s 64 Returns to ScaleandTotalCosts y c y y 2y c y c 2y Slope c 2y 2y AC 2y Slope c y y AC y Av costdecreaseswithyifthefirm stechnologyexhibitsincreasingr t s 65 Returns to ScaleandTotalCosts y c y y 2y c y c 2y 2c y Slope c 2y 2y 2c y 2y c y y soAC y AC 2y Av costisconstantwhenthefirm stechnologyexhibitsconstantr t s 66 Short Run Long RunTotalCosts Inthelong runafirmisfreetovaryallofitsinputlevels Considerashort runinwhichafirmcannotchangeitsusageofinput2fromx2 units Howdoestheshort runtotalcostofproducingyoutputunitscomparetothelong runtotalcostofproducingyunitsofoutput 67 Short Run Long RunTotalCosts Thelong runcost minimizationproblemisTheshort runcost minimizationproblemis subjectto subjectto 68 Short Run Long RunTotalCosts Theshort runcost min problemisthereforethelong runproblemsubjecttotheextraconstraintthatx2 x2 Ifthelong runchoiceforx2wasx2 thentheextraconstraintx2 x2 isnotreallyaconstraintatallandsothelong runandshort runtotalcostsofproducingyoutputunitsarethesame 69 Short Run Long RunTotalCosts Theshort runcost min problemisthereforethelong runproblemsubjecttotheextraconstraintthatx2 x2 But ifthelong runchoiceforx2 x2 thentheextraconstraintx2 x2 preventsthefirminthisshort runfromachievingitslong runproductioncost causingtheshort runtotalcosttoexceedthelong runtotalcostofproducingyoutputunits 70 Short Run Long RunTotalCosts x1 x2 Considerthreeoutputlevels 71 Short Run Long RunTotalCosts x1 x2 Inthelong runwhenthefirmisfreetochoosebothx1andx2 theleast costlyinputbundlesare 72 Short Run Long RunTotalCosts x1 x2 Long runoutputexpansionpath 73 Short Run Long RunTotalCosts x1 x2 Long runoutputexpansionpath Long runcostsare 74 Short Run Long RunTotalCosts Nowsupposethefi