managerial economics：applications, strategy, and tactics, th edition

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ManagerialEconomics：Applications,Strategy,andTactics,8thEditionManagerialEconomics:Applications,Strategy,andTactics,8thEditionbyMcGuigan,Moyer,&HarrispreparedbyRichardD>.MarcusUniversityofWisconsin-Milwaukee??1999South-WesternCollegePublishingChapter1IntroductiontoManagerialEconomicsStructureofDecisionModelsProfit’sRoleAgencyProblems&SolutionsNot-for-ProfitOrganizationsWhyCorporationsHaveSucceededOverOtherOrganizationalForms??1999South-WesternCollegePublishingManagerialEconomics:AnAppliedCourseIntegratestheuseofeconomics,math,andfinancialanalysistomakegoodbusinessdecisions ??1999South-WesternCollegePublishingTOPICSDemandandSupplyAnalysisandhowtoestimatedelasticitiesProductionandCostAnalysisandhowtoestimaterelationshipsMonopoly,Competition,andOligopoliesandgoodpricingdecisions??1999South-WesternCollegePublishingEconomicDecisionsConstraints--limitationsoftime,energy,money,productivecapacity,regulatoryclimate,etc>.Information--forecasting,relationships,expectations,possibleretaliationbyrivals,etc>.??1999South-WesternCollegePublishingCONSTRAINTSINFORMATIONGOALS&OBJECTIVESObjectivesoftheFirmProfitmaximizationShareholderwealthThevalueofthefirm,V,isthepresentvalueofexpectedfutureprofits(p)orcashflows,discountedattheshareholdersrequiredrateofreturn,ke,ignoringtaxes>.??V=Spt/(1+ke)t t=1??1999South-WesternCollegePublishingGoalsorObjectivesMaximizePresentValueofProfits=NS(Revenuet-Costst)/(1+ke)tt=1DecisionModelLanguage:ObjectiveFunction=setsupthegoals&theconstraintsDecisionRule=showswhatisoptimal??1999South-WesternCollegePublishingEXAMPLE:MAXP{A,B}simpleobjectivefunction,simpledecisionrulePickAifprofit{A}>profit{B},otherwisepickB>.MaxProfit{Q}foracompetitivefirmproducewhereP=MC??1999South-WesternCollegePublishingMCPQProfit=TR-TC=P??Q-TCQ-Q+Tomakegoodeconomicdecisions,managersneedtobeabletoforecast &estimaterelationshipsWillforecastdemandappliestofor-profitcorporationsnon-profitorganizationsHospitalAdministrators--#patientsUniversityAdministrator--enrollmentWilluseregressionanalysis,timeseriesmethods,andqualitativeforecastingmethods??1999South-WesternCollegePublishingTheRoleofProfitsEconomicCost(oropportunitycost)isthehighestvaluedbenefitthatmustbesacrificedasaresultofchoosinganalternative>.Economicprofitisthedifferencebetweenrevenuesandtotaleconomiccost(includingtheeconomicoropportunitycostofownersuppliedresourcessuchastimeandcapital>.??1999South-WesternCollegePublishingTheoriesofWhyProfitVariesAcrossIndustriesRISK-BEARINGTHEORYOFPROFITDYNAMICEQUILIBRIUM(ORFRICTIONAL)THEORYOFPROFITMONOPOLYTHEORYOFPROFITINNOVATIONTHEORYOFPROFITMANAGERIALEFFICIENCYTHEORYOFPROFIT??1999South-WesternCollegePublishingAgencyProblemsModerncorporationsallowmanagerstohaveno,orlimited,ownership participationintheprofitabilityofthefirm>.Shareholdersmaywantprofits,butmanagersmaywishtorelax>.Theshareholdersareprincipals,whereasthemanagersareagents>.Conflictingmotivationsbetweenthesegroupsarecalledagencyproblems>.??1999South-WesternCollegePublishingThePrincipal-AgentProblemShareholders(principals)wantprofitManagers(agents)wantleisure&securityExamplesTheLBObyO>.M>.ScottfromITTimprovedScott’sperformanceKKR’stakeoverofRJRNabiscotorefocusonwealth-maximization??1999South-WesternCollegePublishingSolutionstoAgencyProblemsCompensationasincentiveExtendingtoallworkersstockoptions,bonuses,andgrantsofstockHelpmakeworkersactasownersoffirmIncentivestohelpthecompany,becausethatimprovesthevalueofstockoptionsandbonuses>.??1999South-WesternCollegePublishingShareholderWealthMaximization:ConditionsCOMPLETEMARKETS-liquidmarketsforfirm'sinputsandby-products(includingpollutingby-products)>.NOSIGNIFICANTASYMMETRICINFORMATION-buyersandsellersallknow thesamethings>.KNOWNRECONTRACTINGCOSTSfutureinputcostsarepartofthepresentvalueofexpectedcashflows>.??1999South-WesternCollegePublishingGoalsinthePublicSectorandtheNot-For-Profit(NFP)EnterpriseInsteadofprofit,NFPorganizationsmayhaveastheirgoals:a>.Maximizationofthequantityofoutput,subjecttoabreakevenconstraint>.b>.Maximizationoftheutility(happiness)ofNFPadministrators>.c>.Maximizationofcashflows>.d>.MaximizationoftheutilityofcontributorstotheNFPorganization>.??1999South-WesternCollegePublishingWhichgoalaNFPmanagerselectsaffectsthetypesofdecisionsmade>.Amanagerofafoodsheltermaydecidetomaximizetheutilityofcontributorsbyselectingonly;healthyfoods;Publicsectormanagersarefrequentlymonitoredwithregardtohowtheyperformtheirjobs>.IfaV>.A>.hospitaladministratorisrewardedbyreducingthecostperbedoverayear,thentheadministratormaybecomequiteefficientwithrespecttocosts>.However,the;friendliness;ofthehospitalstaffishardertomeasure,sofriendlinesswilltendnotbeahighpriorityofthepublicsector manager>.??1999South-WesternCollegePublishingFirmsvs>.HouseholdProductionBusinessclassespresumeproductioninfirmsWecan&doproducethingsathomeSupposeallgoodsproducedinhouseholdsLimitedbysizeofhouseholdSupposethereexistsomeeconomiesofscaleinorganizationalsize??1999South-WesternCollegePublishingTwohouseholdsmergeifmoreproductive,otherhouseholdsemulateFourhouseholdsmergeiftruefor2,whynottruefor2millionhouseholdsmerging?problemsariseasthesizeofthecollectivegrowsLessPersonalIncentivesWhoisinCharge?Disagreements&ConflictResolutionIssues??1999South-WesternCollegePublishingEntrepreneurshipSynonymisCONTRACTORcontractormonitorsproductionhireslaboratfixedratespurchasesmaterialsreceivestheresidualThisisafirm—contractor-entrepreneur 87%ofallproductionbycorporationsremaining13%inproprietorships&otherTheCorporationhasdemonstrateditsresiliencyovertime>.??1999South-WesternCollegePublishingFundamentalEconomicConceptsChapter2Total,Average,andMarginalEquationsandFindingtheOptimumPointPresentValue,Discounting&NPVRisk-Return&ProbabilityUseofaz-value??1999South-WesternCollegePublishingHowtoMaximizeProfitsDecisionMakingIsn’tFreeMaxProfit{A,B},butsupposethatwedon’tknowProfit{A}ortheProfit{B}Shouldwehireaconsultantfor$1,000?ShouldwemarketanAmorettoFlavoredchewinggumforadults?complexcombinationofmarketing,production,andfinancialissues??1999South-WesternCollegePublishingBreakDecisionsIntoSmallerUnits:HowMuchtoProduce?GraphofoutputandprofitPossibleRule:ExpandoutputuntilprofitsturndownButproblemoflocalmaximavs>.globalmaximum ??1999South-WesternCollegePublishingquantityBMAXGLOBALMAXprofitAAverageProfit=Profit/QSlopeofrayfromtheoriginRise/RunProfit/Q=averageprofitMaximizingaverageprofitdoesn’tmaximizetotalprofit??1999South-WesternCollegePublishingMAXCBprofitsQPROFITSquantityMarginalProfits=DP/DQprofitsofthelastunitproducedmaximummarginalprofitsoccurattheinflectionpoint(A)DecisionRule:producewheremarginalprofits=0>.??1999South-WesternCollegePublishing profitsmaxAmarginalprofitsQQaverageprofitsBCUsingEquationsprofit=f(quantity)orP=f(Q)dependentvariable&independentvariable(s)averageprofit=P/Qmarginalprofit=DP/DQ??1999South-WesternCollegePublishingOptimalDecision(oneperiod)exampleofusingmarginalsThescaleofaprojectshouldexpanduntilMB=MCExample:screeningforprostateorbreastcancerHowoften???1999South-WesternCollegePublishing MBMCfrequencyperdecadePresentValuePresentvaluerecognizesthatadollarreceivedinthefutureisworthlessthanadollarinhandtoday>.Tocomparemoniesinthefuturewithtoday,thefuturedollarsmustbediscountedbyapresentvalueinterestfactor,PVIF=1/(1+i),whereiistheinterestcompensationforpostponingreceivingcashoneperiod>.Fordollarsreceivedinnperiods,thediscountfactorisPVIFn=[1/(1+i)]n??1999South-WesternCollegePublishingNetPresentValue,NPV=PresentvalueoffuturereturnsminusInitialoutlay>.Thisisforthesimpleexampleofasinglecosttodayyieldingabenefitorstreamofbenefitsinthefuture>.Forthemoregeneralcase,NPV=Presentvalueofallcashflows(bothpositiveandnegativeones)>.NPVRule:Doallprojectsthathavepositivenetpresentvalues>.Bydoingthis,themanagermaximizesshareholderwealth>.SomeinvestmentsmayincreaseNPV,butatthesametime,theymayincreaserisk>.??1999South-WesternCollegePublishingNetPresentValue(NPV)Mostbusinessdecisionsarelongtermcapitalbudgeting,productassortment,etc>. Objective:maxthepresentvalueofprofitsNPV=PVoffuturereturns-InitialOutlayNPV=St=0NCFt/(1+rt)twhereNCFtisthenetcashflowinperiodtGoodprojectshaveHighNCF’sLowratesofdiscount??1999South-WesternCollegePublishingSourcesofPositiveNPVsBrandidentifyandloyaltyControloverdistributionPatentsorlegalbarrierstoentrySuperiormaterialsDifficultyforotherstoacquirefactorsofproductionSuperiorfinancialresourcesEconomiesoflargescaleorsizeSuperiormanagement??1999South-WesternCollegePublishingMostdecisionsinvolveagambleProbabilitiescanbeknownorunknown,andoutcomescanbeknownorunknownRisk--existswhen:Possibleoutcomesandprobabilitiesareknowne>.g>.,roulettewheelordiceUncertainty--existswhen: Possibleoutcomesorprobabilitiesareunknowne>.g>.,drillingforoilinanunknownfield??1999South-WesternCollegePublishingRiskandUncertaintyConceptsofRiskWhenprobabilitiesareknown,wecananalyzeriskusingprobabilitydistributionsAssignaprobabilitytoeachstateofnature,andbeexhaustive,sothatSpi=1??1999South-WesternCollegePublishingStatesofNatureStrategyRecessionEconomicBoomp=>.30p=>.70ExpandPlant-40100Don’tExpand-1050PayoffMatrixPayoffMatrixshowspayoffsforeachstateofnature,foreachstrategyExpectedValue=r=Spiri>.r=Spiri=>.30(-40)+>.70(100)=58ifExpandr=Spiri=>.30(-10)+>.70(50)=32ifDon’tExpandStandardDeviation=s=??Spi(ri-r)2>.??1999South-WesternCollegePublishing^ ^^^ExampleofFindingStandardDeviationssexpand=SQRT{>.3(-40-58)2+>.7(100-58)2}=SQRT{>.3(-98)2+>.7(42)2}=SQRT{4116}=64>.16sdon’t=SQRT{>.3(-10-32)2+>.7(50-32)2}=SQRT{>.3(-42)2+>.7(18)2}=SQRT{756}=27>.50Expandinghasagreaterstandarddeviation,buthigherexpectedreturn>.??1999South-WesternCollegePublishingCoefficientsofVariationorRelativeRiskCoefficientofVariation(C>.V>.)=s/rC>.V>.isameasureofriskperdollarofexpectedreturn>.Thediscountrateforpresentvaluesdependsontheriskclassoftheinvestment>.LookatsimilarinvestmentsCorporateBonds,orTreasuryBondsCommonDomesticStocks,orForeignStocks??1999South-WesternCollegePublishing^ProjectsofDifferentSizes: Ifdoublethesize,theC>.V>.isnotchanged!!!CoefficientofVariationisgoodforcomparingprojectsofdifferentsizes??1999South-WesternCollegePublishingExampleofTwoGamblesA:ProbX}R=15>.510}s=SQRT{>.5(10-15)2+(20-15)2(>.5)}>.520}=SQRT{25}=5C>.V>.=5/15=>.333B:ProbX}R=30>.520}s=SQRT{>.5(20-30)2+(40-30)2(>.5)}>.540}=SQRT{100}=10C>.V>.=10/30=>.333ContinuousProbabilityDistributions(vs>.Discrete)Expectedvaluedisthemodeforsymmetricdistributions??1999South-WesternCollegePublishingRARBABAisriskier,butithasahigherexpectedvalue^^ z-Valueszisthenumberofstandarddeviationsawayfromthemeanz=(r-r)/s68%ofthetimewithin1standarddeviation95%ofthetimewithin2standarddeviations99%ofthetimewithin3standarddeviationsProblem:incomehasmean$1,000andastandarddeviationof$500>.What’sthechanceoflosingmoney???1999South-WesternCollegePublishing^??1999South-WesternCollegePublishingSTOCKRETURNS1970-1995inUSDollarsAnnual%StdDev%Australia8>.8126>.98Canada9>.3517>.01France11>.9830>.23Germany11>.7631>.07HongKong21>.2552>.73Italy5>.7140>.88Japan16>.3936>.07Mexico12>.3751>.59Netherlands16>.1219>.25 Singapore16>.1250>.63U>.Kingdom12>.9331>.56U>.States11>.3416>.37??1999South-WesternCollegePublishingAustraliaBelgiumCanadaFranceGermanyreturn6>.99%11>.15%8>.30%9>.17%12>.10%stddev13>.08%16>.74%11>.20%15>.29%13>.80%NetherlandsNewZealandIrelandItalyJapanreturn9>.62%7>.84%12>.69%10>.83%6>.45%stddev21>.67%22>.32%16>.37%13>.14%18>.26%SouthAfricaSwedenSwissEnglandUSAreturn4>.42%7>.86%10>.11%7>.81%7>.90%stddev22>.50%13>.84%15>.82%21>.27%7>.84%BONDRETURNS:1967-1995 inUSDollarsChapter3OptimizationTechniquesOverviewUnconstrained&ConstrainedOptimizationCalculusofonevariablePartialDifferentiationinEconomicProblemsAppendix3A:LagrangiansandConstrainedOptimization??1999South-WesternCollegePublishingOptimumCanBeHighestorLowestFindingthemaximumflyingrangefortheStealthBomberisanoptimizationproblem>.Calculusteachesthatwhenthefirstderivativeiszero,thesolutionisatanoptimum>.TheoriginalStealthBomberstudyshowedthatacontroversialflyingV-wingdesignoptimizedthebomber'srange,buttheoriginalresearchersfailedtofindthattheirsolutioninfactminimizedtherange>.Itiscriticalthatmanagersmakedecisionthatmaximize,notminimize,profitpotential!??1999South-WesternCollegePublishingUnconstrainedOptimizationUnconstrainedOptimizationisarelativelysimplecalculusproblemthatcanbesolvedusingdifferentiation,suchasfindingthequantity thatmaximizesprofitinthefunction:p(Q)=16·Q-Q2TheanswerisQ=8,aswewillsee>.??1999South-WesternCollegePublishingConstrainedOptimizationConstrainedOptimizationinvolvesoneormoreconstraintsofmoney,time,capacity,orenergy>.Whenthereareinequalityconstraints(aswhenyoumustspendlessthanorequaltoyourtotalincome),linearprogrammingcanbeused>.Mostoften,managersknowthatsomeconstraintsarebinding,whichmeansthattheyareequalityconstraints>.Lagrangianmultipliersareusedtosolvetheseproblems>.