w ‘ L=-=’-->(!This review of over 100 studies,.;> . . . .,.—.,eonchides that diminishing returns characterize . . . ‘ ~+. . ..,.::...,,THE SHAPE OF THEADVERTISING RESPONSEFUNCTIONJulian L. Simon and Johan ArndtThe general question before us is: What is the effect,for the firm and for society, of a larger rather thana smaller quantity of advertising? As it is stated,tmwever, this question is exlmordintily vague. Andlhe difficulty of putting the right questions in suffi-ciently precise fashion is the cause of much of thecOnUOvemy ~d contisio” about the effect of var-ious quantities of advertising.As passing evidence of this confusion, the entiretopic is often weated under the rubric ‘.ecommdesOf scale in adv~fising,.. even tio”gh the situationsbsing disc”$sed $eldom (if ever) fit into the eccm-omies.of.scale cmcept. This concept refers to tieOUtcomcs Of ~~e.prOpOflion i“cremes in 1711 inputs:that is, the pqotic,ns of ~1 inp”[s remain the sameU I& scale of the firm changes. But when discussingtiverdsing quantities, writers inevitably have in~nd dther an increase i“ advertising alone, or aniac~ in the toti scale of the enterprise withcbanghg pmpordons of inputs. And the advertising-~CS ‘&io that is usually adduced as the =h’~tUICaSWcment is ~Omhle~s for tie purpose at h~d.nere are at least five imerlocking questions about~c effccti of VtiO”S quntities of advertising. SOmeOf Ihese qUCStio”S affect CWr judgment of advertis-i%”S role i“ the fim,~ thinking, a“d d) affect ourJud6rnent of adverdsi”g,s impact on the economy as● whole.(1) Can an increase in the physical quantify ofadvertising-the number of inches in a printed ad-vertisement or the number”of seconds in a televisionor radio commercial-produce a Iarger-than-propor-tionai number of units sold?(2) Can an increase in the expenditure for adver-tising produce a largcr-than-proportional number of unitssold? Because of quantity dis-counts, the answer to thisquestion could be “yes’” evenif the answer to question I is“no.”’Questions 1 and 2 are im-portant on an everyday basisfor business decision makers.They also enter into the s.xialquestions to come.(3) Can a same-proportion increase in all factomJulian L. Simon is professor of economics -d mar-keting at the University of Winois. He k the author ofIssues in the Economics of Advrm”sing, The Manage-ment of Advertising, Bu.ric Research Method$ in SocialScience, The Economics of Population Growth, andAppIied Managen”td Economic.. He has written nu.merous other bootiand articles.11767-.lournai of Advertising Researchof the enterprise-including advertising-produce aIarger-than-proponional increase in a brand’s salesthat is traceable to costs in factory production ortransportation? This is a true economies-of-scalequestio~tba; is, whether a big firm bas an advan-tage over a small firm due to advertising. (There issome inevitable confusion about whether the factors-.1,of production and output are measured in physical;;or monetary terms. But we feel that clarifying the,+::matter is not worthwhile at this point.)(4) Can an increase in the mimber of brands of thesame or related products sold by the firm-with asame-propalion physical increase in all inputs tothe enterprise —produce a Iarger-than-proportionalincrease in the firm’s sales that is not Uaccabk tocost functions in the factory or transportation? Thatis, are there economies of multibrand opemtions dueto adverdsing’s role?(5) The hardest question to properly frame con-cerns dynamic effects and barriers to entry into theindustry. Does the existence of advertising as acompetitive tool lead to a smaller number of tom.petitors and higher industrial concentration thanwould otherwise be found if there were no advertis-ing?After a brief theoretical discussion of the possibleshapes of the response function, we will first examinethe evidence relating to the physical advertisingresponse function, and next the findings concerningAthe monetary respome fmc-Iion. The third question byy[ ~~itself constitutes a volumi.nous —btu separable -ques-tion: on the other hand, there;>~,,lis jittle evidence relevant to, .-questions 4‘ and 5. We shall-itherefore limit ourselves to afew notes on these latter threey,issues at the end of tbe paper.We will review both recent and nOt.~ @recentevidence, but the reader who wishes more detailsJohan Arndt k professor of business adndnktrationat the Nonveo”an School of Sconomics and BusinessAdministration, Bergen. A graduate of the RoyalNorwegian Naval Academy and the Norwegian Schoolof Sconomks and Business Administration, he hokkan M.S. from the University of Minnesota mnd ●D.B.A. from Harvard University. Dr. Arndl has publishcd ● rticks on marketing management and ctmsum-er behavior and k tbe author of Word of MouthAdvem”sing and Markc# .$egmenlti”on and the editor ofInsights into Consumer Behavior.12about older swiies is referred to Simon ( 1%5, 1970)so as to commve space here. (Other reviews cov-ering chunks of Ibis part of tbe advertising literaturemay be fotmd i“ Schmalensee, 1972; Genscb, 1973;Ray, 1975; Asker a“d Myers, 1975; and L.ambin,1976.)‘:.--,What Is the ShaDe of the Function?Adlertixing ,exponse fu”crion is here used to refer10 the quantitative reklionship between some inputof advertising a“d some output or effect of presumedvalue for the advertiser. Input measures include sizeand frequency of ads as well as monetary expendi.tures on advertising. Output measures include sakseffects as well as ..intermediate” indicators such asad rccaIl, attitudes, or intention to buy. The adver-tising response function may refer to the reaction ofa given individual (individual response function) orto the reaction of members of a target group (aggre-gate response function). (While there areimponantproblems in moving from the individual to the grouplevel [see Rae, 1970], these probIems of aggregationare not imponant forlhe present review.)Our survey of the literature shows that almost allwriters on adve.rtisi”g subscribe to one ortbe otherof the following two proposed shapes of tbc responsefunction: (1) the concave-downward function and (2)the S-shaped logistic function. The concave functionimplying monotonically diminishing returns is shownin Figure la. Figure lb shows the S-shaped adver.tising response function, which first has increasingreturns and then, after an inflection point,