管理经济学（第14版） 课件 第3章　优化决策的边际分析

Chapter03MarginalAnalysisforOptimalDecisionsMANAGERIALECONOMICSFoundationsofBusinessAnalysisandStrategyFourteenthEditionCHRISTOPHERR.THOMAS©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.LearningOutcomes3.1 Defineseveralkeyconceptsandterminologyrelatedtomarginalanalysis.3.2 Usemarginalanalysistofindoptimalactivitylevelsinunconstrainedmaximizationproblemsandexplainwhysunkcosts,fixedcosts,andaveragecostsareirrelevantfordecisionmaking.3.3 Employmarginalanalysistofindtheoptimallevelsoftwoormoreactivitiesinconstrainedmaximizationandminimizationproblems.2AnOptimizationProblemAnoptimizationprobleminvolvesthespecificationofthreethings:Theobjectivefunction,whichisthefunctionthedecision-makerseekstomaximizeorminimize.Activitiesorchoicevariablesthatdeterminethevalueoftheobjectivefunction.Anyconstraintsthatmayrestrictthevaluesofthechoicevariables.3OptimizationMaximizationproblemAnoptimizationproblemthatinvolvesmaximizingtheobjectivefunction.MinimizationproblemAnoptimizationproblemthatinvolvesminimizingtheobjectivefunction.4UnconstrainedVersusConstrainedOptimizationUnconstrainedoptimizationAnoptimizationprobleminwhichthedecision-makercanchoosethelevelofactivityfromanunrestrictedsetofvalues.ConstrainedoptimizationAnoptimizationprobleminwhichthedecision-makerchoosesvaluesforthechoicevariablesfromarestrictedsetofvalues.5ChoiceVariablesActivitiesorchoicevariablesdeterminethevalueoftheobjectivefunction.Discretechoicevariablescanonlytakespecificintegervalues.Continuouschoicevariablescantakeanyvaluebetweentwoendpoints.6MarginalAnalysisAnalyticaltechniqueforsolvingoptimizationproblemsthatinvolveschangingvaluesofchoicevariablesbysmallamountstoseeiftheobjectivefunctioncanbefurtherimproved.7NetBenefitNetBenefit(NB)Differencebetweentotalbenefit(TB)andtotalcost(TC)fortheactivity.

NB=TB−TC.Optimalleveloftheactivity(A*)isthelevelthatmaximizesnetbenefit.8Figure3.1:TheOptimalLevelofanActivityAccessthetextalternativeforslideimages.9MarginalBenefitandMarginalCost1Marginalbenefit(MB)Changeintotalbenefit(TB)causedbyanincrementalchangeintheleveloftheactivity.Marginalcost(MC)Changeintotalcost(TC)causedbyanincrementalchangeintheleveloftheactivity.10MarginalBenefitandMarginalCost211RelatingMarginalstoTotalsMarginalvariablesmeasureratesofchangeincorrespondingtotalvariables.Marginalbenefit(marginalcost)ofaunitofactivitycanbemeasuredbytheslopeofthelinetangenttothetotalbenefit(totalcost)curveatthatpointofactivity.12Figure3.2:RelatingMarginalstoTotalsAccessthetextalternativeforslideimages.13Figure3.3:UsingMarginalAnalysistoFindA*Accessthetextalternativeforslideimages.14Table3.1:MarginalAnalysisDecisionRulesMB>MCMB<MCIncreaseactivityNBrisesNBfallsDecreaseactivityNBfallsNBrises15UsingMarginalAnalysistoFindOptimalActivityLevelsIfmarginalbenefit>marginalcostActivityshouldbeincreasedtoreachhighestnetbenefit.Ifmarginalcost>marginalbenefitActivityshouldbedecreasedtoreachhighestnetbenefit.16OptimalActivityLevelOptimallevelofactivityWhennofurtherincreasesinnetbenefitarepossible.OccurswhenMB=MC.17Table3.2OptimizationWithaDiscreteChoiceVariable(1)Levelofactivity(A)(2)Totalbenefitofactivity(TB)(3)Totalcostofactivity(TC)(4)Netbenefitofactivity(NB)(5)Marginalbenefit(MB)(6)Marginalcost(MC)0$0$0$0––11621416223062414434011291054482028895543024610658451341576161031686380−1721918UnconstrainedMaximizationWithDiscreteChoiceVariablesIncreaseactivityifMB>MC.DecreaseactivityifMB<MC.OptimallevelofactivityisthelastlevelforwhichMBexceedsMC.19IrrelevanceofSunk,Fixed,andAverageCosts1SunkcostsPreviouslypaidandcannotberecovered.FixedcostsConstantandmustbepaidnomatterthelevelofactivity.Average(orunit)costsComputedbydividingtotalcostbythenumberofunitsofactivity.20IrrelevanceofSunk,Fixed,andAverageCosts2Decision-makerswishingtomaximizethenetbenefitofanactivityshouldignorethesecostsbecausenoneofthesecostsaffectthemarginalcostoftheactivityandsoareirrelevantforoptimaldecisions.21ConstrainedOptimization1TheratioMB∕Prepresentstheadditionalbenefitperadditionaldollarspentontheactivity.Ratiosofmarginalbenefitstopricesofvariousactivitiesareusedtoallocateafixednumberofdollarsamongactivities.22ConstrainedOptimization2Tomaximizeorminimizeanobjectivefunctionsubjecttoaconstraint:Ratiosofthemarginalbenefittopricemustbeequalforallactivities.Constraintmustbemet.23Summary1Marginalanalysisisananalyticaltechniqueforsolvingoptimizationproblemsbychangingthevalueofachoicevariablebyasmallamounttoseeiftheobjectivefunctioncanbefurtherimproved.TheratioMB∕Pdenotestheadditionalbenefitofthatactivityperadditionaldollarspent(“bangperbuck”).24Summary2Theoptimalleveloftheactivity(A*)isthatwhichmaximizesnetbenefitandoccurswheremarginalbenefitequalsmarginalcost(MB=MC).Sunkcostshavepreviouslybeenpaidandcannotberecovered;Fixedcostsareconstantandmustbepaidnomatterthelevelofactivity;Average(orunit)costisthecostperunitofactivity;thesethreetypesofcostsareirrelevantforoptimaldecisionmaking.25EndofMainContent©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.AccessibilityContent:TextAlternativesforImages27Figure3.1:TheOptimalLevelofanActivity