(seeAppendix3A)>.??1999South-WesternCollegePublishingOptimizationFormatEconomicproblemsrequiretradeoffsforcedonusbythelimitsofourmoney,time,andenergy>.Optimizationinvolvesanobjectivefunctionandoneormoreconstraints,b>.Maximizey=f(x1,x2,>.>.>.,xn)Subjecttog(x1,x2,>.>.>.,xn)<bor:Minimizey=f(x1,x2,>.>.>.,xn)Subjecttog(x1,x2,>.>.>.,xn)>b??1999South-WesternCollegePublishingUsingEquations profit=f(quantity)orP=f(Q)dependentvariable&independentvariable(s)averageprofit=P/Qmarginalprofit=DP/DQCalculususesderivativesdP/dQ=limDP/DQDQ0SLOPE=MARGINAL=DERIVATIVENEWDECISIONRULE:Tomaximizeprofits,findwheredP/dQ=0--firstordercondition??1999South-WesternCollegePublishingQuickDifferentiationReviewConstantY=cdY/dX=0Y=5dY/dX=0LineY=c??XdY/dX=cY=5??XdY/dX=5PowerY=cXbdY/dX=b??c??Xb-1Y=5??X2dY/dX=10??X??1999South-WesternCollegePublishingNameFunctionDerivativeExampleQuickDifferentiationReviewSumRuleY=G(X)+H(X)dY/dX=dG/dX+dH/dX exampleY=5??X+5??X2dY/dX=5+10??XProductRuleY=G(X)??H(X)dY/dX=(dG/dX)H+(dH/dX)GexampleY=(5??X)(5??X2)dY/dX=5(5??X2)+(10??X)(5??X)=75??X2??1999South-WesternCollegePublishingQuickDifferentiationReviewQuotientRuleY=G(X)/H(X)dY/dX=(dG/dX)??H-(dH/dX)??GH2Y=(5??X)/(5??X2)dY/dX=5(5??X2)-(10??X)(5??X)(5??X2)2=-25X2/25??X4=-X-2ChainRuleY=G[H(X)]dY/dX=(dG/dH)??(dH/dX)Y=(5+5??X)2dY/dX=2(5+5??X)1(5)=50+50??X??1999South-WesternCollegePublishingApplicationsofCalculusinManagerialEconomicsmaximizationproblem:Aprofitfunctionmightlooklikeanarch,risingtoapeakandthendecliningatevenlargeroutputs>.Afirmmightsellhugeamountsatverylowprices,butdiscoverthatprofitsarelowornegative>. Atthemaximum,theslopeoftheprofitfunctioniszero>.Thefirstorderconditionforamaximumisthatthederivativeatthatpointiszero>.Ifp=50·Q-Q2,thendp/dQ=50-2·Q,usingtherulesofdifferentiation>.Hence,Q=25willmaximizeprofits>.??1999South-WesternCollegePublishingMoreApplicationsofCalculusminimizationproblem:Costminimizationsupposesthatthereisaleastcostpointtoproduce>.AnaveragecostcurvemighthaveaU-shape>.Attheleastcostpoint,theslopeofthecostfunctioniszero>.Thefirstorderconditionforaminimumisthatthederivativeatthatpointiszero>.IfC=5·Q2-60·Q,thendC/dQ=10·Q-60>.Hence,Q=6willminimizecost>.??1999South-WesternCollegePublishingMoreExamplesCompetitiveFirm:MaximizeProfitswhereP=TR-TC=P??Q-TC(Q)Useourfirstordercondition:dP/dQ=P-dTC/dQ=0DecisionRule:P=MC??1999South-WesternCollegePublishingafunctionofQMaxP=100??Q-Q2100-2??Q=0impliesQ=50andP=2,500MaxP=50+5??X2 So,10??X=0impliesQ=0andP=50SecondOrderCondition:OneVariableIfthesecondderivativeisnegative,thenit’samaximumIfthesecondderivativeispositive,thenit’saminimum??1999South-WesternCollegePublishingMaxP=100??Q-Q2100-2??Q=0secondderivativeis:-2impliesQ=50isaMAXMaxP=50+5??X210??X=0secondderivativeis:10impliesQ=0isaMINPartialDifferentiationEconomicrelationshipsusuallyinvolveseveralindependentvariables>.Apartialderivativeislikeacontrolledexperiment--itholdsthe“other”variablesconstantI>.e>.,supposepriceisincreased,holdingthedisposableincomeoftheeconomyconstantQ=f(P,I)??Q/??Pholdsincomeconstant??1999South-WesternCollegePublishingProblem:Salesareafunctionofadvertisinginnewspapersandmagazines(X,Y)MaxS=200X+100Y-10X2-20Y2+20XY DifferentiatewithrespecttoXandYandsetequaltozero>.??S/??X=200-20X+20Y=0??S/??Y=100-40Y+20X=0solveforX&YandSales??1999South-WesternCollegePublishingSolution:2equations&2unknowns200-20X+20Y=0100-40Y+20X=0Addingthem,the-20Xand+20Xcancel,soweget300-20Y=0,orY=15Plugintooneofthem:200-20X+300=0,henceX=25TofindSales,plugintoequation:S=200X+100Y-10X2-20Y2+20XY=3,250??1999South-WesternCollegePublishingInternationalImportRestraintsImportquotasofJapaneseautomobilesareinequalityconstraints>.Theaddedconstraintwillaffectdecisions>.AJapanesemanufacturerwillshiftmoreproductiontoU>.S>.assemblyfacilitiesandincreasethepriceofcarsexportedtotheU>.S>.Wemayalsoexpectthattheexportedcarswillbe;topoftheline;models,andweexpectU>.S>.manufacturerstoraisedomesticcarprices>.??1999South-WesternCollegePublishingAppendix3A:LagrangiansObjectivefunctionsareoftenconstrainedbyoneormore “constraints”(time,capacity,ormoney)MaxL=(objectivefct>.)-l{constraintsettozero}MinL=(objectivefct>.)+l{constraintsettozero}AnartificialvariableiscreatedforeachconstraintintheLagrangianmultipliertechnique>.Thisartificialvariableistraditionallycalledlambda,l>.??1999South-WesternCollegePublishingMaximizeUtilityExampleexample:MaxUtilitysubjecttoamoneyconstraintMaxU=X??Y2subjecttoa$12totalbudgetwiththepricesofXas$1,thepriceofYas$4(supposeXrepresentssodaandY,movietickets)>.MaxL=X??Y2-l{X+4Y-12}differentiatew>.r>.tX,Yandlambda,l>.??1999South-WesternCollegePublishing??L/??X=Y2-l=0Y2=l??L/??Y=2XY-4l=02XY=4l??L/??l=X+4Y-12=0ThreeequationsandthreeunknownsSolve:Ratiooffirsttwoequationsis:Y/2X=1/4orY=>.5X>.Substituteintothethirdequation:Weget:X=4;Y=2;andl=4Lambdaisthemarginal(objectivefunction)ofthe(constraint)>.Here,l=themarginalutilityofmoney>. ??1999South-WesternCollegePublishingProblemMinimizeCrimeinyourtownPolice,P,costs$15,000each>.Jail,J,costs$10,000each>.Budgetis$900,000>.Crimefunctionisestimated:C=5600-4PJSetuptheproblemasaLagrangianSolveforoptimalPandJ,andCWhatiseconomicmeaningoflambda???1999South-WesternCollegePublishingAnswerMinL=5600-4PJ+l{15,000??P+10,000??J-900,000}ToSolve,differentiate1>.??L/??P:-4??J+15,000??l=02>.??L/??J:-4??P+10,000??l=03>.??L/??l:15,000??P+10,000??J-900,000=0J/P=1>.5soJ=1>.5??P&substituteinto(3>.)15,000??P+10,000??[1>.5??P]-900,000=0solution:P=30,J=45,C=200andl=->.012Lambdaisthemarginalcrime(reduction)foradollarofadditionalbudgetspent??1999South-WesternCollegePublishingDEMANDANALYSISChapter4 OVERVIEWDemandRelationshipsDemandElasticitiesIncomeElasticitiesCrossElasticitiesofDemandAppendix4A:IndifferenceCurves??1999South-WesternCollegePublishingDemandAnalysisAnimportantcontributortofirmriskarisesfromsuddenshiftsindemandfortheproductorservice>.Demandanalysisservestwomanagerialobjectives:(1)itprovidestheinsightsnecessaryforeffectivemanagementofdemand,and(2)itaidsinforecastingsalesandrevenues>.??1999South-WesternCollegePublishingDemandCurvesIndividualDemandCurve-thegreatestquantityofagooddemandedateachpricetheconsumersarewillingtobuy,ceterisparibus>.??1999South-WesternCollegePublishingWillingtoBuyUnwillingtoBuy$/QQ/timeunit TheMarketDemandCurveisthehorizontalsumoftheindividualdemandcurves>.TheDemandFunctionincludesallvariablesthatinfluencethequantitydemanded437SamDianeMarketQ=f(P,Ps,Pc,I,W,E)++-??+SupplyCurvesFirmSupplyCurve-thegreatestquantityofagoodsuppliedateachpricethefirmisprofitablyabletosupply,ceterisparibus>.??1999South-WesternCollegePublishing$/QQ/timeunitAbletoProduceUnabletoProduceTheMarketSupplyCurveisthehorizontalsumofthefirmsupplycurves>.TheSupplyFunctionincludesallvariablesthatinfluencethequantitysupplied437 AcmeUniversalMarketQ=g(P,W,R,TC)+--+Equilibrium:NoTendencytoChangeSuperimposedemandandsupplyIfNoExcessDemandandNoExcessSupplyNotendencytochange??1999South-WesternCollegePublishingDSPewilling&ableQPDownwardSlopePriceandquantityarenegativelyrelatedSomereasonsinclude:incomeeffect--asthepriceofagooddeclines,theconsumercanpurchasemoreofallgoodssincehisorherrealincomeincreased>.substitutioneffect--asthepricedeclines,thegoodbecomesrelativelycheaper>.Arationalconsumermaximizessatisfactionbyreorganizingconsumptionuntilthemarginalutilityineachgoodperdollarisequal: OptimalityConditionisMUA/PA=MUB/PB=MUC/PC=>.>.>.IfMUperdollarinAandBdiffer,theconsumercanimproveutilitybypurchasingmoreoftheonewithhigherMUperdollar>.??1999South-WesternCollegePublishingComparativeStatics&theSupply-DemandModelSupposeashiftinIncome,andthegoodisa“normal”goodDoesdemandorsupplyshift?Supposewagesrose,whatthen???1999South-WesternCollegePublishingDSe1PQElasticityasSensitivityElasticityismeasureofresponsivenessorsensitivityBewareofusingslopes??1999South-WesternCollegePublishingbushelshundredtonspricepriceperperbu>.buSlopeschange withachangeinunitsofmeasurePriceElasticityEP=%changeinQ/%changeinPShortcutnotation:EP=%DQ/%DPApercentagechangefrom100to150Apercentagechangefrom150to100ArcPriceElasticity--averagesoverthetwopoints??1999South-WesternCollegePublishingDarcpriceelasticityArcPriceElasticityExampleQ=1000atapriceof$10ThenQ=1200whenthepricewascutto$6FindthepriceelasticitySolution:EP=%DQ/%DP=+200/1100-4/8or->.3636>.Theanswerisanumber>.A1%increaseinpricereducesquantityby>.36percent>.??1999South-WesternCollegePublishingPointPriceElasticityExampleNeedademandcurveordemandfunctiontofindthepriceelasticity atapoint>.EP=%DQ/%DP=(??Q/??P)(P/Q)IfQ=500-5??P,findthepointpriceelasticityatP=30;P=50;andP=80EQ??P=(??Q/??P)(P/Q)=-5(30/350)=->.7><43EQ??P=(??Q/??P)(P/Q)=-5(50/250)=-1>.0EQ??P=(??Q/??P)(P/Q)=-5(80/100)=-4>.0PriceElasticity(bothpointpriceandarcelasticity)IfEP=-1,unitelasticIfEP>-1,inelastic,e>.g>.,-0>.<43IfEP<-1,elastic,e>.g>.,-4>.0??1999South-WesternCollegePublishingpriceelasticregionunitelasticinelasticregionStraightlinedemandcurveTRandPriceElasticitiesIfyouraiseprice,doesTRrise?Supposedemandiselastic,andraiseprice>.TR=P??Q,so,%DTR=%DP+%DQ Ifelastic,P,butQalotHenceTRFALLS!!!Supposedemandisinelastic,andwedecidetoraiseprice>.WhathappenstoTRandTCandprofit???1999South-WesternCollegePublishingAnotherWaytoRememberLineardemandcurveTRonothercurveLookatarrowstoseemovementinTR??1999South-WesternCollegePublishingElasticUnitElasticInelasticTRQQ1979DeregulationofAirfares PricesdeclinedPassengersincreasedTotalRevenueIncreasedWhatdoesthisimplyaboutthepriceelasticityofairtravel???1999South-WesternCollegePublishingDeterminantsofthePriceElasticityThenumberofclosesubstitutesmoresubstitutes,moreelasticTheproportionofthebudgetlargerproportion,moreelasticThelongerthetimeperiodpermittedmoretime,generally,moreelasticconsiderexamplesofbusinesstravelversusvacationtravelforallthreeabove>.??1999South-WesternCollegePublishingIncomeElasticityEI=%DQ/%DI=(??Q/??I)(I/Q)arcincomeelasticity:supposedollarquantityoffoodexpendituresoffamiliesof$20,000is$5,200;andfoodexpendituresrisesto$6,760forfamiliesearning$30,000>.Findtheincomeelasticityoffood%DQ/%DI=(1560/5980)??