Advertising as a Signal of Quality, A New Explanation
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Garella, Paolo; Fluet, Claude Denys Working Paper Advertising as a Signal of Quality, A New Explanation Quaderni - Working Paper DSE, No. 231 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Garella, Paolo; Fluet, Claude Denys (1995) : Advertising as a Signal of Quality, A New Explanation, Quaderni - Working Paper DSE, No. 231, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/5082 This Version is available at: https://hdl.handle.net/10419/159074 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/
Advertising as a Signal of Quality, A New Explanation Claude D. Fluet Universityof Queb ec at Montreal and Paolo G. Garel la Universita di Bologna Septemb er 1995 JEL Classication : L13, L41 Abstract The present article provides a unied explanation for sev eral phenomena related to advertising by rms. (i) Adv ertising without rep eat purc hase of the pro duct, (ii) advertising from established brands, or p ost-in troductory, (iii) simultaneous advertising from low and high qualit y rms, (iv) its p ersistence and pro-cyclicalit y. The explanation is original b ecause it rests up on oligop olistic interaction. The analysis hinges upon two fundamental results. The rst is that advertising allows separation when a signal via prices only does not. The second is that purely dissipative advertising can b e used to strategically deter entry. Hence, a link is established b et ween entry deterrence and signaling. Keywords: Advertising, signaling, en try deterrence, imp erfect information, oligopoly, vertical dierentiation.
1. Intro duction The 1 explanation of advertising by Nelson [1974] is well known. In a context where consumers rep eatedly purchase an exp erience goo d|namely one of a quality that can be learned only after purchase|apparently wasteful advertising campaigns induce rational consumers to realize that the advertised brands sell a sup erior product. Consumers would not re-purchase the go o d after a rst trial if it were not of goo d qualit y, and the in tro ductory advertising costs could not b e recovered in subsequent p erio ds. Nelson arguments|that apply to any form of wasteful exp enses by rms and not just to advertising|rest on repeat purchase . Along those lines sev eral authors have dev elop ed rigorous mo dels to scrutinize the v alidity of Nelsonian theories (see among others Milgrom and Rob erts [1986], Schmalensee [1982]; see also Martin [1994] for a recen t survey). The limitation in the Nelsonian theory is that it can account only for intro ductory advertising which is terminated after the product b ecomes known. Moreover, most of the literature considers the strategic interaction among one rm and the p opulation of consumers. Kihlstrom and Riordan [1984] represen t an exception since they consider a p erfectly comp etitiv e industry with free entry, where rms are price-takers. They obtain the result that advertising equilibria can arise also when the in teraction among rms and consumers is not rep eated, provided the high quality rms have lower variable costs than their low quality rivals. There seems to lack a unied theory whic h can explain sev eral phenomena related to advertising. First, advertising or other wasteful and observable selling exp enses are common in mark ets where consumption has a transient nature. Think for instance to the owners of restaurants that crowd some touristic areas (this example is also in Tirole [1989]), who invest sometimes considerable sums in luxurious settings, silv er cutlery,numb er of waiters, and the like, although they do not exp ect to receiv e the same customers rep eatedly. One ma y observe that some restauran ts will spend money on these items and others will not. However, a theory based on rep eat purchase cannot assign an informative role to these exp enditures. 1 C-D. Fluet, Departement des Sciences Economiques, Univ ersityofQuebec at Montreal, CP 8888 Succ.A, Montreal -Quebec- (Canada), H3C 3P8. Paolo G. Garella, Dipartimento di Scienze Economic he, Strada Maggiore 45, 40123 Bologna (Italy), e-mail garella@b oph01.cineca.it.We wish to thank participan ts in workshops at Universitat Autonoma de Barcelona, I.G.I.E.R. (Milano), and Johns Hopkins University (Baltimore). F. Forges provided commen ts on an earlier version but do es not share any responsibilit y on the remaining errors. A suggestion by Jacques Rob ert was particularly useful at an earlier stage of the pap er. The nancial supp ort from the Quebec Fund FCAR is gratefully aknowledged. 2