-TextAlternativeReturntoparent-slidecontainingimages.PanelA:Theverticaly-axisislabeledtotalbenefitandtotalcostindollarsrangingfrom0to4,000inincrementsof1,000units.Thehorizontalx-axisislabeledlevelofactivity(A)rangingfrom0to1,000inincrementsof200units.Aconcave-downincreasingcurvelabeledTCstartsattheoriginandrisesfromlefttoright.Aconcave-upincreasingcurve,labeledTB,startsattheoriginandintersectscurveTBatapointlabeledF.ThelabeledpointsoncurveTBareasfollows:C(200,1,500),B(350,2,310),D(600,3,000),F(700,3,500),andG(1,000,3,800).ThelabeledpointsoncurveTCareasfollows:Cprime(200,400),Bprime(350,1,085),Dprime(600,2,500),andF(700,3,500).PointsCandCprimeareconnectedbyalinesegment.Similarly,pointsBandBprimeandDandDprimeareconnectedbyalinesegment.LineBBprimeislabeledNBdoubleprimeequalsdollars1,225.Allthevaluesareapproximated.PanelB:Theverticaly-axisislabelednetbenefitindollarsrangingfrom0to1,225.Thehorizontalx-axisislabeledlevelofactivity(A)rangingfrom0to1,000.Adownwardopeningparaboliccurve,labeledLB,isplottedthatstartsattheorigin,passesthroughpointCdoubleprimeat(200,1,000),reachesitspeakpointMat(350,1,225),andthenstartsdecliningtotheright.Thecurvethenpassesthroughpointddoubleprimeat(600,600),intersectsthehorizontalx-axisatpointfdoubleprimeat(700,0),andendsjustbelowthehorizontalx-axis.Notethatalltheabove-mentionedvaluesareactualvalues.Returntoparent-slidecontainingimages.28Figure3.2:RelatingMarginalstoTotals

-TextAlternativeReturntoparent-slidecontainingimages.PanelA:Theverticaly-axisislabeledtotalbenefitandtotalcostindollarsrangingfrom0to4,000inincrementsof1,000units.Thehorizontalx-axisislabeledlevelofactivity(A)rangingfrom0to1,000inincrementsof200units.Aconcave-downincreasingcurve,labeledTC,startsattheoriginandrisesfromlefttoright.Aconcave-upincreasingcurve,labeledTB,startsattheoriginandintersectscurveTBatapointlabeledF.ThelabeledpointsoncurveTBareasfollows:C(200,1,500),B(350,2,310),D(600,3,000),F(700,3,500),andG(1,000,3,800).ThelabeledpointsoncurveTCareasfollows:Cprime(200,400),Bprime(350,1,085),Dprime(600,2,500),andF(700,3,500).Thepointsonboththecurvesaremarkedwithtangentsformingarighttriangleandthebaseandheightvaluesofthetriangleareasfollows:C,100horizontaland640vertical,Cprime,100horizontaland340vertical,B,100horizontaland520vertical,Bprime,100horizontaland520vertical,D,100horizontaland320vertical,Dprime,100horizontaland820vertical.AverticallinesegmentconnectspointsBandBprime.Notethatalltheabove-mentionedvaluesareapproximate.PanelB:Theverticaly-axisislabeledmarginalbenefitandmarginalcostindollarsrangingfrom0to8inincrementsof2units.Thehorizontalx-axisislabeledlevelofactivity(A)rangingfrom0to1,000inincrementsof200units.Twolines,labeledMC(equalstheslopeofTC)andMB(equalstheslopeofTB),areplotted.LineMChasanincreasingslopestartingapproximatelyfrom(0,1),passingthroughpointCprimeat(200,3.40),andgoinguptopointBat(200,6.40).Thelinefurthergoesuptopointdprimeat(600,8.20).LineMBhasadecliningslopestartingapproximatelyfrom(20,8),passingthroughpointCat(200,6.40),andgoingfurtherdowntointersectlineMCatapointlabeledb.Thelinefurthergoesdownthroughpointdat(600,3.20)andintersectsthehorizontalx-axisatpointg(1,000,0).Notethatalltheabove-mentionedvaluesareapproximate.Returntoparent-slidecontainingimages.29Figure3.3:UsingMarg