(10,000/25,000)=>.652??1999South-WesternCollegePublishingDefinitions IfEIispositive,thenanormalgoodsomegoodsareLuxuries:EI>1somegoodsareNecessities:EI<1IfEQ??Iisnegative,thenaninferiorgoodconsider:ExpendituresonautomobilesExpendituresonChevroletsExpenditureson1991ChevyCavalier??1999South-WesternCollegePublishingPointIncomeElasticityProblemSupposethedemandfunctionis:Q=10-2??P+3??IfindtheincomeandpriceelasticitiesatapriceofP=2,andincomeI=10So:Q=10-2(2)+3(10)=36EI=(??Q/??I)(I/Q)=3(10/36)=>.833EP=(??Q/??P)(P/Q)=-2(2/36)=->.111Characterizethisdemandcurve!??1999South-WesternCollegePublishingCrossPriceElasticitiesEX=%DQx/%DPy=(??Qx/??Py)(Py/Qx)Substituteshavepositivecrosspriceelasticities:Butter&MargarineComplementshavenegativecrosspriceelasticities:VCRmachines andtherentalpriceoftapesWhenthecrosspriceelasticityiszeroorinsignificant,theproductsarenotrelated??1999South-WesternCollegePublishingHOMEWORKPROBLEM:Findthepointpriceelasticity,thepointincomeelasticity,andthepointcross-priceelasticityatP=10,I=20,andPs=9,ifthedemandfunctionwereestimatedtobe:Qd=90-8·P+2·I+2·PsIsthedemandforthisproductelasticorinelastic?Isitaluxuryoranecessity?Doesthisproducthaveaclosesubstituteorcomplement?Findthepointelasticitiesofdemand>.??1999South-WesternCollegePublishingIndifferenceCurveAnalysisAppendix4AConsumersattempttomaxhappiness,orutility:U(X,Y)Subjecttoanincomeconstraint:I=Px??X+Py??YGraphin3-dimensions??1999South-WesternCollegePublishingYXUUoUoConsumerChoice-assumeconsumerscanrankpreferences,thatmore isbetterthanless(nonsatiation),thatpreferencesaretransitive,andthatindividualshavediminishingmarginalratesofsubstitution>.Thenindifferencecurvesslopedown,neverintersect,andareconvextotheorigin>.??1999South-WesternCollegePublishingXY567976convexUoU1U2giveup2XforaY??1999South-WesternCollegePublishingXYYUoU1acdemand bIndifferenceCurves??Wecan;derive;ademandcurvegraphicallyfrommaximizationofutilitysubjecttoabudgetconstraint>.Aspricefalls,wetendtobuymoredueto(i)theIncomeEffectand(ii)theSubstitutionEffect>.PyConsumerChoice&LagrangiansTheconsumerchoiceproblemcanbemadeintoaLagrangianMaxL=U(X,Y)-l{Px??X+Py??Y-I}i)??L/??X=??U/??X-lPx=0MUx=Pxii)??L/??Y=??U/??Y-lPy=0MUy=Pyiii)Px??X+Py??Y-I=0Equationsi)andii)arerearrangedontheright-handsideafterthebrackettoshowthattheratioofMUsequalstheratioofprices>.Thisistheequi-marginalprincipleforoptimalconsumption>.??1999South-WesternCollegePublishing}OptimalConsumptionPointRearrangingwegettheDecisionRule:MUx/Px=MUy/Py=MUz/Pz“themarginalutilityperdollarineachuseisequal”LambdaisthemarginalutilityofmoneySupposeMU1=20,andMU2=50andP1=5,andP2=25areyoumaximizingutility? ??1999South-WesternCollegePublishingProblemMaxL=2X+2Y->.5X2+XY->.6Y2-l{48-4X-6Y}1>.Lx:2-X+Y=4l2>.Ly:2+X-1>.2Y=6l3>.Ll:48-4X-6Y=0(1)and(2)yields:X=1>.08??Y+>.4(3)canbereducedtoX=12-1>.5YTogetherweget:X=5>.256,Y=4>.496SubstituteXandYinto(1)wefindl=>.31??1999South-WesternCollegePublishingX=1>.08??Y+>.4EstimationofDemandChapter5Objective:Learnhowtoestimateademandfunctionusingregressionanalysis,andinterprettheresultsAchiefuncertaintyformanagers--whatwillhappentotheirproduct>.forecasting,prediction&estimationneedfordata:FrankKnight:“Ifyouthinkyoucan’tmeasuresomething,measureitanyway>.”??1999South-WesternCollegePublishingSourcesofinformationondemandConsumerSurveysaskasampleofconsumerstheirattitudes ConsumerClinicsexperimentalgroupstrytoemulateamarket(Hawthorneeffect)MarketExperimentsgetdemandinformationbytryingdifferentpricesHistoricalDatawhathappenedinthepastisguidetothefuturePlotHistoricalDataLookattherelationshipofpriceandquantityovertimePlotitIsitademandcurveorasupplycurve?Problem--notheldotherthingsequal??1999South-WesternCollegePublishingquantityPrice92979493969895D?orS?IdentificationProblemQ=a+bPcanappearupwardordownwardsloping>.SupposesupplyvariesanddemandisFIXED>. Allpointslieonthedemandcurve??1999South-WesternCollegePublishing|____________________________QuantityquantityPS1S2S3DemandSupposeSUPPLYisFixedLetDEMANDshiftandsupplybeFIXED>.AllpointsareontheSUPPLYcurve>.WesaythattheSUPPLYcurveisidentified>.??1999South-WesternCollegePublishingquantityP8><#004699'>D1D2D3SupplyWhenbothSupplyandDemandVaryOftenbothsupplyanddemandvary>.Equilibriumpointsareinshadedregion>. AregressionofQ=a+bPwillbeneitherademandnorasupplycurve>.??1999South-WesternCollegePublishingquantityP<#004699'>D1D2S1S2StatisticalEstimationoftheaDemandFunctionStepstotake:Specifythevariables--formulatethedemandmodel,selectaFunctionalFormlinearQ=a+b??P+c??IdoubleloglnQ=a+b??lnP+c??lnIquadraticQ=a+b??P+c??I+d??P2Estimatetheparameters--determinewhicharestatisticallysignificanttryothervariables&otherfunctionalformsDevelopforecastsfromthemodelSpecifyingtheVariablesDependentVariable--quantityinunits,quantityindollarvalue(asinsalesrevenues)IndependentVariables--variablesthoughttoinfluencethequantitydemanded InstrumentalVariables--proxyvariablesfortheitemwantedwhichtendstohavearelativelyhighcorrelationwiththedesiredvariable:e>.g>.,TastesTimeTrend??1999South-WesternCollegePublishingFunctionalFormsLinearQ=a+b??P+c??ITheeffectofeachvariableisconstantTheeffectofeachvariableisindependentofothervariablesPriceelasticityis:EP=b??P/QIncomeelasticityis:EI=c??I/Q??1999South-WesternCollegePublishingFunctionalFormsMultiplicativeQ=A??Pb??IcTheeffectofeachvariabledependsonalltheothervariablesandisnotconstantItisloglinearLnQ=a+b??LnP+c??LnIthepriceelasticityisbtheincomeelasticityisc??1999South-WesternCollegePublishingSimpleLinearRegressionQt=a+bPt+ettimesubscripts&errortermFind“bestfitting”lineet=Qt-a-bPt et2=[Qt-a-bPt]2minSet2=S[Qt-a-bPt]2Solution:b=Cov(Q,P)/Var(P)anda=mean(Q)-b??mean(P)??1999South-WesternCollegePublishing_PQ_QOLS--ordinaryleastsquaresOrdinaryLeastSquares:Assumptions&SolutionMethodserrortermhasameanofzeroandafinitevariancedependentvariableisrandomtheindependentvariablesareindeedindependentSpreadsheets-StatisticalcalculatorsMinitab,SAS,SPSSForeProfitExcel,Lotus,QuatroPro,JoeSpreadsheettools/dataanalysisinExcel/Data/RegressioninLotus ??1999South-WesternCollegePublishingDemandEstimationCase(p>.181)Riders=785-2>.14??Price+>.110??Pop+>.0015??Income+>.995??ParkingPredictorCoefSt>.devt-ratiopConstant784>.7396>.31>.98>.083Price-2>.14>.4890-4>.38>.002Pop>.1096>.2114>.520>.618Income>.0015>.03534>.040>.966Parking>.9947>.57151>.74>.120R-sq=90>.8%R-sq(adj)=86>.2%??1999South-WesternCollegePublishingCoefficientsofDetermination:R2R-square--%ofvariationindependentvariablethatisexplained^RatioofS[Qt-Qt]2toS[Qt-Qt]2Asmorevariablesareincluded,R-squarerisesAdjustedR-square,however,candecline??1999South-WesternCollegePublishing_PQ_Q QtT-testsDifferentsampleswouldyielddifferentcoefficientsTestthehypothesisthatcoefficientequalszeroHo:b=0Ha:b??0RULE:Ifabsolutevalueoftheestimatedt>Critical-t,thenREJECTHo>.It’ssignificant>.estimatedt=(b-0)/sbcriticaltLargeSamples,criticalt@2N>30SmallSamples,criticaltisonStudent’st-tableD>.F>.=#observations,minusnumberofindependentvariables,minusone>.N<30??1999South-WesternCollegePublishingDoubleLogorLogLinearWiththedoublelogform,thecoefficientsareelasticities!!!Q=A??Pb??Ic??PsdmultiplicativefctformSo:LnQ=a+b??LnP+c??LnI+d??LnPsTransformallvariablesintonaturallogs??1999South-WesternCollegePublishing EconometricProblemsSimultaneityProblem--IndentificationProblem:someindependentvariablesmaybeendogenousMulticollinearityindependentvariablesmaybehighlyrelatedSerialCorrelation--AutocorrelationerrortermsmayhaveapatternHeteroscedasticityerrortermsmayhavenon-constantvariance??1999South-WesternCollegePublishingIdentificationProblemProblem:CoefficientsarebiasedSymptom:IndependentvariablesareknowntobepartofasystemofequationsSolution:UseasmanyindependentvariablesaspossibleorUse2SLS??1999South-WesternCollegePublishingMulticollinearitySometimesindependentvariablesaren’tindependent>.EXAMPLE:Q=EggsQ=a+bPd+cPgwherePdisforadozen andPgisforagross>.CoefficientsareUNBIASED,butt-valuesaresmall>.SymptomsofMulticollinearity--highR-sqr,butlowt-values>.Q=22-7>.8Pd->.9Pg(1>.2)(1>.45)R-square=>.87t-valuesinparenthesesSolutions:Dropavariable>.Donothingifforecasting??1999South-WesternCollegePublishingPROBLEMSerialCorrelationProblem:Coefficientsareunbiasedbutt-valuesareunreliableSymptoms:lookatascatteroftheerrortermstoseeifthereisapattern,orseeifDurbinWatsonstatisticisfarfrom2>.Solution:FindmoredataTakefirstdifferencesofdata:DQ=a+b??DP??1999South-WesternCollegePublishing ScatterofErrorTermsSerialCorrelation??1999South-WesternCollegePublishingQPHeteroscedasticityProblem:Coefficientsareunbiasedt-valuesareunreliableSymptoms:differentvariancesfordifferentsub-samplesscatteroferrortermsshowsincreasingordecreasingdispersionSolution:Transformdata,e>.g>.,logsTakeaveragesofeachsubsample:weightedleastsquaresScatterofErrorTermsHeteroscedasticity??1999South-WesternCollegePublishingHeightAGE1258alternativelogHt=a+b??AGENonlinearFormsAppendix5A Semi-logarithmictransformations>.SometimestakingthelogarithmofthedependentvariableoranindependentvariableimprovestheR2>.Examplesare:logY=a+??·X>.Here,Ygrowsexponentiallyatrate??inX;thatis,??percentgrowthperperiod>.Y=a+??·logX>.Here,YdoubleseachtimeXincreasesbythesquareofX>.XYLnY=>.01+>.05XReciprocalTransformationsTherelationshipbetweenvariablesmaybeinverse>.Sometimestakingthereciprocalofavariableimprovesthefitoftheregressionasintheexample:Y=a+??·(1/X)shapescanbe:decliningslowlyifbetapositiverisingslowlyifbetanegativeXYE>.g>.,Y=500+2(1/X) PolynomialTransformationsQuadratic,cubic,andhigherdegreepolynomialrelationshipsarecommoninbusinessandeconomics>.Profitandrevenuearecubicfunctionsofoutput>.Averagecostisaquadraticfunction,asitisU-shapedTotalcostisacubicfunction,asitisS-shapedTC=a·Q+??·Q2+g·Q3isacubictotalcostfunction>.IfhigherorderpolynomialsimprovetheR-square,thentheaddedcomplexitymaybeworthit>.BusinessandEconomicForecastingChapter6??1999South-WesternCollegePublishingDemandForecasting:criticalmanagerialactivitywhichcomesintwoforms:QualitativeForecastingGivestheExpectedDirectionQuantitativeForecastingGivesthepreciseAmount2>.7654%WhyForecastDemand?Bothpublicandprivateenterprisesoperateunderconditionsofuncertainty>.Managementwishestolimitthisuncertaintybypredictingchangesincost,price,sales,andinterestrates>. Accurateforecastingcanhelpdevelopstrategiestopromoteprofitabletrendsandtoavoidunprofitableones>.Aforecastisapredictionconcerningthefuture>.Goodforecastingwillreduce,butnoteliminate,theuncertaintythatallmanagersfeel>.??1999South-WesternCollegePublishingHierarchyofForecastingTheselectionofforecastingtechniquesdependsinpartonthelevelofeconomicaggregationinvolved>.Thehierarchyofforecastingis:NationalEconomy(GDP,interestrates,inflation,etc>.)sectorsoftheeconomy(durablegoods)industryforecasts(automobilemanufacturers)firmforecasts(FordMotorCompany)ForecastingCriteriaThechoiceofaparticularforecastingmethoddependsonseveralcriteria:costsoftheforecastingmethodcomparedwithitsgainscomplexityoftherelationshipsamongvariablestimeperiodinvolvedaccuracyneededinforecastleadtimebetweenreceivinginformationandthedecisiontobemadeSignificanceofForecastingTheaccuracyofaforecastingmodelismeasuredbyhowclosetheactualvariable,Y,endsuptotheforecastingvariable,Y>.Forecasterroristhedifference>.(Y-Y)Modelsdifferinaccuracy,oftenbasedonthesquarerootofthe averagesquaredforecasterroroveraseriesofNforecastsandactualfiguresCalledarootmeansquareerror,RMSE>.RMSE=S(Y-Y)2/N??1999South-WesternCollegePublishing^^^??1999South-WesternCollegePublishingQualitativeForecastingFlexibility--easilyalteredaseconomychangesEarlySignals--cancatchchangesandanomaliesindataComplex--hardtokeeptrackofinteractionsintheprimaryvariablesLackofTestsforAccuracy--can’teasilytesttheaccuracyinpriorperiods>.??1999South-WesternCollegePublishingADVANTAGESLIMITATIONSQuantitativeForecastingandtheUseofModelsAdvantages OrganizerelationshipsBehavioralrelationshipsTestsofreliabilityLimitationsEconomychangesDataminingofsameinformationOnlyacrudeapproximation??1999South-WesternCollegePublishing“Economicforecastingisreallytheartofidentifyingtensionsorimbalancesintheeconomicprocessandunderstandinginwhatmannertheywillberesolved>.”