Second, as a cursory lo ok at television campaigns may conrm, rms with brands of long-established reputation also sp end considerable sums on advertising. This phenomenon cannot b e explained by Nelsonian theories, unless one admits a constant inow of new consumers at each p erio d who are unaware of the qualit y of the brand b eing advertised and who enter a rep eat purchase process. Another way out would b e to assume that consumers do not have p erfect recall|or that the characteristics of the products on the market c hange fast while purchases happen infrequen tly 2 . It seems dicult to accept the idea however that the magnitude of this inow b e large enough to justify the large stream over time of advertising exp enditures that one observes. Similarly, this type of advertising is not encompassed by the explanation in Kihlstrom and Riordan since, although they do not assume rep eat purchase, rms need to advertise only in the introductory phase. Third, the empirical literature (as well as some non-signal theories of advertising lik e Dorfman and Steiner[1954] ) had long since noted the relative constancy of the advertising-sales ratio of rms over time (see for instance Schmalensee [1972]). This means in particular that advertising v aries pro-cyclically. Fourth, in various mark ets where rms of higher quality comp ete against riv als of lower qualit y, advertising by low qualit y rms is conspicuous and sometimes it compares to that of the high qualit y rms. The explanation provided in the present paper encompasses all these four typ es of advertising and it therefore enlarges the quota of advertising exp enditures that can b e attributed to a signaling eort by rms. Furthermore, quite surprisingly, the explanation we provide conrms an old idea, namely that high advertising exp enditures can b e used as a strategic entry barrier. It is worth emphasizing that the entry prev enting attribute of advertising is derived in the present paper without recurring to ad hoc assumptions about the inuence of advertising on consumers' tastes. The mo del b elo w abandons the repeat purchase (which however could b e reintroduced at no cost) and the one-rm assumptions. It explicitly considers the problem of nding separating instrumen ts for the case where two rms comp ete on the same mark et. None of these t w o rms has an established reputation but it can b e of high or of low qualit y; therefore the consumers are confronted with the problem of interpreting the price-advertising strategies of b oth rms at the same time. In teresting situations ma y arise that do not appear in the monop oly case. For instance, a rm ma y try and exploit the consumers imp erfect information by copying the strategy adopted by its rival. This typ e of mimic king b ehavior is rather dierent from the one to whic h the signaling literature in economics is used: in our case, in fact, it is quite ob vious that if two rms send the same signal (whether along or outside the equilibrium path) then the consumers m ust attribute them the same probability of b eing of a giv en typ e. In other words 2 We thank Guido Candela for drawing our atten tion to this case. 3
each rm is aware that the strategy it plays is liable to aect the b eliefs that the uninformed party, here the consumers, holds ab out the other rm's typ e as well as of its own typ e. This feature of beliefs do es not dep end on the number of informed parties|it is eviden t that in the job mark et game of Sp ence [1973] there are man y workers but the b eliefs of the emplo yer on the typ e of worker Smith do not take into account what worker Jones has sp ent on education 3 . It dep ends rather on the propert y that the payo (here the prots) of an informed player dep ends up on what the other player do es (e.g. its pricing b ehavior), and on the fact that this recipro cal dep endence is common knowledge to all players. The pap er pro ceeds as follows. First, in Section 2, the problem with one rm only is in tro duced and the notation established. The main reason for Section 2 rests not up on its novelty but on the need to briey clarify why in the absence of rep eat purchase the monop oly case is insucient to explain an y form of advertising, and to pave the way for the remaining Sections. Section 3, then, constitutes the core of the pap er. Tw o rms comp ete, eac h b eing of one among two p ossible typ es, each rm knows its typ e and that of the comp etitor while consumers do not observe the realized state of Nature but only the strategies played by the rms. On the basis of this observation consumers form their b eliefs. The purp ose of the Section is that of deriving a characterization of separating equilibria that does not dep end on the b elief system adopted by consumers. As a metho d, the approach consists of writing down two necessary conditions that the strategies played by the two rms must satisfy in the states