管理经济学（第14版） 课件 第15章　风险和不确定性下的决策

Chapter15DecisionsUnderRiskandUncertaintyMANAGERIALECONOMICSFoundationsofBusinessAnalysisandStrategyFourteenthEditionCHRISTOPHERR.THOMAS©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.LearningObjectives15.1Explainthedifferencebetweendecisionmakingunderriskandunderuncertainty.15.2Computetheexpectedvalue,variance,standarddeviation,andcoefficientofvariationofaprobabilitydistribution.15.3Employtheexpectedvaluerule,mean‐variancerules,andthecoefficientofvariationruletomakedecisionsunderrisk.15.4Explainexpectedutilitytheoryandapplyittodecisionsunderrisk.15.5Makedecisionsunderuncertaintyusingthemaximaxrule,themaximinrule,theminimaxregretrule,andtheequalprobabilityrule.2RiskVersusUncertaintyRiskAdecision-makingconditionunderwhichamanagercanlistalltheoutcomesandassignprobabilitiestoeachoutcome.UncertaintyAdecision-makingconditionunderwhichamanagercannotlistallpossibleoutcomesand/orcannotassignprobabilitiestothevariousoutcomes.3MeasuringRiskWithProbabilityDistributionsAprobabilitydistributionisatableorgraphshowingallpossibleoutcomesorpayoffsofadecisionandtheprobabilitiesthateachoutcomewilloccur.Tomeasureriskassociatedwithadecision:Examinestatisticalcharacteristicsoftheprobabilitydistributionofoutcomesforthedecision.4Figure15.1TheProbabilityDistributionforSalesFollowinganAdvertisingCampaignAccessthetextalternativeforslideimages.5ExpectedValueExpectedvalueofaprobabilitydistribution(ormeanofthedistribution)istheweightedaverageoftheoutcomes,withtheprobabilitiesofeachoutcomeservingastherespectiveweights:whereistheithoutcomeofadecision,istheprobabilityoftheith

outcome,andnisthetotalnumberofpossibleoutcomes.Doesnotgivetheactualvalueoftherandomoutcome.Indicates“average”valueoftheoutcomesiftheriskydecisionweretoberepeatedalargenumberoftimes.6VarianceVarianceisameasureofabsoluterisk.Measuresthedispersionofadistributionaboutitsmeanorexpectedvalue:Thehigherthevariance,thegreatertheriskassociatedwithaprobabilitydistribution.7Figure15.2TwoProbabilityDistributionsWithIdenticalMeansbutDifferentVariancesAccessthetextalternativeforslideimages.8StandardDeviationStandarddeviationisthesquarerootofthevariance.Thehigherthestandarddeviation,thegreatertherisk.9Figure15.3ProbabilityDistributionsWithDifferentVariancesAccessthetextalternativeforslideimages.10CoefficientofVariationWhenexpectedvaluesofoutcomesdiffersubstantially,managersshouldmeasureriskinessofadecisionrelativetoitsexpectedvalueusingthecoefficientofvariation.Thecoefficientofvariationisameasureofrelativeriskandiscalculatedbytakingthestandarddeviationanddividingbytheexpectedvalueoftheprobabilitydistribution.11DecisionsUnderRiskNosingledecisionruleguaranteesprofitswillactuallybemaximized.Decisionrulesdonoteliminateriskbutprovideamethodtosystematicallyincluderiskinthedecision-makingprocess.ExpectedvalueruleMean-varianceanalysisCoefficientofvariationrule12DecisionsRulesExpectedvalueruleChoosethedecisionwiththehighestexpectedvalue.Mean-varianceanalysisMethodofdecisionmakingthatemploysboththemeanandvariancetomakedecisions.GiventworiskydecisionsAandB:IfAhashigherexpectedoutcomeandlowervariancethanB,choosedecisionA.IfAandBhaveidenticalvariances(orstandarddeviations),choosedecisionwithhigherexpectedvalue.IfAandBhaveidenticalexpectedvalues,choosedecisionwithlowervariance(standarddeviation).CoefficientofvariationruleChoosethedecisionwiththesmallestcoefficientofvariation.13Figure15.4ProbabilityDistributionsforWeeklyProfitatThreeRestaurantLocationsAccessthetextalternativeforslideimages.14WhichRuleIsBest?Forarepeateddecisionwithidenticalprobabilitieseachtime:Expectedvalueruleismostreliableformaximizing(expected)profit.Averagereturnofagivenriskycourseofactionrepeatedmanytimesapproachestheexpectedvalueofthataction.Foraone-timedecisionunderrisk:Norepetitionsto“averageout”abadoutcome.Nobestruletofollow.Rulesshouldbeusedtohelpanalyzeandguidethedecision-makingprocess.Asmuchartasscience.15ExpectedUtilityTheoryExpectedutilitytheoryisatheoryofdecisionmakingunderriskthataccountsforamanager’sattitudetowardrisk.Managersareassumedtoderiveutilityfromearningprofits.Managersmakeriskydecisionsinawaythatmaximizesexpectedutilityoftheprofitoutcomes.Expectedutilityisthesumoftheprobability-weightedutilitiesofeachpossibleprofitoutcome:Utilityfunctionmeasuresutilityassociatedwithaparticularlevelofprofit.Indextomeasurelevelofutilityreceivedforagivenamountofearnedprofit.16Manager’sUtilityFunctionforProfitDeterminedbythemanager’smarginalutilityofprofit,whichistheamountbywhichtotalutilityincreaseswithanadditionaldollarofprofitearnedbythefirm:Marginalutility(slopeofutilitycurve)determinesattitudetowardrisk.17Manager’sAttitudeTowardRisk1RiskaverseDescribesadecision-makerwhomakesthelessriskyoftwodecisionsthathavethesameexpectedvalue.RisklovingDescribesadecision-makerwhomakestheriskieroftwodecisionsthathavethesameexpectedvalue.RiskneutralDescribesadecision-makerwhoignoresriskindecisionmakingandconsidersonlyexpectedvaluesofdecisions.18Manager’sAttitudeTowardRisk2Canrelateamanager’sattitudetowardrisktothemarginalutilityofprofit:Riskaverse:diminishingRiskloving:increasingRiskneutral:constant19Figure15.5AManager’sAttitudeTowardRiskAccessthetextalternativeforslideimages.20CertaintyEquivalentAcertaintyequivalentisthedollaramountthatamanagerwouldbejustwillingtotradefortheopportunitytoengageinariskydecision.Toimplementthecertaintyequivalentmethodofderivingautilityofprofitfunction,thefollowingstepscanbeemployed:Settheutilityindexequalto1forthehighestpossibleprofitand0forthelowestpossibleprofitDefineariskydecisiontohaveprobabilityofprofitoutcomeandprobabilityofprofitoutcomeForeachpossibleoutcomethemanagerdeterminessubjectivelytheprobabilitythatgivesthatriskydecisionthesameexpectedutilityasreceivingwithcertainty:Thecertainsumiscalledthecertaintyequivalentoftheriskydecision.21Figure15.6FindingaCertaintyEquivalentforaRiskyDecisionAccessthetextalternativeforslideimages.22Figure15.7AManager’sUtilityFunctionforProfitAccessthetextalternativeforslideimages.23ExpectedUtilityofProfitsAccordingtoexpectedutilitytheory,decisionsaremadetomaximizethemanager’sexpectedutilityofprofits.Suchdecisionsreflectrisk-takingattitude.Generallydifferfromthosereachedbydecisionrulesthatdonotconsiderrisk.Forarisk-neutralmanager,decisionsareidenticalundermaximizationofexpectedutilityormaximizationofexpectedprofit.24Table15.1ExpectedUtilityofProfit:ARisk-NeutralManager(1)(2)(3)(4)(5)(6)(7)(8)(9)ProbabilitiesProbability-WeightedUtilityProfit(π)Utility[U(π)]MarginalUtility[∆U(π)∕∆π]AtlantaBostonCleveland$1,0000–00.10.3000$2,0000.20.00020.20.150.10.040.030.02$3,0000.40.00020.30.150.10.120.060.04$4,0000.60.00020.30.250.10.180.150.06$5,0000.80.00020.20.20.10.160.160.08$6,0001.00.000200.150.300.150.3Expectedutility=0.500.550.5025Table15.2ExpectedUtilityofProfit:ARisk-LovingManager(1)(2)(3)(4)(5)(6)(7)(8)(9)ProbabilitiesProbability-WeightedUtilityProfit(π)Utility[U(π)]MarginalUtility[∆U(π)∕∆π]AtlantaBostonCleveland$1,0000–00.10.3000$2,0000.080.000080.20.150.10.0160.0120.008$3,0000.20.000120.30.150.10.060.030.02$4,0000.380.000180.30.250.10.1140.0950.038$5,0000.630.000250.20.20.10.1260.1260.036$6,0001.00.0003700.150.300.150.3Expectedutility=0.320.410.4326DecisionsUnderUncertaintyWithuncertainty,decisionscienceprovideslittleguidance.Fourbasicdecisionrulesareprovidedtoaidmanagersinanalysisofuncertainsituations:MaximaxruleMaximinruleMinimaxregretruleEqualprobabilityrule27MaximaxRuleandMaximinRuleMaximaxruleDecision-makingguidethatcallsforidentifyingthebestoutcomeforeachpossibledecisionandchoosingthedecisionwiththemaximumpayoffofallthebestoutcomes.MaximinruleDecision-makingguidethatcallsforidentifyingtheworstoutcomeforeachdecisionandchoosingthedecisionwiththemaximumworstpayoff.28Table15.3ThePayoffMatrixforDuraPlastic,Inc.StatesofNatureDecisionsRecoveryStagnationRecessionExpandplantcapacityby20%$5million−$1million−$3.0millionMaintainsameplantcapacity3million2million0.5millionReduceplantcapacityby20%2million1million0.75million29MinimaxRegretRuleandEqualProbabilityRuleMinimaxregretruleDecision-makingguidethatcallsfordeterminingtheworstpotentialregretassociatedwitheachdecision,thenchoosingthedecisionwiththeminimumworstpotentialregret.Foragivenstateofnature,potentialregretistheimprovementinpayoffthemanagercouldhaveexperiencedhadthedecisionbeenthebestonewhenthatstateofnatureactuallyoccurs.EqualprobabilityruleDecision-makingguidethatcallsforassumingeachstateofnatureisequallylikelytooccur,computingtheaveragepayoffforeachequallylikelypossiblestateofnature,andchoosingthedecisionwiththehighestaveragepayoff.30Table15.4PotentialRegretMatrixforDuraPlastic,Inc.StatesofNatureDecisionsRecoveryStagnationRecessionExpandplantcapacityby20%$0million$3million$3.75millionMaintainsameplantcapacity2million0million0.25millionReduceplantcapacityby20%3million1million0million31Summary1Underconditionsofrisk,themanagercanlistallpossibleoutcomesandassignprobabilitiestothem;uncertaintyexistswhenonecannotlistallpossibleoutcomesand/orcannotassignprobabilitiestothevariousoutcomes.Tomeasureriskassociatedwithadecision,managerscanexamineseveralstatisticalcharacteristicsoftheprobabilitydistributionofoutcomesforthedecision.Whiledecisionrulesdonoteliminaterisk,theydoprovideamethodofsystematicallyincludingtheriskintheprocessofdecisionmaking.Threedecisionrules:theexpectedvaluerule,themean-variancerule,andthecoefficientofvariationrule.32Summary2Expectedutilitytheoryisatheory,notarule,ofdecisionmakingunderriskthatformallyaccountsforamanager’sattitudetowardrisk,whichpostulatesthatmanagersmakeriskydecisionswiththeobjectiveofmaximizingtheexpectedutilityofprofit.Inthecaseofuncertainty,decisionsciencecanprovideverylittleguidancetomanagersbeyondofferingthemsomesimpledecisionrulestoaidthemintheiranalysisofuncertainsituations.Fourbasicrulesfordecisionmakingunderuncertaintyare:themaximaxrule,themaximinrule,theminimaxregretrule,andtheequalprobabilityrule.33EndofMainContent©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.AccessibilityContent:TextAlternativesforImages35Figure15.1TheProbabilityDistributionforSalesFollowinganAdvertisingCampaign-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledprobabilityrangingfrom0to0.30inincrementsof0.10units.Thehorizontalaxisislabeledsalesrangingfrom0to57,500inincrementsof2,500units.Thereisajaggedlinefrom0to47,500onthehorizontalaxis.Thebarat47,500hasaheightof0.10.Thebarat50,000hasaheightof0.20.Thebarat52,500hasaheightof0.30.Thebarat55,000hasaheightof0.25.Thebarat57,500hasaheightof0.15.Returntoparent-slidecontainingimages.36Figure15.2TwoProbabilityDistributionsWithIdenticalMeansbutDifferentVariances-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledprobability.Thehorizontalaxisislabeledprofitinpi.Movingtotherightfromtheorigin,atickmarkonthehorizontalaxisislabeledEofpi.AdashedverticallineisdrawnatEofpi.Alongbell-shapedcurve,labeleddistributionA,centeredatE(pi)entersneartheorigin,concavedown,graduallyrisestoapeak,thenconcaveup,andgraduallyfalls.Anothershortbell-shapedcurve,labeleddistributionB,centeredatE(pi)entersfromapointontheverticalaxis,concavedown,graduallyrisestopeakbelowthefirstcurve,thenconcaveup,andgraduallyfalls.Itiswiderthanthefirstcurve.Returntoparent-slidecontainingimages.37Figure15.3ProbabilityDistributionsWithDifferentVariances-TextAlternativeReturntoparent-slidecontainingimages.DistributionA:Theverticalaxisislabeledprobability.ThehorizontalaxisislabeleddistributionA,rangingfrom0to70inincrementsof10units.Thereisajaggedlinefrom0to30onthehorizontalaxis.Thebarat30hasaheightof5percent.Thebarat40hasaheightof20percent.Thebarat50hasaheightof50percent.Thebarat60hasaheightof20percent.Thebarat70hasaheightof5percent.DistributionB:Theverticalaxisislabeledprobability.ThehorizontalaxisislabeleddistributionBrangingfrom0to70inincrementsof10units.Thereisajaggedlinefrom0to30onthehorizontalaxis.Thebarat30hasaheightof10percent.Thebarat40hasaheightof25percent.Thebarat50hasaheightof30percent.Thebarat60hasaheightof25percent.Thebarat70hasaheightof10percent.Returntoparent-slidecontainingimages.38Figure15.4ProbabilityDistributionsforWeeklyProfitatThreeRestaurantLocations-TextAlternativeReturntoparent-slidecontainingimages.ThefirstgraphistitledAtlanta.Theverticalaxisislabeledprobabilityrangingfrom0to0.40inincrementsof0.10.Thehorizontalaxisislabeledprofitindollarsrangingfrom0to5,000inincrementsof1,000units.Thebarat2,000hasaheightof0.20.Thebarat3,000hasaheightof0.30.Thebarat4,000hasaheightof0.30.Thebarat5,000hasaheightof0.20.Thetextonthegraphreads,EofXequals3,500,sigmasubscriptAequals1,025andnuequals0.29.ThesecondgraphistitledBoston.Theverticalaxisislabeledprobabilityrangingfrom0to0.40inincrementsof0.10.Thehorizontalaxisislabeledprofitindollarsrangingfrom0to6,000inincrementsof1,000units.Thebarat1,000hasaheightof0.10.Thebarat2,000hasaheightof0.15.Thebarat3,000hasaheightof0.15.Thebarat4,000hasaheightof0.25.Thebarat5,000hasaheightof0.20.Thebarat6,000hasaheightof0.15.Thetextonthegraphreads,EofXequals3,750,sigmasubscriptBequals1,545andnuequals0.41.ThethirdgraphistitledCleveland.Theverticalaxisislabeledprobabilityrangingfrom0to0.40inincrementsof0.10.Thehorizontalaxisislabeledprofitindollarsrangingfrom0to6,000inincrementsof1,000units.Thebarat1,000hasaheightof0.30.Thebarat2,000hasaheightof0.10.Thebarat3,000hasaheightof0.10.Thebarat4,000hasaheightof0.10.Thebarat5,000hasaheightof0.10.Thebarat6,000hasaheightof0.30.Thetextonthegraphreads,EofXequals3,500,sigmasubscriptCequals2,062andnuequals0.59.Returntoparent-slidecontainingimages.39Figure15.5AManager’sAttitudeTowardRisk-TextAlternativeReturntoparent-slidecontainingimages.PanelA:Theverticalaxisislabeledutilityindexrangingfrom0to50.Thehorizontalaxisislabeledprofitinthousandsrangingfrom0to150inincrementsof50units.Aconcave-downincreasingcurve,labeledUofpi,startsattheorigin,andpassesthroughthepointsC(50,25),A(100,40),andB(150,50).PanelB:Theverticalaxisi