??1999South-WesternCollegePublishingIseeTroubleahead>.AlanGreenspan--ChairmanoftheBoardofGovernorsoftheFederalReserveQualitativeForecasting1>.ComparativeStaticsShiftsinDemandShiftsinSupplyForecastChangesinPricesandQuantitiesSupposeIncomeShifts PriceRisesQuantityRisesquantityPsupply<#004699'>D1D2AB2>.ExpertOpinionTheaverageforecastfromseveralexpertsisaConsensusForecast>.MeanMedianModeTruncatedMeanProportionpositiveornegative??1999South-WesternCollegePublishingEXAMPLES:IBESandZacksInvestment--earningsforecastsofstockanalystsConferenceBoard--macroeconomicpredictionsLivingstonSurveys--macroeconomicforecastsof50-60 economistsDelphiTechnique--panelofdiverseexperts>.1>.Writeoutforecasts2>.Showthemtootherpanelists3>.meettoarriveatconsensusNote:problemsofexpenseandintransigenceChicagoDailyNewsSportswritersNFLpredictionsof16forecasters??1999South-WesternCollegePublishingTheconsensuspredictedbetterovertimethanany1writer>.Year1Year2Year33>.SurveysSamplebias--telephone,magazineBiasedquestions--advocacysurveysAmbiguousquestionsRespondentsmaylieonquestionnaires??1999South-WesternCollegePublishingNewProductshavenohistoricaldata--Surveyscanassessinterestinnewideas>.SurveyResearchCenter ofU>.ofMich>.doesrepeatsurveysofhouseholdsonBigTicketitems(Autos)CommonSurveyProblems4>.EconomicIndicators(BarometricForecasting)Directionofsalescanbeindicatedbyothervariables>.TIMEIndexofCapitalGoodspeakPEAKMotorControlSales4MonthsExample:IndexofCapitalGoodsisa“leadingindicator”TherearealsolaggingindicatorsandcoincidentindicatorsLEADINGINDICATORS*M2moneysupply(-10>.9)S&P500stockprices(-6>.9)Newhousingpermits(-10>.1)Initialunemploymentclaims(-7>.3)Ordersforplantandequipment(-3>.9)COINCIDENTINDICATORSNonagriculturalemployment(+>.9)Indexofindustrialproduction(->.6)Personalincomelesstransferpayment(->.6)LAGGINGINDICATORS Primerate(+12>.2)Durationofunemployment(+4>.4)*HandbookofCyclicalIndicators,1984TimegiveninmonthsfromchangeQuestionsWhyarecontractsandordersforplantandequipmentappropriateleadingindicators?Whyistheindexofindustrialproductionanappropriatecoincidentindicator?Whyistheprimerateanappropriatelaggingindicator?ExamplesofIndicatorsCompositeExample:Oneindicatorrises4%andanotherrises6%,thecompositeisa5%increase>.DiffusionExample:LouisRukeyser’sElevenElves,where4arenegativeaboutstocksand7arepositive:indexis7/11,or63>.3%InterpretingandUsingIndicescompositeindex-weightedaverageindexofindividualindicatorsindexinterpretedintermsof%changecompositeindexofleadingeconomicindicators:sustainedincreaseindicateseconomicgrowthdiffusionindex-measureoftheproportionofindividualtimeseries thatincreasefordiffusionindexofleadingeconomicindicators,ifindex>50%,improvedconditionsareexpected??1999South-WesternCollegePublishingQuantitativeForecastingTimeSeriesLooksForPatternsOrderedbyTimeNoUnderlyingStructureEconometricModelsExplainsrelationshipsSupply&DemandRegressionModels??1999South-WesternCollegePublishingLiketechnicalsecurityanalysisLikefundamentalsecurityanalysis??1999South-WesternCollegePublishingTimeSeriesExaminePatternsinthePastTIMEToX XXDependentVariableTimeSeriesisaquantitativeforecastingmethodUsespastdatatoprojectthefuturelooksforhighestACCURACYpossibleAccuracy(MSE&MAD)MeanSquaredError&MeanAbsoluteDeviationFt+1=f(At,At-1,At-2,>.>.>.)LetF=forecastandLetA=actualdataMSE=SNt=1[Ft-At]2/NTheLOWERtheMSEorMAD,thegreatertheaccuracyMAD=SNt=1|(Ft-At)|/N??1999South-WesternCollegePublishingMethodsofTimeSeriesAnalysisforEconomicForecasting1>.NaiveForecastFt+1=AtMethodbestwhenthereisnotrend,onlyrandomerrorGraphsofsalesovertimewithandwithouttrends??1999South-WesternCollegePublishing NOTrendTrendFFFFFssssss2>.MovingAverageAsmoothingforecastmethodfordatathatjumpsaroundBestwhenthereisnotrend3-PeriodMovingAv>.Ft+1=[At+At-1+At-2]/3??1999South-WesternCollegePublishing*****Forecast LineTIMEDependentVariable3>.ExponentialSmoothingAhybridoftheNaiveandMovingAveragemethodsFt+1=a>.??At+(1-a)FtAweightedaverageofpastactualandpastforecast>.EachforecastisafunctionofallpastobservationsCanshowthatforecastisbasedongeometricallydecliningweights>.Ft+1=a>.??At+(1-a)??a??At-1+(1-a)2??a??At-1+…FindlowestMSEtopickthebestalpha>.??1999South-WesternCollegePublishing4>.Linear&5>.Semi-logUsedwhentrendhasaconstantAMOUNTofchangeAt=a+b??T,whereAtaretheactualobservationsandTisanumericaltimevariableUsedwhentrendisaconstantPERCENTAGErateLogAt=a+b??T,wherebisthecontinuouslycompoundedgrowthrate??1999South-WesternCollegePublishingLinearTrendRegressionSemi-logRegressionMoreonSemi-logForm- AproofSuppose:Salest=Sales0(1+G)twhereGistheannualgrowthrateTakethenaturallogofbothsides:LnSt=LnS0+t??Ln(1+G)butLn(1+G)=g,theequivalentcontinuouslycompoundedgrowthrateSO:LnSt=LnS0+t??gLnSt=LnS0+g??t??1999South-WesternCollegePublishingNumericalExamples:6observationsMTB>Printc1-c3SalesTimeLn-sales100>.014>.60517109>.824>.69866121>.634>.80074133>.744>.89560146>.254>.98498164>.365>.10169??1999South-WesternCollegePublishingUsingthissalesdata,estimatesalesinperiod7usingalinearandasemi-log functionalform??1999South-WesternCollegePublishingTheregressionequationisSales=85>.0+12>.7TimePredictorCoefStdevt-ratiopConstant84>.9872>.41735>.160>.000Time12>.65140>.620720>.380>.000s=2>.596R-sq=99>.0%R-sq(adj)=98>.8%TheregressionequationisLn-sales=4>.50+0>.0982TimePredictorCoefSt>.devt-ratiopConstant4>.504160>.00642701>.350>.000Time0>.0981830>.00164959>.540>.000s=0>.006899R-sq=99>.9%R-sq(adj)=99>.9%ForecastedSales@Time=7LinearModelSales=85>.0+12>.7TimeSales=85>.0+12>.7(7)Sales=173>.9 Semi-LogModelLn-sales=4>.50+0>.0982TimeLn-sales=4>.50+0>.0982(7)Ln-sales=5>.1874Toanti-log:e5>.1874=179>.0??1999South-WesternCollegePublishing85linear7SalesTimeLn-sales100>.014>.60517109>.824>.69866121>.634>.80074133>.744>.89560146>.254>.98498164>.365>.10169179>.07semi-log173>.97linear??1999South-WesternCollegePublishingWhichpredictiondoyouprefer?Semi-logis exponential76>.ProceduresforSeasonalAdjustmentsTakeratiosofA/Fforpastyears>.Findtheaverageratio>.AdjustbythispercentageIfaverageratiois1>.02,adjustforecastupward2%UseDummyVariablesinaregression:D=1if4thquarter;0otherwise??1999South-WesternCollegePublishing12-quartersofdataIIIIIIIVIIIIIIIVIIIIIIIVttt§ttt§ttt§Quartersdesignatedwithromannumerals>.DummyVariablesforSeasonalAdjustmentsLetD=1,if4thquarterand0otherwise Runanewregression:At=a+b??T+c??Dthe“c”coefficientgivestheamountoftheadjustmentforthefourthquarter>.ItisanInterceptShifter>.EXAMPLE:Sales=300+10??T+18??D12Observations,93I-95IV,Forecast‘97Sales(97I)=<430;Sales(97II)=440;Sales(97III)=450;Sales(97IV)=478??1999South-WesternCollegePublishingDummyVariableInteractionsCanintroduceaslopeshifterby“interacting”twovariablesAt=a+b??T+c??D+d??D??TcistheinterceptshifterdistheslopeshifterE>.g>.,Sales=300+10??T+18??D-3??D??TimpliesthattheInterceptis318,whenD=1impliesthattheslopeis7,whenD=1??1999South-WesternCollegePublishingEconometricModelsSpecifythevariablesinthemodelEstimatetheparameterssingleequationorperhapsseveralstagemethodsQd=a+b??P+c??I+d??Ps+e??PcButforecastsrequireestimatesforfutureprices,futureincome, etc>.Oftencombineeconometricmodelswithtimeseriesestimatesoftheindependentvariable>.GarbageinGarbageout??1999South-WesternCollegePublishingexampleQd=400->.5??P+2??Y+>.2??PsanticipatepricingthegoodatP=$20Incomeisgrowingovertime,theestimateis:LnYt=2>.4+>.03??T,andnextperiodisT=17>.ThepricesofsubstitutesarelikelytobeP=$18>.FindQdY=e2>.910=18>.357HenceQd=<430>.31??1999South-WesternCollegePublishingAWARDforExcellenceinEconomicForecastingExchangeRatesandManagingExportsChapter7Import-ExportSales&ExchangeRatesMarketforUSDollarsRiskManagementPurchasingPowerParity ComparativeAdvantage&Trade??1999South-WesternCollegePublishingExchangeRatesandInternationalTradeOVERVIEW:Moreandmorefirmarebecomingmultinationalenterprises>.Exportingandimportingcanbeimpactedbychangesininternationalexchangerates>.Differencesinlongruninflationrates(accordingtothetheoryofpurchasingpowerparity)helpexplainlong-termexchangeratemovements>.WealsolookatregionaltradingblocsinEurope,NorthAmerican,andtheFarEast>.??1999South-WesternCollegePublishingImport&ExportSalesandExchangeRatesTheinternationalcompetitivenessofproductscanbeaffectedbyexchangerates>.IftheDM-priceofaBMWstaysthesameinGermany,theexportrevenueinreceivedbyBMWchangesasthe$/DMpricechanges>.Ifthepriceofthemarkfalls,BMWreceiveslessrevenuefromUSdealerships,whenthedollarpriceofcarsstaysthesame>.CumminsEngine,aUSexporter,facesaproblemwhenthedollarstrengthensinvalue>.Theirenginesbecomemoreexpensivetoforeignpurchasers,iftheykeepthedollarpriceofenginesconstant>.??1999South-WesternCollegePublishingLanguageusedtodiscussexchangeratechangesdependsonwhetherunderfloatingorfixedexchangerates AppreciatesorDepreciates--UnderFlexibleFXRateRegimesRevaluesorDevalues--UnderFixedFXRatesSpotPriceforFX--currentprice(2daydelivery)canappearindifferenttermsForwardFXPrice--priceofaforeigncurrencyfordeliveryatafuturedateagreedbycontracttoday??1999South-WesternCollegePublishingExchangeRates(1998)DMSpotandForwardRates??1999South-WesternCollegePublishingCountryUS$equivalentPerUS$Thurs>.Wed>.Thurs>.Wed>.Germany(DM)>.5562>.55761>.79811>.798530dayforward>.5571>.55851>.79511>.790590dayforward>.5589>.56041>.78921>.7845180dayforward>.5616>.56311>.78051>.7760Supply&DemandModelofExchangeRatesFXisusedfortradeandinvestment>.Useasupply&demandmodeltoexploreFXratesDemandforMarks:DemandisassociatedwithUSdemandforimportsfromGermanyandpurchaseofGermansecuritiesD$/DM DMDMWeexpectthatasthepriceofGermanproductstoU>.S>.customersgoesdown,therewillbegreaterdemandforDM>.AsthedollarhasmorepurchasingpowerinGermany(atpointB),AmericanswillwantmoreMarks>.DM$/DMABSupplyofDM&MarketClearinginFXSupplyofDM--SupplyisassociatedwithGermandemandforUSexportsandUSinvestments>.MarketClears--noexcessdemandorexcesssupplyofDMInFlexibleMarkets,buying&sellingthroughinternationalbanksD$/DMDMS1SUPPOSE:ThereisariseintheInflationRateintheUSBothSupply&DemandofDMShiftGermanproductsappearcheaperUSexportsappearmoreexpensiveTheMarkappreciates,andthedollardepreciates D$1/DMDMSD'S'$2/DM??1999South-WesternCollegePublishingExchangeRates:OneYearChangesin‘9752WkHigh52WKLowClose%Change52WksBritishPoundinUS$$1>.71$1>.50$1>.657+7>.96%CanadianDollarinUS$$0>.75$0>.71$0>.703-4>.5%SwissFrancPerUS$1>.491>.191>.44-15>.30%or$0>.67$0>.84$>.69(itwasat$>.81)JapaneseYenPerUS$131>.33104>.59130>.2-18>.09%or$>.0079$>.0096$>.0077(itwasat$>.0094)GermanMarkPerUS$1>.731>.471>.78-15>.15%or$0>.58$>.0>.68$0>.56(itwasat$0>.66)CrossRates:DowJonesTelerate Interbankfor$1millionormore(1998)USDollarPoundYenD-MarkCanada1>.<43622>.3913>.01103>.79873France6>.030010>.040>.046333>.3535Germany1>.79812>.9938>.01381---------Italy1777>.02958>.713>.652988>.27Japan130>.16216>.72---------72>.388Mexico8>.467014>.098>.065054>.7098Netherlands2>.02343>.3690>.015551>.1253Switzerland1>.48972>.4804>.01145>.82849U>.K>.>.60060--------->.00461>.33402U>.S>.---------1>.6650>.00768>.55614Uppertriangle(abovedashedlines)areinhomecountryasin130yenforadollar,??/$>.LowerBOLDtriangleareinforeigncurrencyasinlessthanapennyayen,$/??Bid-AskSpreadsMarketmakersearntheirprofitonthespread??1999South-WesternCollegePublishingASKpricepricewillingtosell Bidpricepricewillingtobuy>.66627>.66539KeyCurrencies&CrossRatesMarketsdevelopineachpairofcurrenciesIfthereareN=4countries,thereareasmanyasN??