《义利润最大化》教学课件

ChapterNineteenProfit-MaximizationChapterNineteenProfit-Maximiz1StructureEconomicprofitShort-runprofitmaximizationComparativestaticsLong-runprofitmaximizationProfitmaximizationandreturnstoscaleRevealedprofitmaximizationStructureEconomicprofit2EconomicProfitAfirmusesinputsj=1…,mtomakeproductsi=1,…n.Outputlevelsarey1,…,yn.Inputlevelsarex1,…,xm.Productpricesarep1,…,pn.Inputpricesarew1,…,wm.

EconomicProfitAfirmusesinp3TheCompetitiveFirmThecompetitivefirmtakesalloutputpricesp1,…,pnandallinputpricesw1,…,wmasgivenconstants.TheCompetitiveFirmThecompet4EconomicProfitTheeconomicprofitgeneratedbytheproductionplan(x1,…,xm,y1,…,yn)isEconomicProfitTheeconomicpr5EconomicProfitOutputandinputlevelsaretypicallyflows.E.g.x1mightbethenumberoflaborunitsusedperhour.Andy3mightbethenumberofcarsproducedperhour.Consequently,profitistypicallyaflowalso;e.g.thenumberofdollarsofprofitearnedperhour.EconomicProfitOutputandinpu6OpportunityCosts(时机本钱)Allinputsmustbevaluedattheirmarketvalue.LaborCapitalOpportunityCosts(时机本钱)Allin7EconomicProfitHowdowevalueafirm?Supposethefirm’sstreamofperiodiceconomicprofitsisP0,P1,P2,…andristherateofinterest.Thenthepresent-valueofthefirm’seconomicprofitstreamisEconomicProfitHowdowevalue8ProfitMaximizationAcompetitivefirmseekstomaximizeitspresent-value.How?ProfitMaximizationAcompetiti9Supposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionis

Thefirm’sfixedcostis

anditsprofitfunctionisShort-RunProfitMaximizationSupposethefirmisinashort10Short-RunIso-ProfitLinesA$P

iso-profitline(等利润线)containsalltheproductionplansthatyieldaprofitlevelof$P.Theequationofa$Piso-profitlineis

I.e.Short-RunIso-ProfitLinesA$P11Short-RunIso-ProfitLineshasaslopeofandaverticalinterceptofShort-RunIso-ProfitLineshas12Short-RunIso-ProfitLinesIncreasing

profityx1Short-RunIso-ProfitLinesIncr13Short-RunProfit-MaximizationThefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.Q:Whatisthisconstraint?A:Theproductionfunction.Short-RunProfit-MaximizationT14Short-RunProfit-Maximizationx1Technically

inefficient

plansyTheshort-runproductionfunctionand

technologysetforShort-RunProfit-Maximizationx15Short-RunProfit-Maximizationx1Increasing

profityShort-RunProfit-Maximizationx16Short-RunProfit-Maximizationx1yShort-RunProfit-Maximizationx17Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanisShort-RunProfit-Maximizationx18Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanis

Andthemaximum

possibleprofit

isShort-RunProfit-Maximizationx19Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.Short-RunProfit-Maximizationx20Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.Short-RunProfit-Maximizationx21Short-RunProfit-Maximization

isthemarginalrevenueproduct(边际收益产量)ofinput1,therateatwhichrevenueIncreaseswiththeamountusedofinput1.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.

Short-RunProfit-Maximization22Short-RunProfit-Maximization;ACobb-DouglasExampleSupposetheshort-runproduction

functionisThemarginalproductofthevariable

input1isTheprofit-maximizingconditionisShort-RunProfit-Maximization;23Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesShort-RunProfit-Maximization;24Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,Short-RunProfit-Maximization;25Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,soShort-RunProfit-Maximization;26Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.Short-RunProfit-Maximization;27Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.Thefirm’sshort-runoutputlevelisthusShort-RunProfit-Maximization;28ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?ComparativeStaticsofShort-R29ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinpcauses

--areductionintheslope,and--areductionintheverticalintercept.ComparativeStaticsofShort-R30ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R31ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R32ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R33ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinp,thepriceofthefirm’soutput,causesanincreaseinthefirm’soutputlevel(thefirm’ssupplycurveslopesupward),andanincreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputshiftsoutward).ComparativeStaticsofShort-R34ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyisComparativeStaticsofShort-R35ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyisComparativeStaticsofShort-R36ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyisincreasesaspincreases.ComparativeStaticsofShort-R37ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanasthevariableinputpricew1changes?ComparativeStaticsofShort-R38ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinw1causes

