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ID:7273909
大小:1.06 MB
页数:31页
时间:2018-02-10
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1、Chapter7ApplicationstoMarketingOvertheyears,anumberofapplicationsofoptimalcontroltheoryhavebeenmadetothefieldofmarketing.Manyoftheseapplicationsdealwiththeproblemoffindingorcharacterizinganoptimaladvertisingpriceovertime.Othersdealwiththeproblemofdetermini
2、ngoptimalpriceandqualityovertime,inadditiontoorwithoutadvertising.ThereaderisreferredtoSethi(1977a)andFeichtinger,Hartl,andSethi(1994)forcomprehensivereviewsondynamicoptimalcontrolproblemsinadvertisingandrelatedproblems.Inthischapterwediscussoptimaladverti
3、singpoliciesfortwoofthewell-knownmodelscalledtheNerlove-ArrowmodelandtheVidale-Wolfemodel.Todescribethespecificproblemsimderconsideration,letusassimiethatafirmhassomewayofknowingorestimatingthedynamicsofsalesandadvertising.Suchknowledgeisexpressedintermsof
4、adifferentialequationwithgoodwillorrateofsalesasthestatevariableandtherateofadvertisingexpendituresasthecontrolvariable.Weassumethatthefirmwishestomaximizeanobjectivefunction(thecriterionfunction)whichrefiectsitsprofitmotivesexpressedintermsofsalesandadver
5、tisingrates.Theoptimalcontrolproblemistofindanadvertisingpolicywhichmaximizesthefirm'sobjectivefimction.Theplanofthischapterisasfollows.Section7.1wiUcovertheNerlove-Arrowmodelaswellasanonlinearextensionofit.Section7.2dealswiththeVidale-Wolfeadvertisingmode
6、landitsdetailedanaly•sisusingGreen'stheoreminconjunctionwiththemaximimaprinciple.Theswitching-pointanalysisforthisproblemisagoodexampleofthereverse-timeconstructiontechniqueusedearlierinChapters4and5.Ex•tensionsofthesemodelstomulti-stateproblemsaretreatedi
7、nTurner1867.ApplicationstoMarketingandNeuman(1976)andSrinivasan(1976).7.1TheNerlove-ArrowAdvertisingModelThebeliefthatadvertisingexpendituresbyafirmaffectsitspresentandfuturesales,andhenceitspresentandfuturenetrevenues,hasledanumberofeconomistsincludingNer
8、loveandArrow(1962)totreatad•vertisingasaninvestmentinbuildingupsomesortofadvertisingcapitalusuallycalledgoodwillFurthermore,thestockofgoodwilldepreciatesovertime.VidaleandWolfe(1957),Palda(1964),andotherspres
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