(N-1)/2=6differentpossibleFXratesWiththeUSasaKeycurrency,canreducethenumbertoonly3Forhundredsofcountries,chieforkeycurrenciesisnatural??1999South-WesternCollegePublishingBACDEconomicExposure(orRisk)involvestheimpactofexchangeratesonafirm’scashflowsEconomicdecisionsshouldincorporateexpectationsaboutfutureexchangerates>. Firmsmayselfinsurebyacceptingtheserisksortheymaybuyforeignexchangeinsuranceviaenteringintocontractssuchasforwardcontracts>.??1999South-WesternCollegePublishingExchangeRates,CashFlows,&RiskTypesofHedgesInternalhedges–multinationalfirmsbuyandsellwithinthefirminanycurrencythattheyselect>.Hedgesusingforwardcontracts–firmscanoffsetexposureinforeigncurrencybybuyingorsellingthatamountofcurrencyinaforwardcontract>.Hedgesusingfuturecontracts–firmmayoffsetriskwithafuturescontractinthatcurrency>.Hedgesusingcurrencyswaps–firmsmayagreetoexchange(swap)streamsofpaymentsindifferentcurrencies,withadjustmentsateachsettlementdate>.??1999South-WesternCollegePublishingAsset-LiabilityManagementforExchangeRiskOnesimpleapproachtoreduceexchangerateexposureistostructureparentandsubsidiariessuchthatexchangeratechangesaffectassetsandliabilitiesintandem>.Method:SupposethatapercentofthebusinessexportedtocountryX,thefirmcouldborrowtheapercentageinthecurrencyofcountryX>.Hence,financingisaconvenientwaytoarrangeformsofhedging “revenue”assets>.??1999South-WesternCollegePublishingExchangeRisk&StockholdersEliminatingallexchangeriskmaynotbeintheinterestofshareholders>.Ifshareholdersarewelldiversified,theymaynotbeparticularlysensitivetounsystematicvariationsduetochangesinexchangeratesand;exchangerisk;,especiallyifreducingthatrisksacrificesprofits>.??1999South-WesternCollegePublishingLong-RunExchangeRateDeterminants1>.Countriestendtohavedecliningvalueoftheircurrencywhentheyruntradedeficits,andtendtohaverisingcurrencyvaluesiftheyruntradesurpluses>.2>.Long-runtrendsinexchangeratesareaffectedbydifferencesininflation-adjustedinterestrates>.Highrelativeinterestratesattractinvestors,tendingtoraisethevalueofthecurrency>.3>.Countrieswithhighinflationtendtodepreciate;countrieswithlowrelativeinflationappreciate>.??1999South-WesternCollegePublishingPurchasingPowerParity(PPP)Purchasingpowerparitysaysthatthepriceoftradedgoodstendstobeequalaroundtheworld>.Thelawofoneprice>.ifexchangeratesareflexibleandtherearenosignificantcostsorbarrierstotrade>.S11+(ph) S0(1+pf)S1/S0showstheexpectedchangeinthedirectquoteofacurrency>.Therightsideoftheequationistheratioofhomeandforeigninflationrates>.Iftheforeigninflationrises(pf),thenthedomesticexpectedfuturespotratesS1declines>.??1999South-WesternCollegePublishing=Problems(orqualifications)withrelativePPP:PPPissensitivetothestartingpoint,S0>.ThebasetimeperiodmaynotinequilibriumDifferencesinthetradedgoods,orcross-culturaldifferences,maymakepreventthelawofonepricetoequilibratepricedifferences>.Theinflationratemayincludenon-tradedgoods>.PPPtendstoworkbetterinthelongrunthaninshortrunchangesininflationaryexpectations>.??1999South-WesternCollegePublishingInternationalTradeandTradingBlocsCountriesrestricttradethroughtariffs,quotas,andcurrencyrestrictions>.SeveralregionshavereducedtraderestrictionsMERCOSUR(inSouthAmerica)NAFTA(inNorthAmerica)EU(theEuropeanUnion,oroftentheEuropeanCommunity)looserarrangementsinSoutheastAsia(ASEAN)APECthroughoutthePacificareaincludingtheUS,Mexico,and Canada>.??1999South-WesternCollegePublishingComparativeAdvantageCountriesorfirmsshouldproducemoreofthosegoodsforwhichtheyhavelowerrelativecost>.??1999South-WesternCollegePublishingRelativeCostinUSRelativeCostinJapanAutomotivecarburetors>.4Chips1>.25ChipsComputerChips2>.5Carburetors>.8CarburetorsItcosts$120intheUStomakeacarburetorand$300tomakechips,the“cost”ofacarburetoristhe>.4chipsforegone(taketheratio$120/$300tofind>.4chips)>.TheUSrelativecostofcarburetorsismuchlowerthanthatoftheJapanese(1>.25Chips),whereastheJapaneserelativecostofchips(>.8Carburetors)ismuchlowerthanthatoftheUS>.JapanshouldmakechipsandUSshouldmakecarburetors>.TradeDeficitsandtheBalanceofPaymentsCurrentaccount=goodsandservicetradeflows,receiptsandpaymentsUSassetsabroadandforeignassetsintheUS,andunilateralgovernmentalandprivatetransfersCapitalaccount=capitalinflowsandoutflowsofforeignassets>.Thecurrentaccount(deficitorsurplus)comesfromacapitalaccount (surplusordeficit)tobalancepayments>.Thisistheideabehindtheaccountingidentityofthebalanceofpayments>.??1999South-WesternCollegePublishingExchangeRatesandInternationalTradeMarketforU>.S>.dollarsComparativeadvantageFreetradeU>.S>.balanceofpaymentsImport&ExportSalesandExchangeRatesTheinternationalcompetitivenessofproductscanbeaffectedbyexchangerates>.CumminsEngine,aUSexporter,facesaproblemwhenthedollarstrengthensinvalue>.Theirenginesbecomemoreexpensivetoforeignpurchasers,iftheykeepthedollarpriceofenginesconstant>.??1999South-WesternCollegePublishingForeignExchangeTerminologyLanguageuseddependsonexchangerateregime:floatingorfixedAppreciatesorDepreciates--UnderFlexibleFXRateRegimesRevaluesorDevalues--UnderFixedFXRatesSpotPriceforFX--currentprice(2daydelivery)ForwardFXPrice--currencypriceforfuturedelivery??1999South-WesternCollegePublishing ExchangeRates(1998)DMSpotandForwardRates??1999South-WesternCollegePublishingCountryUS$equivalentPerUS$Thurs>.Wed>.Thurs>.Wed>.Germany(DM)>.5562>.55761>.79811>.798530dayforward>.5571>.55851>.79511>.790590dayforward>.5589>.56041>.78921>.7845180dayforward>.5616>.56311>.78051>.7760Supply&DemandModelofExchangeRatesFXisusedfortradeandinvestment>.Useasupply&demandmodeltoexploreFXratesDemandforMarks:DemandisassociatedwithUSdemandforimportsfromGermanyandpurchaseofGermansecuritiesD$/DMDMDMWeexpectthatasthepriceofGermanproductstoU>.S>.customersgoesdown,therewillbegreaterdemandforDM>.AsthedollarhasmorepurchasingpowerinGermany(atpointB),AmericanswillwantmoreMarks>.DM $/DMABSupplyofDM&MarketClearinginFXSupplyofDM--SupplyisassociatedwithGermandemandforUSexportsandUSinvestments>.MarketClears--noexcessdemandorexcesssupplyofDMInFlexibleMarkets,buying&sellingthroughinternationalbanksD$/DMDMS1SUPPOSE:ThereisariseintheInflationRateintheUSBothSupply&DemandofDMShiftGermanproductsappearcheaperUSexportsappearmoreexpensiveTheMarkappreciates,andthedollardepreciatesD$1/DMDMSD'S'$2/DM ??1999South-WesternCollegePublishingExchangeRates:OneYearChangesin‘9752WkHigh52WKLowClose%Change52WksBritishPoundinUS$$1>.71$1>.50$1>.657+7>.96%CanadianDollarinUS$$0>.75$0>.71$0>.703-4>.5%SwissFrancPerUS$1>.491>.191>.44-15>.30%or$0>.67$0>.84$>.69(itwasat$>.81)JapaneseYenPerUS$131>.33104>.59130>.2-18>.09%or$>.0079$>.0096$>.0077(itwasat$>.0094)GermanMarkPerUS$1>.731>.471>.78-15>.15%or$0>.58$>.0>.68$0>.56(itwasat$0>.66)CrossRates:DowJonesTelerateInterbankfor$1millionormore(1998)USDollarPoundYenD-MarkCanada1>.<43622>.3913>.01103>.79873France6>.030010>.040>.046333>.3535Germany1>.79812>.9938>.01381---------Italy1777>.02958>.713>.652988>.27Japan130>.16216>.72---------72>.388 Mexico8>.467014>.098>.065054>.7098Netherlands2>.02343>.3690>.015551>.1253Switzerland1>.48972>.4804>.01145>.82849U>.K>.>.60060--------->.00461>.33402U>.S>.---------1>.6650>.00768>.55614Uppertriangle(abovedashedlines)areinhomecountryasin130yenforadollar,??/$>.LowerBOLDtriangleareinforeigncurrencyasinlessthanapennyayen,$/??Bid-AskSpreadsMarketmakersearntheirprofitonthespread??1999South-WesternCollegePublishingASKpricepricewillingtosellBidpricepricewillingtobuy>.66627>.66539KeyCurrencies&CrossRates MarketsdevelopineachpairofcurrenciesIfthereareN=4countries,thereareasmanyasN??(N-1)/2=6differentpossibleFXratesWiththeUSasaKeycurrency,canreducethenumbertoonly3Forhundredsofcountries,chieforkeycurrenciesisnatural??1999South-WesternCollegePublishingBACDEconomicExposure(orRisk)involvestheimpactofexchangeratesonafirm’scashflowsEconomicdecisionsshouldincorporateexpectationsaboutfutureexchangerates>.Firmsmayselfinsurebyacceptingtheserisksortheymaybuyforeignexchangeinsuranceviaenteringintocontractssuchasforwardcontracts>.??1999South-WesternCollegePublishingExchangeRates,CashFlows,&RiskTypesofHedgesInternalhedges–multinationalfirmsbuyandsellwithinthefirm inanycurrencythattheyselect>.Hedgesusingforwardcontracts–firmscanoffsetexposureinforeigncurrencybybuyingorsellingthatamountofcurrencyinaforwardcontract>.Hedgesusingfuturecontracts–firmmayoffsetriskwithafuturescontractinthatcurrency>.Hedgesusingcurrencyswaps–firmsmayagreetoexchange(swap)streamsofpaymentsindifferentcurrencies,withadjustmentsateachsettlementdate>.??1999South-WesternCollegePublishingAsset-LiabilityManagementforExchangeRiskOnesimpleapproachtoreduceexchangerateexposureistostructureparentandsubsidiariessuchthatexchangeratechangesaffectassetsandliabilitiesintandem>.Method:Supposethat????percentofthebusinessexportedtocountryX,thefirmcouldborrowthe??percentageinthecurrencyofcountryX>.Hence,financingisaconvenientwaytoarrangeformsofhedging“revenue”assets>.??1999South-WesternCollegePublishingExchangeRisk&StockholdersEliminatingallexchangeriskmaynotbeintheinterestofshareholders>.Ifshareholdersarewelldiversified,theymaynotbeparticularly sensitivetounsystematicvariationsduetochangesinexchangeratesand;exchangerisk;,especiallyifreducingthatrisksacrificesprofits>.??1999South-WesternCollegePublishingLong-RunExchangeRateDeterminants1>.Countriestendtohavedecliningvalueoftheircurrencywhentheyruntradedeficits,andtendtohaverisingcurrencyvaluesiftheyruntradesurpluses>.2>.Long-runtrendsinexchangeratesareaffectedbydifferencesininflation-adjustedinterestrates>.Highrelativeinterestratesattractinvestors,tendingtoraisethevalueofthecurrency>.3>.Countrieswithhighinflationtendtodepreciate;countrieswithlowrelativeinflationappreciate>.??1999South-WesternCollegePublishingPurchasingPowerParity(PPP)Purchasingpowerparitysaysthatthepriceoftradedgoodstendstobeequalaroundtheworld>.Thelawofoneprice>.ifexchangeratesareflexibleandtherearenosignificantcostsorbarrierstotrade>.S11+(??h)S0(1+??f)S1/S0showstheexpectedchangeinthedirectquoteofacurrency>.Therightsideoftheequationistheratioofhomeandforeigninflationrates>.Iftheforeigninflationrises(??f),thenthedomesticexpectedfuturespotratesS1declines>.??1999South-WesternCollegePublishing =Problems(orqualifications)withrelativePPP:PPPissensitivetothestartingpoint,S0>.ThebasetimeperiodmaynotinequilibriumDifferencesinthetradedgoods,orcross-culturaldifferences,maymakepreventthelawofonepricetoequilibratepricedifferences>.Theinflationratemayincludenon-tradedgoods>.PPPtendstoworkbetterinthelongrunthaninshortrunchangesininflationaryexpectations>.??1999South-WesternCollegePublishingInternationalTradeandTradingBlocsCountriesrestricttradethroughtariffs,quotas,andcurrencyrestrictions>.SeveralregionshavereducedtraderestrictionsMERCOSUR(inSouthAmerica)NAFTA(inNorthAmerica)EU(theEuropeanUnion,oroftentheEuropeanCommunity)looserarrangementsinSoutheastAsia(ASEAN)APECthroughoutthePacificareaincludingtheUS,Mexico,andCanada>.??1999South-WesternCollegePublishingComparativeAdvantageCountriesorfirmsshouldproducemoreofthosegoodsforwhichtheyhaveloweropportunitycost>.??1999South-WesternCollegePublishing RelativeCostinUSRelativeCostinJapanAutomotivecarburetors>.4Chips1>.25ChipsComputerChips2>.5Carburetors>.8CarburetorsItcosts$120intheUStomakeacarburetorand$300tomakechips,the“cost”ofacarburetoristhe>.4chipsforegone(taketheratio$120/$300tofind>.4chips)>.TheUSrelativecostofcarburetorsismuchlowerthanthatoftheJapanese(1>.25Chips),whereastheJapaneserelativecostofchips(>.8Carburetors)ismuchlowerthanthatoftheUS>.JapanshouldmakechipsandUSshouldmakecarburetors>.TradeDeficitsandtheBalanceofPaymentsCurrentaccount=goodsandservicetradeflows,receiptsandpaymentsUSassetsabroadandforeignassetsintheUS,andunilateralgovernmentalandprivatetransfersCapitalaccount=capitalinflowsandoutflowsofforeignassets>.Thecurrentaccount(deficitorsurplus)comesfromacapitalaccount(surplusordeficit)tobalancepayments>.Thisistheideabehindtheaccountingidentityofthebalanceofpayments>.??1999South-WesternCollegePublishingProductionEconomicsChapter8Managersmustdecidenotonlywhattoproduceforthemarket,butalso howtoproduceitinthemostefficientorleastcostmanner>.Wedevelopawidelyacceptedtoolforjudgingwhetherornotproductionchoicesareleastcost>.Aproductionfunctionrelatesthemostthatcanbeproducedfromagivensetofinputs>.Thisallowsthemanagertomeasurethemarginalproductofeachinput>.??1999South-WesternCollegePublishing1>.ProductionEconomics:IntheShortRunShortRunProductionFunctions:Maxoutput,fromanysetofinputsQ=f(X1,X2,X3,X4,>.>.