--anincreaseintheslope,and--nochangetotheverticalintercept.ComparativeStaticsofShort-R39ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R40ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R41ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R42ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinw1,thepriceofthefirm’svariableinput,causesadecreaseinthefirm’soutputlevel(thefirm’ssupplycurveshiftsinward),andadecreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputslopesdownward).ComparativeStaticsofShort-R43ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyisComparativeStaticsofShort-R44ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.anditsshort-run

supplyisComparativeStaticsofShort-R45ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.decreasesasw1increases.anditsshort-run

supplyisComparativeStaticsofShort-R46Long-RunProfit-MaximizationNowallowthefirmtovarybothinputlevels,i.e.,bothx1andx2arevariable.Sincenoinputlevelisfixed,therearenofixedcosts.Long-RunProfit-MaximizationNo47Theprofit-maximizationproblemisFOCsare:Long-RunProfit-MaximizationTheprofit-maximizationproble48FactorDemandFunctionsDemandforinputs1and2canbesolvedas,FactorDemandFunctionsDemand49InverseFactorDemandFunctionsForagivenoptimaldemandforx2,inversedemandfunctionforx1isForagivenoptimaldemandforx1inversedemandfunctionforx2isInverseFactorDemandFunction50InverseFactorDemandCurvesx1w1InverseFactorDemandCurvesx151Example:C-DProductionFunctionTheproductionfunctionisFirst-orderconditionsare:Example:C-DProductionFuncti52Solvingforx1andx2:Plug-inproductionfunctiontoget:Example:C-DProductionFunctionSolvingforx1andx2:Plug-in53Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsdecreasingreturns-to-scalethenthefirmhasasinglelong-runprofit-maximizingproductionplan.Returns-to-ScaleandProfit-Ma54Returns-toScaleandProfit-Maximizationxyy*x*Decreasing

returns-to-scaleReturns-toScaleandProfit-Ma55Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsexhibitsincreasingreturns-to-scalethenthefirmdoesnothaveaprofit-maximizingplan.Returns-to-ScaleandProfit-Ma56Returns-toScaleandProfit-Maximizationxyy〞x’Increasing

returns-to-scaley’x〞Increasing

profitReturns-toScaleandProfit-Ma57Returns-to-ScaleandProfit-MaximizationSoanincreasingreturns-to-scaletechnologyisinconsistentwithfirmsbeingperfectlycompetitive.Returns-to-ScaleandProfit-Ma58Returns-to-ScaleandProfit-MaximizationWhatifthecompetitivefirm’stechnologyexhibitsconstantreturns-to-scale?Returns-to-ScaleandProfit-Ma59Returns-toScaleandProfit-Maximizationxyy〞x’Constant

returns-to-scaley’x〞Increasing

profitReturns-toScaleandProfit-Ma60Returns-toScaleandProfit-MaximizationSoifanyproductionplanearnsapositiveprofit,thefirmcandoubleupallinputstoproducetwicetheoriginaloutputandearntwicetheoriginalprofit.Returns-toScaleandProfit-Ma61Returns-toScaleandProfit-MaximizationTherefore,whenafirm’stechnologyexhibitsconstantreturns-to-scale,earningapositiveeconomicprofitisinconsistentwithfirmsbeingperfectlycompetitive.Henceconstantreturns-to-scalerequiresthatcompetitivefirmsearneconomicprofitsofzero.Returns-toScaleandProfit-Ma62Returns-toScaleandProfit-Maximizationxyy〞x’Constant

returns-to-scaley’x〞P=0Returns-toScaleandProfit-Ma63RevealedProfitabilityConsideracompetitivefirmwithatechnologythatexhibitsdecreasingreturns-to-scale.Foravarietyofoutputandinputpricesweobservethefirm’schoicesofproductionplans.Whatcanwelearnfromourobservations?RevealedProfitabilityConsider64RevealedProfitabilityIfaproductionplan(x’,y’)ischosenatprices(w’,p’)wededucethattheplan(x’,y’)isrevealedtobeprofit-maximizingfortheprices(w’,p’).RevealedProfitabilityIfapro65RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.RevealedProfitabilityxy66RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.