of Nature when their qualities dier: these simply say that neither rm m ust nd it protable to mimic exactly the b ehavior of the riv al when their typ es dier. Only using these t wo conditions it is shown that there are cases in which a separating equilibrium, if it exists, must involve the use of advertising by the high qualit y rm if the qualit y typ es dier. The rst task of the present research is therefore accomplished in Section 3, since an explanation is provided for advertising that does not impinge on rep eat purc hase. The issue of existence of separating equilibria is solved in App endix 2, which, however, does not develop a complete typ ology of possible belief systems since this is irrelevant for our results and it would lead us astray from the non-technical issues that motivate the analysis. In Section 4, the idea that entry ma y b e deterred through advertising is examined using the results of Section 3. The Section presents an extension of the basic mo del obtained intro ducing the p ossibility that the duopoly market structure b e contestable by a rm which can also b e of two typ es: low and "very low", and which can mimic the b ehavior of a low quality . A true low- 3 Similarly, if the industry is perfectly comp etitive a rm cannot aect with its b eha vior the b eliefs that consumers hold ab out the typ es of the other rms. Khilstrom and Riordan [1984] mo del therefore do es not share this feature. 4
qualit y rm m ust then also protect its p osition, and it can do so only through advertising. In terestingly, this typ e of advertising does not serv e to separate from existing rms, but from p otential entrants, and therefore where observed it may b e erroneously ascrib ed to other reasons not dep ending on imp erfect information about qualit y. This typ e of advertising p ersists over time as long as the threat by lower qualit y rms p ersists, and it varies in the same direction as demand varies, namely it varies pro-cyclically. Our explanation of the entry barrier attribute of advertising is not based up on the eects on consumers' tastes, as advertising is here purely dissipativ e. It is interesting to note that in an article on limit pricing and advertising Bagwell and Ramey [1988] used price-advertising couples as informativ e strategies by an incum bent to signal its cost of production to an en trant. They found that purely dissipative advertising could not be used as an entry barrier. Other mo dels (of rep eat-purchase) that are related to the study of exp erience goo ds are the reputation mo dels like Klein and Leer [1981] and Shapiro [1983], based on the imp ortance of qualit y premia for the inducement to a monop olist to in tro duce a high quality instead of a low one (see also Riordan [1986]). In this resp ect our analysis also has some consequences, in spite of the assumption we mak e that the typ es of the rms are c hosen by Nature. Where rms cannot rely on rep eat purchase, in fact, a high qualit y can b e in tro duced only if it can separate from the low qualities. 2. Monop oly in the Absence of Rep eat-Purchase The main implications of the analysis can b e deriv ed via a simple example, already used for the monop oly case by Bagw ell and Riordan [1991], and here rearranged, where needed, to intro duce a v ertically dierentiated duopoly 4 . Consider a mark et where a monop olist sells a goo d that can b e of quality H or L. Unit production costs are c for the high qualit y and 0 for the low qualit y. There are no xed costs of production, although the monop olist can volun tarily add a discretionary amoun t of xed cost, a; in the form of wasteful advertising campaigns. Each consumer buys either one unit or none. If the goo d is of qualit y H the consumer's utility after purc hase is u H = v + m 0 p H (2.1) 4 Although several examples exist (see Gabszewicz and Thisse[1979] seminal pap er, and Shaked and Sutton [1981]) we do not ha ve yet a general theory of vertical dierentiation in oligoply under complete information. The authors have worked out a set of necessary conditions for a duop oly to b e dened as vertically dieren tiated, and havechecked that the main character of the analysis can be preserv ed in that more general set-up. The exp osition, ho w ever, then b ecomes mingled to conceptual issues p ertaining to the full information generalization of the vertical dierentiation mo dels that do not add an y useful insigh ts while the dierence b et ween our explanation of advertising and the traditional one b ecomes unclear. 5