>.)FIXEDINSRVARIABLEINSR_??1999South-WesternCollegePublishingQ=f(K,L)fortwoinputcase,whereKasFixedAverageProduct=Q/LoutputperlaborMarginalProduct=??Q/??L=dQ/dLoutputattributabletolastunitoflaborappliedSimilartoprofitfunctions,thePeakofMPoccursbeforethePeak ofaverageproductWhenMP=AP,we’reatthepeakoftheAPcurve??1999South-WesternCollegePublishingProductionElasticitiesTheproductionelasticityforanyinput,X,EX=MPX/APX=(??Q/??X)/(Q/X)=(??Q/??X)·(X/Q),whichisidenticalinformtootherelasticities>.WhenMPL>APL,thenthelaborelasticity,EL>1>.A1percentincreaseinlaborwillincreaseoutputbymorethan1percent>.WhenMPL<APL,thenthelaborelasticity,EL<1>.A1percentincreaseinlaborwillincreaseoutputbylessthan1percent>.??1999South-WesternCollegePublishingShortRunProductionFunctionNumericalExample??1999South-WesternCollegePublishingMarginalProductL12345AverageProductLaborElasticityisgreaterthenone,forlaboruseupthroughL=3unitsWhenMP>AP,thenAPisRISING IFYOURMARGINALGRADEINTHISCLASSISHIGHERTHANYOURAVERAGEGRADEPOINTAVERAGE,THENYOURG>.P>.A>.ISRISINGWhenMP<AP,thenAPisFALLINGIFTHEMARGINALWEIGHTADDEDTOATEAMISLESSTHANTHEAVERAGEWEIGHT,THENAVERAGETEAMWEIGHTDECLINESWhenMP=AP,thenAPisatitsMAXIFTHENEWHIREISJUSTASEFFICIENTASTHEAVERAGEEMPLOYEE,THENAVERAGEPRODUCTIVITYDOESN’TCHANGE??1999South-WesternCollegePublishingLawofDiminishingReturns??1999South-WesternCollegePublishingINCREASESINONEFACTOROFPRODUCTION,HOLDINGONEOROTHERFACTORSFIXED,AFTERSOMEPOINT,MARGINALPRODUCTDIMINISHES>.ASHORTRUNLAWpointofdiminishingreturnsMPThreestagesofproduction:Stage1:averageproductrising>.Stage2:averageproductdeclining(butmarginalproduct positive)>.Stage3:marginalproductisnegative,ortotalproductisdeclining>.??1999South-WesternCollegePublishingLTotalOutputStage1Stage2Stage3OptimalEmploymentofaFactorHIREIFGETMOREREVENUETHANCOSTHIREIFDTR/DL>DTC/DLHIREIFMRPL>MFCLATOPTIMUM,MRPL=WMRPL??MPL??PQ=W??1999South-WesternCollegePublishingoptimallaborMPLMRPLWWLwage ??MRPListheDemandforLaborIfLaborisMOREproductive,demandforlaborincreasesIfLaborisLESSproductive,demandforlabordecreasesSupposeanEARTHQUAKEdestroyscapital??MPLdeclineswithlesscapital,wagesandlaborareHURT??1999South-WesternCollegePublishingDLD'LSLW??L'L2>.LongRunProductionFunctionsAllinputsarevariablegreatestoutputfromanysetofinputsQ=f(K,L)istwoinputexampleMPofcapitalandMPoflaborarethederivativesoftheproductionfunctionMPL=??Q/??LMPoflabordeclinesasmorelaborisapplied>.AlsoMPofcapitaldeclinesasmorecapitalisapplied>.??1999South-WesternCollegePublishingHomogeneousFunctionsofDegreenAfunctionishomogeneousofdegree-nifmultiplyingallinputsbyl,increasesthedependentvariableby lnQ=f(K,L)So,f(lK,lL)=ln??QHomogenousofdegree1isCRS>.Cobb-DouglasProductionFunctionsarehomogeneousofdegreea+b??1999South-WesternCollegePublishingCobb-DouglasProductionFunctions:Q=A??Ka??LbisaCobb-DouglasProductionFunctionIMPLIES:CanbeIRS,DRSorCRS:ifa+b=1,thenCRSifa+b<1,thenDRSifa+b>1,thenIRSCoefficientsareelasticitiesaisthecapitalelasticityofoutputbisthelaborelasticityofoutput,whichareEKandEL??1999South-WesternCollegePublishingProblemSuppose:Q=1>.4L>.70K>.35Isthefunctionhomogeneous?Istheproductionfunctionconstantreturnstoscale?Whatisthelaborelasticityofoutput?Whatisthecapitalelasticityofoutput?WhathappenstoQ,ifLincreases3%andcapitaliscut10%? ??1999South-WesternCollegePublishingAnswersIncreasesinallinputsbyl,increaseoutputbyl1>.05IncreasingReturnstoScale>.70>.35%DQ=EQL??%DL+EQK??%DK=>.7(+3%)+>.35(-10%)=2>.1%-3>.5%=-1>.4%??1999South-WesternCollegePublishingIsoquants&LRProductionFunctionsIntheLONGRUN,ALLfactorsarevariableQ=f(K,L)ISOQUANTS--locusofinputcombinationswhichproducesthesameoutputSLOPEofISOQUANTisratioofMarginalProductsISOQUANTMAP??1999South-WesternCollegePublishingBACQ1Q2Q3KL OptimalInputCombinationsintheLongRunTheObjectiveistoMinimizeCostforagivenOutputISOCOSTlinesarethecombinationofinputsforagivencostC0=CX·X+CY·YY=C0/CY-(CX/CY)·XEquimarginalCriterionProducewhereMPX/CX=MPY/CYwheremarginalproductsperdollarareequal??1999South-WesternCollegePublishingQ1EXYatE,slopeofisocost=slopeofisoquantUseoftheEfficiencyCriterionIsthefollowingfirmEFFICIENT?Supposethat:MPL=30MPK=50W=10(costoflabor)R=25(costofcapital)Labor:30/10=3Capital:50/25=2 Adollarspentonlaborproduces3,andadollarspentoncapitalproduces2>.USERELATIVELYMORELABORIfspend$1lessincapital,outputfalls2units,butrises3unitswhenspentonlabor??1999South-WesternCollegePublishingEconomiesofScaleCONSTANTRETURNSTOSCALE(CRS)doublingofallinputsdoublesoutputINCREASINGRETURNSTOSCALE(IRS)doublingofallinputsMOREthandoublesoutputDECREASINGRETURNSTOSCALE(DRS)doublingofallinputsDOESN’TQUITEdoubleoutput??1999South-WesternCollegePublishingIncreasingReturnstoScaleSpecializationintheuseofcapitalandlabor>.Laborbecomesmoreskilledattasks,ortheequipmentismorespecialized,less;ajackofalltrades,;asscaleincreases>.Otheradvantagesinclude:avoidinherentlumpinessinthesizeofequipment,quantitydiscounts,technicalefficienciesinbuildinglargervolumeequipment>.??1999South-WesternCollegePublishingREASONSFORDECREASINGRETURNSTOSCALE Problemsofcoordinationandcontrolasitishardtosendandreceiveinformationasthescalerises>.Otherdisadvantagesoflargesize:slowdecisionladderinflexibilitycapacitylimitationsonentrepreneurialskills(therearediminishingreturnstotheC>.E>.O>.whichcannotbecompletelydelegated)>.??1999South-WesternCollegePublishingREASONSFOREconomiesofScopeFORMULTI-PRODUCTFIRMS,COMPLEMENTARYINPRODUCTIONMAYCREATESYNERGIESespeciallycommoninVerticalIntegrationoffirmsTC(Q1+Q2)<TC(Q1)+TC(Q2)??1999South-WesternCollegePublishing+=CostEfficienciesChemicalfirmPetroleumfirmStatisticalEstimationofLRProductionFunctionsChoiceofdatasets crosssectionoutputandinputmeasuresfromagroupoffirmsoutputandinputmeasuresfromagroupofplantstimeseriesoutputandinputdataforafirmovertime??1999South-WesternCollegePublishingEstimationComplexitiesIndustriesvary--hence,theappropriatevariablesforestimationareindustry-specificsingleproductfirmsvs>.multi-productfirmsmulti-plantfirmsservicesvs>.manufacturingmeasurableoutput(goods)vsunmeasurableoutput(customersatisfaction)??1999South-WesternCollegePublishingChoiceofFunctionalFormLinear?Q=a??K+b??LisCRSmarginalproductoflaborisconstant,MPL=bcanproducewithzerolabororzerocapitalisoquantsarestraightlines--perfectsubstitutesinproduction??1999South-WesternCollegePublishingK LQ3Q2Multiplicative--CobbDouglasProductionFunctionQ=A??Ka??LbIMPLIESCanbeCRS,IRS,orDRSMPL=b??Q/LMPK=a??Q/KCannotproducewithzeroLorzeroKLoglinear--doublelogLnQ=a+a??LnK+b??LnLcoefficientsareelasticities??1999South-WesternCollegePublishingDataon15plantsthatproducefertilizerwhatsortofdatasetisthis?whatfunctionalformshouldwetry?DetermineifIRS,DRS,orCRSTestifcoefficientsarestatisticallysignificantDeterminelaborandcapitalproductionelasticitiesandgiveaneconomicinterpretationofeachvalue??1999South-WesternCollegePublishingCASE:WilsonCompany??1999South-WesternCollegePublishingOutputCapitalLabor 1605>.318891700>.22566>.119201651>.83647>.120655822>.94523>.715082650>.35712>.320300859>.06487>.516079613>.07761>.624194851>.38442>.511504655>.49821>.125970900>.610397>.810127550>.411896>.725622842>.212359>.312477540>.513979>.124002949>.414331>.78042575>.7151064>.923972925>.8LnOutputLn-CapLn-labor6>.405729>.84646>.551376>.338779>.86276>.479746>.472509>.93576>.712836>.260929>.62136>.477<436>.568509>.91846>.755776>.189299>.68536>.418376>.6354210>.09396>.746766>.092449>.35056>.485256>.7106410>.16476>.80306 5>.985959>.22306>.310656>.7987210>.15126>.736025>.884169>.<43166>.292496>.8866310>.08596>.855835>.804238>.99246>.355596>.9706410>.08466>.83066DataSet:15plants??1999South-WesternCollegePublishingThelinearregressionequationisOutput=-351+0>.0127Capital+1>.02LaborPredictorCoefStdevt-ratiopConstant-350>.5123>.0-2>.850>.015Capital>.012725>.0076461>.660>.122Labor1>.02270>.31343>.260>.007s=73>.63R-sq=91>.1%R-sq(adj)=89>.6%??1999South-WesternCollegePublishingThelog-linearregressionequationisLnOutput=-4>.75+0>.415LnCapital+1>.08Ln-laborPredictorCoefStdevt-ratiopConstant-4>.75470>.8058-5>.900>.000LnCapital0>.41520>.13453>.090>.009Ln-labor1>.07800>.24934>.320>.001 s=0>.08966R-sq=94>.8%R-sq(adj)=94>.0%MoreProblems??1999South-WesternCollegePublishingSupposethefollowingproductionfunctionisestimatedtobe:lnQ=2>.33+>.19lnK+>.87lnLR2=>.97QUESTIONS:1>.IsthisCRS?2>.IfLincreasesby2%,whathappenstooutput?3>.What’stheMPLatL=50,K=100,&Q=741?Answers??1999South-WesternCollegePublishing1>.)Takethesumofthecoefficients>.19+>.87=1>.06,whichshowsthatthisproductionfunctionisIncreasingReturnstoScale2>.)UsetheLaborElasticityofOuptut>.%DQ=EL??%DL%DQ=(>.87)??(+2%)=+1>.74% 3)>.MPL=bQ/L=>.87??(741/50)=12>.893ElectricalGeneratingCapacityAcrosssectionof20electricalutilities(standarderrorsinparentheses):LnQ=-1>.54+>.53LnK+>.65LnL(>.65)(>.12)(>.14)R2=>.966Doesthisappeartobeconstantreturnstoscale?Ifincreaselabor10%,whathappenstoelectricaloutput???1999South-WesternCollegePublishingAnswersNo,constantreturnstoscale>.Ofcourse,itsincreasingreturnstoscaleassumofcoefficientsexceedsone>.>.53+>.65=1>.18If%DL=10%,then%DQ=EL??%DL=>.65(10%)=6>.5%??1999South-WesternCollegePublishingLagrangiansandOutputMaximization:Appendix8AMaxoutputtoacostobjective>.LetrbethecostofcapitalandwthecostoflaborMaxL=A??Ka??Lb-l{w??L+r??K-C}LK:a??A??Ka-1??Lb-r??l=0MPK=rLL:b??A??Ka??Lb-1-w??l=0MPL=wLl:C-w??L-r??K=0SolutionaQ/K/bQ/L=w/rorMPK/r=MPL/w??1999South-WesternCollegePublishing }ProductionandLinearProgramming:Appendix8BManufacturershavealternativeproductionprocesses,someinvolvingmostlylabor,othersusingmachinerymoreintensively>.Theobjectiveistomaximizeoutputfromtheseproductionprocesses,givenconstraintsontheinputsavailable,suchasplantcapacityorunionlaborcontractconstraints>.ThelinearprogrammingtechniquesarediscussedinChapter11>.CostAnalysisChapter9ThemeaningandmeasurementofcostShort-runCostFunctionsLong-runCostFunctionsScaleEconomiesandCostAppendix9A:Cobb-Douglas&LRCOST??1999South-WesternCollegePublishingTheObjectofCostAnalysisManagersseektoproducethehighestqualityproductsatthelowestpossiblecost>.Firmsthataresatisfiedwiththestatusquofindthatcompetitorsarisethatcanproduceatlowercosts>.Theadvantagesonceassignedtobeinglargefirms(economiesofscaleandscope)havenotprovidedtheadvantagesofflexibilityandagilityfoundinsomesmallercompanies>.Costanalysisishelpfulinthetaskoffindinglowercostmethods toproducegoodsandservices>.??1999South-WesternCollegePublishingMeaningofCostThereareManyEconomicCostConceptsOpportunityCost--valueofnextbestalternativeuse>.Explicitvs>.ImplicitCost--actualpricespaidvs>.opportunitycostofownersuppliedresources>.??1999South-WesternCollegePublishingExamplesofRelevantCostConceptsDepreciationCostMeasurement>.Accountingdepreciation(e>.g>.,straight-linedepreciation)tendstohavelittlerelationshiptotheactuallossofvalueToaneconomist,theactuallossofvalueisthetruecostofusingmachinery>.InventoryValuation>.AccountingvaluationdependsonitsacquisitioncostEconomists6><#00aa00'>viewthecostofinventoryasthecostofreplacement>.??1999South-WesternCollegePublishingUnutilizedFacilities>.Emptyspacemayappeartohave;nocost”Economists<#00aa00'>viewitsalternativeuse(e>.g>.,rentalvalue)asitsopportunitycost>.MeasuresofProfitability>.Accountantsandeconomists<#00aa00'>viewprofitdifferently>. Accountingprofit,atitssimplest,isrevenuesminusexplicitcosts>.Economistsincludeotherimplicitcosts(suchasanormalprofitoninvestedcapital)>.EconomicProfit=TotalRevenues-ExplicitCosts-ImplicitCosts??1999South-WesternCollegePublishing??1999South-WesternCollegePublishingSunkCosts--alreadypaidfor,orthereisalreadyacontractualobligationtopayIncrementalCost--extracostofimplementingadecision=DTCofadecisionMarginalCost--costoflastunitproduced=??TC/??QSHORTRUNCOSTFUNCTIONS1>.TC=FC+VCfixed&variablecosts2>.ATC=AFC+AVC=FC/Q+VC/QShortRunCostGraphs??1999South-WesternCollegePublishingAFCQQ1>.2>. AVC3>.QAFCAVCATCMCMCintersectslowestpointofAVCandlowestpointofATC>.WhenMC<AVC,AVCdeclinesWhenMC>AVC,AVCrisesRelationofCost&ProductionFunctionsinSRAP&AVCareinverselyrelated>.