wouldgivelower

profits,soRevealedProfitabilityxy67RevealedProfitabilityxy

ischosenatprices

so(x〞,y〞)ischosenatprices(w〞,p〞)so

(x〞,y〞)isprofit-maximizingattheseprices.RevealedProfitabilityxy68WeakAxiomofProfitMaximizationxy

ischosenatprices

so

ischosenatprices

soWeakAxiomofProfitMaximizat69RevealedProfitabilityandsoandAddinggivesRevealedProfitabilityandsoand70RevealedProfitabilitysoThatis,isanecessaryimplicationofprofit-

maximization.RevealedProfitabilitysoThati71RevealedProfitabilityisanecessaryimplicationofprofit-

maximization.

Supposetheinputpricedoesnotchange.

ThenDw=0andprofit-maximization

implies;i.e.,acompetitive

firm’soutputsupplycurvecannotslope

downward.RevealedProfitabilityisanec72RevealedProfitabilityisanecessaryimplicationofprofit-

maximization.

Supposetheoutputpricedoesnotchange.

ThenDp=0andprofit-maximization

implies;i.e.,acompetitive

firm’sinputdemandcurvecannotslopeupward.RevealedProfitabilityisanec73ChapterNineteenProfit-MaximizationChapterNineteenProfit-Maximiz74StructureEconomicprofitShort-runprofitmaximizationComparativestaticsLong-runprofitmaximizationProfitmaximizationandreturnstoscaleRevealedprofitmaximizationStructureEconomicprofit75EconomicProfitAfirmusesinputsj=1…,mtomakeproductsi=1,…n.Outputlevelsarey1,…,yn.Inputlevelsarex1,…,xm.Productpricesarep1,…,pn.Inputpricesarew1,…,wm.

EconomicProfitAfirmusesinp76TheCompetitiveFirmThecompetitivefirmtakesalloutputpricesp1,…,pnandallinputpricesw1,…,wmasgivenconstants.TheCompetitiveFirmThecompet77EconomicProfitTheeconomicprofitgeneratedbytheproductionplan(x1,…,xm,y1,…,yn)isEconomicProfitTheeconomicpr78EconomicProfitOutputandinputlevelsaretypicallyflows.E.g.x1mightbethenumberoflaborunitsusedperhour.Andy3mightbethenumberofcarsproducedperhour.Consequently,profitistypicallyaflowalso;e.g.thenumberofdollarsofprofitearnedperhour.EconomicProfitOutputandinpu79OpportunityCosts(时机本钱)Allinputsmustbevaluedattheirmarketvalue.LaborCapitalOpportunityCosts(时机本钱)Allin80EconomicProfitHowdowevalueafirm?Supposethefirm’sstreamofperiodiceconomicprofitsisP0,P1,P2,…andristherateofinterest.Thenthepresent-valueofthefirm’seconomicprofitstreamisEconomicProfitHowdowevalue81ProfitMaximizationAcompetitivefirmseekstomaximizeitspresent-value.How?ProfitMaximizationAcompetiti82Supposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionis

Thefirm’sfixedcostis

anditsprofitfunctionisShort-RunProfitMaximizationSupposethefirmisinashort83Short-RunIso-ProfitLinesA$P

iso-profitline(等利润线)containsalltheproductionplansthatyieldaprofitlevelof$P.Theequationofa$Piso-profitlineis

I.e.Short-RunIso-ProfitLinesA$P84Short-RunIso-ProfitLineshasaslopeofandaverticalinterceptofShort-RunIso-ProfitLineshas85Short-RunIso-ProfitLinesIncreasing

profityx1Short-RunIso-ProfitLinesIncr86Short-RunProfit-MaximizationThefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.Q:Whatisthisconstraint?A:Theproductionfunction.Short-RunProfit-MaximizationT87Short-RunProfit-Maximizationx1Technically

inefficient

plansyTheshort-runproductionfunctionand

technologysetforShort-RunProfit-Maximizationx88Short-RunProfit-Maximizationx1Increasing

profityShort-RunProfit-Maximizationx89Short-RunProfit-Maximizationx1yShort-RunProfit-Maximizationx90Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanisShort-RunProfit-Maximizationx91Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanis

Andthemaximum

possibleprofit

isShort-RunProfit-Maximizationx92Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.Short-RunProfit-Maximizationx93Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.Short-RunProfit-Maximizationx94Short-RunProfit-Maximization

isthemarginalrevenueproduct(边际收益产量)ofinput1,therateatwhichrevenueIncreaseswiththeamountusedofinput1.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.