(ex:oneinput)AVC=WL/Q=W/(Q/L)=W/APLAsAPLrises,AVCfallsMPandMCareinverselyrelatedMC=dTC/dQ=WdL/dQ=W/(dQ/dL)=W/MPLAsMPLdeclines,MCrisesprod>.fcts>.costfcts>.MPLMCAP AVCProblemLettherebeacubicVCfunction:VC=>.5Q3-10Q2+150QfindAVCfromVCfunctionfindminimumvariablecostoutputandfindMCfromVCfunctionMinimumAVC,wheredAVC/dQ=0AVC=>.5Q2-10Q+150dAVC/dQ=Q-10=0Q=10,soAVC=100@Q=10MC=dVC/dQ=1>.5Q2-20Q+150??1999South-WesternCollegePublishingLongRunCostsInlongrun,ALLinputsarevariableLRAClongrunaveragecostENVELOPEofSRACcurvesLRMCisFLATTERthanSRMCcurves??1999South-WesternCollegePublishingQLRACLRMCSRAC1SRMC1 LongRunCostFunctions:EnvelopeofSRACcurves??1999South-WesternCollegePublishingQSRAC-smallcapitalSRAC-med>.capitalSRAC-bigcapitalLRAC--EnvelopeofSRACcurvesAveCostEconomiststhinkthattheLRACisU-shapedDownwardsectiondueto:Product-specificeconomieswhichincludespecializationandlearningcurveeffects>.Plant-specificeconomies,suchaseconomiesinoverhead,requiredreserves,investment,orinteractionsamongproducts(economiesofscope)>.Firm-specificeconomieswhichareeconomiesindistributionandtransportationofageographicallydispersedfirm,oreconomiesinmarketing,salespromotion,orR&Dofmulti-productfirms>.??1999South-WesternCollegePublishingFlatsectionConstantreturnstoscaleUpwardrisingsectionofLRACisdueto:diseconomiesofscale>.Theseincludetransportationcosts, imperfectionsinthelabormarket,andproblemsofcoordinationandcontrolbymanagement>.Theminimumefficientscale(MES)isthesmallestscaleatwhichminimumperunitcostsareattained>.Modernbusinessmanagementofferstechniquestoavoiddiseconomiesofscalethroughprofitcenters,transferpricing,andtyingincentivestoperformance>.??1999South-WesternCollegePublishingEqui-marginalPrincipleinLRSinceLRcostsareleastcost,theymustbeefficient;theymustobeytheequi-marginalprinciple:MPX/CX=MPY/CYThatis,themarginalproductperdollarineachuseisequal>.??1999South-WesternCollegePublishingCostFunctionsandProductionFunctions:LRRelationshipsandtheImportanceofFactorCostsA>.CRS&ConstantFactorPricesTCACQ2QB>.IRS&ConstantFactorPricesQ2QTCACC>.DRS&ConstantFactorPrices Q2QACD>.CRS&RisingFactorPrices--lookslike“C”Problem:LetTC&MCbe:TC=200+5Q->.4Q2+>.001Q3MC=5->.8Q+>.003Q2a>.FINDfixedcostFINDAVCfunctionb>.FINDminimumaveragevariablecostpointc>.IfFCrises$500,whathappenstominimumaveragevariablecost?TC=200+5Q->.4Q2+>.001Q3MC=5->.8Q+>.003Q2a>.FINDfixedcostFINDAVCfunctionAnswer:FC=200andAVC=5->.4Q+>.001Q2>.b>.FINDminimumaveragevariablecostpointAnswer:FirstfinddAC/dQ=0:From(a)thatis:->.4+>.002Q=0,soQ=2,000c>.IfFCrises$500,whathappenstominimumaveragevariablecost?Answer:Nochange,sinceAVCdoesn’tchange>. Cobb-DouglasProductionFunctionandtheLong-RunCostFunction:Appendix9ALongRunCosts&ProductionFunctions:1InputInthelongrun,totalcostis:TC=w·L,wherewisthewagerate>.productionfunctionisCobb-Douglas:Q=L??>.SolvingforLintheCobb-Douglasproductionfunction,wefind:L=Q1/??>.Substitutingthisintothetotalcostfunction,weget:??1999South-WesternCollegePublishingOneInputCaseTC=w·Q1/??>.Thisalsodemonstratesthatiftheproductionfunctionwereconstantreturnstoscale(??=1),thenTCriseslinearlywithoutputandaveragecostisconstant>.Iftheproductionfunctionisincreasingreturnstoscale(??>1),thenTCrisesatadecreasingrateinoutputandaveragecostisdeclining>.Iftheproductionfunctionisdecreasingreturnstoscale(??<1),thenTCrisesatanincreasingrateinoutputandaveragecostrises>.??1999South-WesternCollegePublishingTWOInputCaseWithtwoinputs,longruncostis:TC=w·L+r·K,wherewisthewagerateandristhecostofcapital,K>. Cobb-Douglas:Q=Ka·L??>.Themanagerattemptstominimizecost,subjecttoanoutputconstraint>.ThisisaLagrangianMultiplierproblem>.MinL=w·L+r·K+l·[Ka·L??-Q]Takingderivativesandsolvingyieldsatotalcost:TC=w·L*+r·K*=C=w·Q(1/(a+??))·(a·w/??·r)(??/(a+??))+r·Q(1/(a+??))·(a·w/??·r)(a/(a+??))If(a+??>1),then1/(a+??)lessthan1,andtotalcostrisesatadecreasingrateinoutput>.Thatmeansthataveragecostdeclines>.??1999South-WesternCollegePublishingApplicationsofCostTheoryChapter10Industriesvary--hence,theappropriatevariablesforestimationareindustry-specificsingleproductfirmsvs>.multi-productfirmsmulti-plantfirmsservicesvs>.manufacturingmeasurableoutput(goods)vsunmeasurableoutput(customersatisfaction)??1999South-WesternCollegePublishingEstimatingCostsintheSRTypicallyuseTIMESERIESdataforaplantorfirm>.Typicallyuseafunctionalformthat“fits”thepresumedshape>.ForTC,oftenCUBIC ForAC,oftenQUADRATIC??1999South-WesternCollegePublishingquadraticisU-shapedorarchshapedcubicisS-shapedorbackwardS-shapedEstimatingShortRunCostFunctionsExample:TIMESERIESdataoftotalcostQuadraticTotalCost(tothepoweroftwo)TC=C0+C1Q+C2Q2TCQQ2900204008001522583419361??????REGRc11c2c3TimeSeriesDataPredictorCoeffStdErrT-valueConstant10003003>.3Q-5020-2>.5Q-squared102>.54>.0R-square=>.91 AdjR-square=>.90N=35RegressionOutput:????1999South-WesternCollegePublishingPROBLEMS:1>.Writethecostregressionasanequation>.2>.FindtheACandMCfunctions>.1>.TC=1000-50Q+10Q2(3>.3)(-2>.5)(4)2>.AC=1000/Q-50+10QMC=-50+20Qt-valuesintheparenthesesNOTE:WecanestimateTCeitherasquadraticorasCUBIC:TC=C1Q+C2Q2+C3Q3IfTCisCUBIC,thenACwillbequadratic:AC=C1+C2Q+C3Q2EstimatingLRCostRelationshipsUseaCROSSSECTIONoffirmsSRcostsusuallyusesatimeseriesAssumethatfirmsareneartheirlowestaveragecostforeachoutput??1999South-WesternCollegePublishingQ ACLRACLogLinearLRCostCurvesOnefunctionalformisLogLinearLogTC=a+b??LogQ+c??LogW+d??LogRCoefficientsareelasticities>.“b”istheoutputelasticityofTCIFb=1,thenCRSlongruncostfunctionIFb<1,thenIRSlongruncostfunctionIFb>1,thenDRSlongruncostfunction??1999South-WesternCollegePublishingExample:ElectricalUtilitiesSampleof20UtilitiesQ=megawatthoursR=costofcapitalonratebase,W=wagerateElectricalUtilityExampleRegressionResults:LogTC=->.4+>.83LogQ+1>.05Log(W/R)(1>.04)(>.03)(>.21)R-sqr=>.9745??1999South-WesternCollegePublishingStd-errorsareintheparentheses ??1999South-WesternCollegePublishingQUESTIONS:1>.AreutilitiesCRS,IRS,orDRS?2>.Arecoefficientsstatisticallysignificant?3>.Testthehypothesis:Ho:b=1Answers1>.ThecoefficientonLogQislessthanone>.A1%increaseinoutputleadonlytoa>.83%increaseinTC--It’sIRS!2>.Thet-valuesarecoeff/std-errors:t=>.83/>.03=27>.7isSignificantandt=1>.05/>.21=5>.0whichisSignificant>.3>.Thet-valueis(>.83-1)/>.03=-0>.17/>.03=-5>.6whichisSignificantlydifferentthanCRS>.??1999South-WesternCollegePublishingCementMixProcessingPlants13cementmixprocessingplantsprovideddataforthefollowingcostfunction>.Testthehypothesisthatcementmixingplantshaveconstantreturnstoscale?LnTC=>.03+>.35LnW+>.65LnR+1>.21LnQ(>.01)(>.24)(>.33)(>.08)R2=>.563parenthesescontainstandarderrors??1999South-WesternCollegePublishing DiscussionCementplantsareCRSifthecoefficientonLnQwere11>.21ismorethan1,whichappearstobeDRSTEST:t=(1>.21-1)/>.08=2>.65SmallSample,d>.f>.=13-3-1=9criticalt=2>.262Werejectconstantreturnstoscale>.??1999South-WesternCollegePublishingEngineeringCostApproachEngineeringCostTechniquesofferanalternativetofittinglinesthroughhistoricaldatapointsusingregressionanalysis>.Itusesknowledgeabouttheefficiencyofmachinery>.Someprocesseshavepronouncedeconomiesofscale,whereasotherprocesses(includingthecostsofrawmaterials)donothaveeconomiesofscale>.Sizeandvolumearemathematicallyrelated,leadingtoengineeringrelationships>.Largewarehousestendtobecheaperthansmallonespercubicfootofspace>.??1999South-WesternCollegePublishingSurvivorTechniqueTheSurvivorTechniqueexamineswhatsizeoffirmsaretendingtosucceedovertime,andwhatsizesaredeclining>.ThisisasortofDarwiniansurvivaltestforfirmsize>.Presentlymanybanksaremerging,leadingonetoconcludethatsmallsizeoffersdisadvantagesatthistime>. Drycleanersarenotparticularlygrowinginaveragesize,however>.??1999South-WesternCollegePublishingBreak-evenAnalysis&D>.O>.LCanhavemultipleB/EpointsIflineartotalcostandtotalrevenue:TR=P??QTC=F+v??QwherevisAverageVariableCostFisFixedCostQisOutputcost-volume-profitanalysis??1999South-WesternCollegePublishingTotalCostTotalRevenueB/EB/EQTheBreak-evenQuantity:QB/EAtbreak-even:TR=TCSo,P??Q=F+v??QQB/E=F/(P-v)=F/CMwherecontributionmarginis:CM=(P-v)??1999South-WesternCollegePublishing TRTCB/EQPROBLEM:Asagaragecontractor,findQB/Eif:P=$9,000pergaragev=$7,000pergarage&F=$40,000peryearAmountofsalesrevenuesthatbreaksevenP??QB/E=P??[F/(P-v)]=F/[1-v/P]??1999South-WesternCollegePublishingBreak-evenSalesVolumeVariableCostRatioEx:AtQ=20,B/ESalesVolumeis$9,000??20=$180,000SalesVolumeAnswer:Q=40,000/(2,000)=40/2=20garagesatthebreak-evenpoint>.TargetProfitOutput??1999South-WesternCollegePublishingQuantityneededtoattainatargetprofitIfpisthetargetprofit, Qtargetp=[F+p]/(P-v)Supposewanttoattain$50,000profit,then,Qtargetp=($40,000+$50,000)/$2,000=$90,000/$2,000=45garagesDegreeofOperatingLeverageorOperatingProfitElasticityDOL=Epsensitivityofoperatingprofit(EBIT)tochangesinoutputOperatingp=TR-TC=(P-v)??Q-FHence,DOL=??p/??Q??(Q/p)=(P-v)??(Q/p)=(P-v)??Q/[(P-v)??Q-F]??1999South-WesternCollegePublishingAmeasureoftheimportanceofFixedCostorBusinessRisktofluctuationsinoutputSupposeContractorBuilds45Garages,WhatistheD>.O>.L?DOL=(9000-7000)??45{(9000-7000)??45-40000}=90,000/50,000=1>.8A1%INCREASEinQ??1>.8%INCREASEinoperatingprofit>.Atthebreak-evenpoint,DOLisINFINITE>.AsmallchangeinQincreaseEBITbyastronomicallylargepercentage rates??1999South-WesternCollegePublishingDOLasOperatingProfitElasticityDOL=[(P-v)Q]/{[(P-v)Q]-F}WecanuseempiricalestimationmethodstofindoperatingleverageElastiticitiescanbeestimatedwithdoublelogfunctionalformsUseatimeseriesofdataonoperatingprofitandoutputLnEBIT=a+b??LnQ,wherebistheDOLthena1%increaseinoutputincreasesEBITbyb%btendstobegreaterthanorequalto1??1999South-WesternCollegePublishingRegressionOutputDependentVariable:LnEBITuses20quarterlyobservationsN=20??1999South-WesternCollegePublishingThelog-linearregressionequationisLnEBIT=->.75+1>.23LnQPredictorCoefStdevt-ratiopConstant->.75210>.04805-15>.6500>.001LnQ1>.23410>.13459>.1750>.001s=0>.0876R-sq=98>.2%R-sq(adj)=98>.0%TheDOLforthisfirm,1>.23>.So,a1%increaseinoutputleadstoa1>.23%increaseinoperatingprofit OperatingProfitandtheBusinessCycle??1999South-WesternCollegePublishingOutputrecessionTIMEEBIT=operatingprofitTroughpeak1>.EBITismorevolatilethatoutputovercycle2>.EBITtendstocollapselateinrecessionsAppendix10A:LearningCurve”Learningbydoing;haswideapplicationinproductionprocesses>.Workersandmanagementbecomemoreefficientwithexperience>.thecostofproductiondeclinesastheaccumulatedpastproduction,Q=Sqt,increases,whereqtistheamountproducedinthetthperiod>.Airlinemanufacturing,shipbuilding,andappliancemanufacturinghavedemonstratedthelearningcurveeffect>.??1999South-WesternCollegePublishingFunctionally,thelearningcurverelationshipcanbewrittenC=a·Qb, whereCistheinputcostoftheQthunit:Takingthe(natural)logarithmofbothsides,weget:logC=loga+b·logQThecoefficientbtellsustheextentofthelearningcurveeffect>.Iftheb=0,thencostsareataconstantlevel>.Ifb>0,thencostsriseinoutput,whichisexactlyoppositeofthelearningcurveeffect>.Ifb<0,thencostsdeclineinoutput,aspredictedbythelearningcurveeffect>.??1999South-WesternCollegePublishingLinearProgrammingApplicationsChapter11ConstrainedOptimizationproblemsoccurfrequentlyineconomics:maximizingoutputfromagivenbudget;orminimizingcostofasetofrequiredoutputs>.Lagrangianmultiplierproblemsrequiredbindingconstraints>.Anumberofbusinessproblemshaveinequalityconstraints>.??1999South-WesternCollegePublishingProfitMaximizationProblemUsingLinearProgrammingConstraintsofproductioncapacity,time,money,rawmaterials,budget,space,andotherrestrictionsonchoices>.TheseconstraintscanbeviewedasinequalityconstraintsA;linear;programmingproblemassumesalinearobjectivefunction,andaseriesoflinearinequalityconstraints??1999South-WesternCollegePublishing Linearityimplies:1>.constantpricesforoutputs(asinaperfectlycompetitivemarket)>.2>.constantreturnstoscaleforproductionprocesses>.3>.typically,eachdecisionvariablealsohasanon-negativityconstraint>.Forexample,thetimespentusingamachinecannotbenegative>.??1999South-WesternCollegePublishingSolutionMethodsLinearprogrammingproblemscanbesolvedusinggraphicaltechniques,SIMPLEXalgorithmsusingmatrices,orusingsoftware,suchasForeProfitsoftware>.Inthegraphicaltechnique,eachinequalityconstraintisgraphedasanequalityconstraint>.TheFeasibleSolutionSpaceistheareawhichsatisfiesalloftheinequalityconstraints>.TheOptimalFeasibleSolutionoccursalongtheboundaryoftheFeasibleSolutionSpace,attheextremepointsorcornerpoints>.??1999South-WesternCollegePublishingThecornerpointthatmaximizetheobjectivefunctionistheOptimalFeasibleSolution>.Theremaybeseveraloptimalsolutions>.Examinationoftheslopeoftheobjectivefunctionandtheslopesoftheconstraintsisusefulin