Short-RunProfit-Maximization95Short-RunProfit-Maximization;ACobb-DouglasExampleSupposetheshort-runproduction

functionisThemarginalproductofthevariable

input1isTheprofit-maximizingconditionisShort-RunProfit-Maximization;96Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesShort-RunProfit-Maximization;97Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,Short-RunProfit-Maximization;98Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,soShort-RunProfit-Maximization;99Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.Short-RunProfit-Maximization;100Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.Thefirm’sshort-runoutputlevelisthusShort-RunProfit-Maximization;101ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?ComparativeStaticsofShort-R102ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinpcauses

--areductionintheslope,and--areductionintheverticalintercept.ComparativeStaticsofShort-R103ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R104ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R105ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R106ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinp,thepriceofthefirm’soutput,causesanincreaseinthefirm’soutputlevel(thefirm’ssupplycurveslopesupward),andanincreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputshiftsoutward).ComparativeStaticsofShort-R107ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyisComparativeStaticsofShort-R108ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyisComparativeStaticsofShort-R109ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyisincreasesaspincreases.ComparativeStaticsofShort-R110ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanasthevariableinputpricew1changes?ComparativeStaticsofShort-R111ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinw1causes

--anincreaseintheslope,and--nochangetotheverticalintercept.ComparativeStaticsofShort-R112ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R113ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R114ComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-R115ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinw1,thepriceofthefirm’svariableinput,causesadecreaseinthefirm’soutputlevel(thefirm’ssupplycurveshiftsinward),andadecreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputslopesdownward).ComparativeStaticsofShort-R116ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyisComparativeStaticsofShort-R117ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.anditsshort-run

supplyisComparativeStaticsofShort-R118ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.decreasesasw1increases.anditsshort-run

supplyisComparativeStaticsofShort-R119Long-RunProfit-MaximizationNowallowthefirmtovarybothinputlevels,i.e.,bothx1andx2arevariable.Sincenoinputlevelisfixed,therearenofixedcosts.Long-RunProfit-MaximizationNo120Theprofit-maximizationproblemisFOCsare:Long-RunProfit-MaximizationTheprofit-maximizationproble121FactorDemandFunctionsDemandforinputs1and2canbesolvedas,FactorDemandFunctionsDemand122InverseFactorDemandFunctionsForagivenoptimaldemandforx2,inversedemandfunctionforx1isForagivenoptimaldemandforx1inversedemandfunctionforx2isInverseFactorDemandFunction123InverseFactorDemandCurvesx1w1InverseFactorDemandCurvesx1124Example:C-DProductionFunctionTheproductionfunctionisFirst-orderconditionsare:Example:C-DProductionFuncti125Solvingforx1andx2:Plug-inproductionfunctiontoget:Example:C-DProductionFunctionSolvingforx1andx2:Plug-in126Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsdecreasingreturns-to-scalethenthefirmhasasinglelong-runprofit-maximizingproductionplan.Returns-to-ScaleandProfit-Ma127Returns-toScaleandProfit-Maximizationxyy*x*Decreasing

returns-to-scaleReturns-toScaleandProfit-Ma128Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsexhibitsincreasingreturns-to-scalethenthefirmdoesnothaveaprofit-maximizingplan.Returns-to-ScaleandProfit-Ma129Returns-toScaleandProfit-Maximizationxyy〞x’Increasing

returns-to-scaley’x〞Increasing

profitReturns-toScaleandProfit-Ma130Returns-to-ScaleandProfit-MaximizationSoanincreasingreturns-to-scaletechnologyisinconsistentwithfirmsbeingperfectlycompetitive.Returns-to-ScaleandProfit-Ma131Returns-to-ScaleandProfit-MaximizationWhatifthecompetitivefirm’stechnologyexhibitsconstantreturns-to-scale?Returns-to-ScaleandProfit-Ma132Returns-toScaleandProfit-Maximizationxyy〞x’Constant

returns-to-scaley’x〞Increasing

profitReturns-toScaleandProfit-Ma133Returns-toScaleandProfit-