determiningwhichistheoptimalcornerpoint>.Oneormoreoftheconstraintsmaybeslack,whichmeansitisnotbinding>.Eachconstrainthasanimplicitprice,theshadowpriceoftheconstraint>.Ifaconstraintisslack,itsshadowpriceiszero>.EachshadowpricehasmuchthesamemeaningasaLagrangianmultiplier>.??1999South-WesternCollegePublishingGRAPHICALX1X2ABCCONSTRAINT#1CONSTRAINT#2CornerPointsA,B,andCFeasibleRegionOABCO??1999South-WesternCollegePublishingGRAPHICALX1 X2ABCCONSTRAINT#1CONSTRAINT#2OptimalFeasibleSolutionatPointBHighestProfitLineOTheDualProblemEachlinearprogrammingproblem(theprimalproblem)hasanassociateddualproblem>.EXAMPLE:Amaximizationofprofitobjectivefunction,subjecttoresourceconstraintshasanassociateddualproblemThedualisaminimizationofthetotalcostsoftheresourcessubjecttoconstraintsthatthevalueoftheresourcesusedinproducingoneunitofeachoutputbeatleastasgreatastheprofitreceivedfromthesaleofthatoutput>.??1999South-WesternCollegePublishingDualityTheorem THEOREM:themaximumvalueoftheprimal(profitmaxproblem)equalstheminimumvalueofthedual(costminimization)problem>.Theresourceconstraintsoftheprimalproblemappearintheobjectivefunctionofthedualproblem??1999South-WesternCollegePublishingPrimal:Maximizep=P1·Q1+P2·Q2subjectto:c·Q1+d·Q2<R1Thebudgetconstraint,forexample>.e·Q1+f·Q2<R2Themachineschedulingtimeconstraint>.whereQ1andQ2>0Non-negativityconstraint>.??1999South-WesternCollegePublishingDual:MinimizeC=R1·w1+R2·w2subjectto:c·W1+e·W2>P1ProfitContributionofProduct1d·W1+f·W2>P2ProfitContributionofProduct2 whereW1andW2>0Non-negativityconstraint>.??1999South-WesternCollegePublishingComplexityandtheMethodofSolutionThesolutionstoprimalanddualproblemsmaybesolvedgraphically,solongasthisinvolvestwodimensions>.Withmanyproducts,thesolutioninvolvestheSIMPLEXalgorithm,orsoftwareavailableinForeProfit??1999South-WesternCollegePublishingCostMinimizationProblemUsingLinearProgrammingMulti-plantfirmswanttoproducewiththelowestcostacrosstheirdisparatefacilities>.Sometimes,therelativeefficienciesofthedifferentplantscanbeexploitedtoreducecosts>.Afirmmayhavetwominesthatproducesdifferentqualitiesofore>.Thefirmhasoutputrequirementsineachorequality>.Schedulingofhoursperweekineachminehastheobjectiveofminimizingcost,butachievingtherequiredoutputs>.??1999South-WesternCollegePublishingIfonemineismoreefficientinallcategoriesofore,andislesscostlytooperate,theoptimalsolutionmayinvolveshuttingoneminedown>.Thedualofthisprobleminvolvestheshadowpricesoftheoreconstraints>.Ittellstheimplicitvalueofeachqualityof ore>.??1999South-WesternCollegePublishingCapitalRationingProblemFinancialdecisionssometimesmaybeviewedasalinearprogrammingproblem>.EXAMPLE:Afinancialofficermaywanttomaximizethereturnoninvestmentsavailable,givenalimitedamountofmoneytoinvest>.Theusualprobleminfinanceistoacceptallprojectswithpositivenetpresentvalues,butsometimesthecapitalbudgetsarefixedorlimitedtocreate;capitalrationing;amongprojects>.??1999South-WesternCollegePublishingThesolutioninvolvesdeterminingwhatfractionofmoneyallottedshouldbeinvestedineachofthepossibleprojectsorinvestments>.Insomeproblems,projectscannotbebrokenintosmallparts>.Whenthisisthecase,integerprogrammingcanbeaddedtotheproblem>.??1999South-WesternCollegePublishingPrice,Output,andStrategy:PureandMonopolisticCompetitionChapter12Purecompetitionisastandardagainstwhichothermarketstructuresarecompared>.Theproductisperfectlyundifferentiated>.Whentherearemanyfirms,buttheproductisdifferentiated,themarketismonopolisticallycompetitive>.Thisbrandcompetitionofteninvolvesadvertisingcampaignsandpromotionalexpenditurestostresssometimesminordistinctionsamong products??1999South-WesternCollegePublishingTheMarketConceptAmarketisagroupofeconomicagentsthatinteractinabuyer-sellerrelationship>.Thenatureofthatrelationshipisaffectedbythenumberandsizeofthebuyersandsellers>.Apopularmeasureofsellerconcentrationisthepercentageofanindustrycomprisedofthetop4firms>.Similarly,thetop4buyersisapopularmeasureofbuyerconcentration>.??1999South-WesternCollegePublishingIndividualFirmDemandConditions&theMarketa>.thenumberoffirmsandtheirrelativesizes>.b>.whethertheproductisdifferentiatedorstandardized>.c>.whetherdecisionsbyfirmsareindependentorcoordinated(collusion)>.??1999South-WesternCollegePublishing4MarketStructuresa>.purecompetitionb>.monopolisticcompetitionc>.oligopolyd>.monopoly??1999South-WesternCollegePublishingABriefOverviewoftheFourMarketStructures PureCompetition1>.averylargenumberofbuyersandsellers2>.homogeneousproduct(standardized)3>.freeentryandexit(nobarriers)4>.nocollusionamongthefirms5>.completeknowledgeofallmarketinformationEachfirmviewsitsdemandcurveasperfectlyelastic>.Wesaythatpurecompetitionmakesfirmspricetakers>.??1999South-WesternCollegePublishingMonopolisticCompetition1>.manybuyersandsellers2>.differentiatedproduct3>.freeentryandexit4>.nocollusionamongthefirmsEachfirmwill<#00aa00'>viewitsdemandcurveasdeclininginitsownprice>.Amonopolisticallycompetitivefirmwillhavetohaveapricingstrategy,unlikeapurelycompetitivefirm>.??1999South-WesternCollegePublishingOligopoly1>.fewfirms2>.theproductsmaybedifferentiatedorstandardized3>.thereisanoticeabledegreeofinterdependenceamongthefirms Manyoutcomesarepossibleinoligopolies,rangingfromactingnearlycompetitivelytoactinglikeamonopoly>.??1999South-WesternCollegePublishingMonopoly1>.onefirm2>.aperfectlydifferentiatedproduct(lowcrosspriceelasticitieswithotherproducts>.3>.substantialbarrierstoentry,suchasabsolutecostadvantages,consumerloyalty,scaleeconomies,largecapitalrequirements,orlegalbarrierstoentry>.??1999South-WesternCollegePublishingForcesofCompetitionMichaelPorter,inhisCompetitiveAdvantage,lists5forcesthatdeterminecompetitiveadvantage:Substitutes(threatofsubstitutescanbeoffsetbybrandsandspecialfunctionsservedbytheproduct)>.PotentialEntrants(threatofentrantscanbereducedbyhighfixedcosts,scaleeconomies,restrictionofaccesstodistributionchannels,orproductdifferentiation)>.BuyerPower(threatofconcentrationofbuyers)>.SupplierPower(threatsfromconcentratedsuppliersofkeyinputsaffectprofitability)>.IntensityofRivalry(marketconcentration,pricecompetitiontactics,exitbarriers,amountoffixedcosts,andindustrygrowthratesimpactprofitability)>. Price-costmarginpercentage(PCM)=(P–MC)/PApricecutmayhelporhurtprofitabilitydependingonpriceelasticitiesandpricecostmargins>.SeehowmuchquantitymustchangeafterapricecuttobreakevenIfthepricecutwere10%,tobreakeventhepercentagechangeinquantity(DQ/Q)mustbelargeenoughtosatisfytheequation:PCM/(PCM–>.10)>(1+DQ/Q)>.Thelargertheprice-costmarginpercentage,thesmallerthenecessaryquantityresponsetojustifycuttingprice>.PriceandOutputUnderPureCompetitionCompetitivefirmsattempttomaximizeprofits>.Competitivefirmscannotchargemorethanthemarketpriceofothers,sincetheirproductisidenticaltoallothers>.Hence,competitivefirmsarepricetakers>.Totalrevenue,TR,isP·Q,wherepriceisgiven>.Therefore,marginalrevenue,MR,isprice,P>.Profitistotalrevenueminustotalcost(p=TR-TC)??1999South-WesternCollegePublishingProfitmaximizationimpliesthateachfirmproducesanoutputwherePrice=MarginalCost(P=MC)>.ToproducemorethanthisquantityimpliesthatP<MC,whichisnotthemostprofitabledecision>.ToproducelessthanwhereP=MC,impliesthatP>MC,andthefirmcouldincreaseprofitsbyexpandingoutput>. Inshortrun,acompetitivefirmmayearneconomicprofits>.Inlongrun,entrypushespricedowntotheminimumpointoftheaveragecostcurve,sothateconomicprofitsarezero>.??1999South-WesternCollegePublishingWelcomePropertiesofPureCompetition1>.FirmsarePriceTakersAssumetheoppositeP1>P2ButeveryoneknowsthisTheproductsarehomogeneous>.So,noonebuyfromfirm2>.??1999South-WesternCollegePublishing??1999South-WesternCollegePublishingQfirm’sdemandcurveddMCP2>.Afirm’sdemandcurveisperfectlyelasticatthecompetitivepriceDiagramoffirmdemandinpurecompetition??1999South-WesternCollegePublishing3>.ProfitMaximizationimplieseachfirm producesataquantitywhereP=MCMaxP=P??Q-TC(Q)??P/??Q=0impliesthat:P=MCdecisionrule4>.Thefirm’sMCcurveisthefirm’sSUPPLYCURVEpricesquantities{Aspricechanges,theoptimalamountSUPPLIEDchangesMCEquilibriumPriceinaCompetitiveMarketEquilibriumforeachfirmifP=MC>.Eachfirmis“happy”Equilibriumfortheindustryif:DemandequalsSupplyatthegoingpriceWhenbothoccur,themarketisinaCompetitiveEquilibrium??1999South-WesternCollegePublishingafirmtheindustryMCDSMCACCANEARNECONPROFITS INTHESHORTRUNACompetitiveEquilibriumImplies:??1999South-WesternCollegePublishingNOTICE:1>.CompetitivefirmcanearneconomicprofitsinSR2>.IfPrice<AVC,firmwillshutdownso-called“shutdownprice”isAVC3>.InLR,entryforcespricedowntotheminimumoftheACcurveACMCAVCP??1999South-WesternCollegePublishingNORMATIVEPROPERTIESofCompetitiveMarkets:1>.TheDivisionofOutputAmongFirmsisEFFICIENTSuppose2firmswithdifferentMCIffirm2expandsandfirm1contractsproduction,TCrises>.firm1firm2MCMC??1999South-WesternCollegePublishing2>.ThetotaloutputoftheIndustryisCORRECT,i>.e>.,MaximizestheSumofConsumer&ProducerSurplus demandsupplyCSPScorrectoutputConsumersurplusisareaBelowdemandandAbovepriceProducersurplusisareaBelowpriceandAbovesupply??1999South-WesternCollegePublishing3>.IntheLR,eachfirmproducesatthelowestpointoftheirACcurvesACMCQ(atleastcostpoint)PLR4>.PoliticalDecentralization5>.Pricesignalsthetruecosttosociety6>.EconomicprofitsarezerointheLR??1999South-WesternCollegePublishingFortheindustry:QS=3000+200PandQD=13500-500P Forthefirm:FC=50MC=15-4Q+3Q2/10AVC=15-2Q+Q2/10FINDOPTIMALoutputforthisfirm>.PROBLEM-Thefollowingisgiven:??1999South-WesternCollegePublishingAnswer:Findequilibriumprice>.SetD=Swesee3000+200P=13500-500P>.Thisimplies:10500/700=P=$15>.Atthisprice,thefirmproduceswhereP=MC,so$15=15-4Q+3Q2/104Q=>.3Q2soQ=13>.33PROFIT=TR-TCatthisoutput>.Profit=(15)(13>.33)-50-81>.<43=$68>.52=TR-FC-VCTwoTheoriesonCompetition&PriceTheMOREfirmsthereare,thegreaterthecompetitionandthelowertheprice>.ContestableMarkets--PotentialEntryaswellasactualnumberof firms,sothenumberofactualfirmsmaynotmatterempirically??1999South-WesternCollegePublishingN=numberoffirmsPRICEofAirTravelnoeffectafteracertainnumberoffirmsMESMonopolisticCompetitionMonopolisticCompetitionMARKETSTRUCTUREManyFirmsandManyBuyersEasyEntry&ExitPRODUCTDIFFERENTIATION!!!HistoricalBackgroundJoanRobinson“EconomicsofImperfectCompetition,1933EdwardChamberlin,“TheoryofMonopolisticCompetition,1933SmallGroups&LargeGroups??1999South-WesternCollegePublishingProductDifferentiationAmongGasStationsProductDifferentiationDifferentiationoccurswhenconsumersperceivethataproductdiffers fromitscompetitiononanyphysicalornonphysicalcharacteristic,includingprice>.Examples:restaurants,dealer-ownedgasstations,Videorentalstores,book&conveniencestores,etc>.AssumptionsoftheModel:LargenumberoffirmsDifferentiatedProductConditionsofCostandDemandareSimilarEasyEntry&Exit??1999South-WesternCollegePublishingBasicModelofMonopolisticCompetitionIntheShortRunproducewhereMR=MCpriceonthedemandcurveNOTICE:P>MCeconomicprofitsexistP>ACthereexistsincentivesforentryintothisindustry??1999South-WesternCollegePublishingACMCDMR PMQMSHORTRUNDIAGRAMProfitsintheSRInducesEntryEntryinthisindustry“steals”customers>.DemandcurveshiftsinwardRESULTSMR=MC(likemonopoly)P=AC(likecompetition)ProfitsinLRarezero(likecompetition)notatLeastCostPointofACcurve(likemonopoly)??1999South-WesternCollegePublishingACD’DLONGRUNDIAGRAMPQMCMRPropertiesofMonopolisticCompetitionDeadWeightSocialLosscontinuestoexistInefficientProductionEXCESSCAPACITYnotatleastcostpointofACcurve CouldAvoidExcessCapacitybyJOINTLYPRODUCINGatthesameplantKrogerSalt&MortonSaltORSears’KenmoreandWhirlpoolLocation--hardtojointlyproduceDoesthedeclineinprofitsstifleinnovation?Istheretoomuchproductdifferentiation???1999South-WesternCollegePublishingOptimalAdvertisingIntensitySupposetheprice-costmarginpercentageisconstant,(P-MC)/P>.Advertisingmoreiftheprofitcontributionmargin(PCM)timestheadvertisingelasticity,Ea,isgreaterthantheperunitcostofanadvertisingmessage,k,timestheadvertisingtototalsalesratio,A/PQ>.[(P-MC)/P]Ea>kA/PQIfthecontributionmarginpercentagewere50%,andtheadvertisingelasticitywere2>.Theleft-handsideis1>.Lettheadvertisingtosalesratiobe20%>.Thedecisiontoexpan