where v is a p ositiv e constant, p H is the price paid to the seller, and m is a taste parameter, ranging in the unit in terval [0 ; 1], uniformly distributed over this range so that the consumers p opulation has unit mass. If a consumer does not buy her utilit y is zero. The consumer that is indieren t b et ween buying or not a high qualit y pro duct has taste parameter m = p H 0 v . The demand to the monop olist of high qualit y under p erfect information is then D H ( p H ) = min[1 + v 0 p H ; 1] if 1 + v p H , and D H =0 if 1+ v p H . If the goo d is of low quality, then utilit y is assumed to b e invariant with m and to be giv en by u L = v 0 p L : (2.2) Therefore demand to the monop olist of low qualit y under p erfect information is D L =1 if v p L , and D L =0 if v<p H . The p erfect information prices are p m H = max f (1 + v + c ) = 2 ;v g and p m L = v for the high and the low qualit y resp ectiv ely . The case where (1 + v + c ) = 2 v is of no in terest since then the monop olist has no incen tiv e to separate when her qualit y is H. Eliminating this case, then, the full information prots are resp ectiv ely given by m H = [(1 + v 0 c ) = 2] 2 and m L = v . Under imp erfect information, assume that consumers know that the monopolist ma y b e of one of the tw o qualities, so that there are only two p ossible states of Nature, denoted by (H) and (L) . Let denote a couple ( p; a ) of price and advertising used by the monop olist. F or any observation of the consumers form a b elief about the pro duct qualit y. More precisely a b elief is dened as a function b ( ) indicating the probabilit y that the pro duct is of high qualit y . Then, given a particular price and advertising com bination c hosen by the rm, the consumer's exp ected utilit y is u ( )= b ( )( v + m 0 p )+(1 0 b ( ))( v 0 p ), with u ( )= u H if b ( ) = 1 and u ( )= u L if b ( )= 0. A separating equilibrium, lo osely sp eaking, is constituted by strategies and b eliefs with the prop ert y that ,say, is played if the state is H, and L ,say,is played if the state is L, and the b eliefs are such that no deviation from these strategy prescription is protable. It is well known that application of the elimination of dominated strategies implies that at a separating equilibrium L =( p m L ; 0), and we shall not rep eat the argumen t here (see Milgrom and Rob erts 1986). This implies that there are two necessary conditions for separation, they are resp ectiv ely: ( i ) (1 + v 0 p ) p 0 a v; (2.3) and ( ii ) (1 + v 0 p )( p 0 c ) 0 a v 0 c: (2.4) Condition (i) states that a strategy can b e part of a separating equilibrium only if the monop olist has no incentiv e to play if its qualit y is low. Condition 6
(ii) states that a strategy can b e part of a separating equilibrium only if the monop olist has no incentive to deviate from the play of to the play of ( v; 0) if the qualit y is high. Note that, as Milgrom and Rob erts[1986] show, although man y other deviations are p ossible from the equilibrium prescription, the two deviations here stated are generally regarded as crucial. In fact it is generally the case that one can nd a system of b eliefs that supp orts the play of in state (H) and of ( v; 0) in state (L) if satises the two conditions (i) and (ii). The characterization of is usually the fo cus of the analysis, since it c haracterizes the typ e of signal used. In general is not uniquely iden tied by the constraints, while these rather iden tify a set of regions in the space of couples ( p; a ) to whic h must b elong. In this resp ect the following result indicates that the use of advertising is not essential for separation. Prop osition 1 : Under monop oly if there exists a strategy =( p; a ) with a> 0 , that satises constraints (i) and (ii), then there also exists a strategy 0 =( p 0 ; 0) satisfying the same constraints. Proof: See the App endix. Note that Proposition-1 can b e in terpreted as follows: the existence of a separating equilibrium, under monop oly and in a one-shot game, does not impinge on the p ossibilit y of advertising; in other terms, the p ossibilit y to advertise does not enlarge the sp ectrum of circumstances under which separation ma y o ccur. This however does not mean that advertising can b e excluded on some game theoretic ground b ecause to do that one needs use of an equilibrium selection criterion. This is done in Milgrom and Rob erts[1986] who sho w that advertising resists the application of standard renements criteria only if rep eat purchase is assumed, and we do not restate the argumen t here. There is an economic reason, however, why advertising is not necessary: it is more costly to signal through advertising than through price. The proof of this statement is simple: dene a ( p ) = (1 + v 0 p ) p 0 v . For any given price this function gives the minimal amount of advertising that is necessary to separate. Then, maximize the prot of the high qualit y monop olist with resp ect to price and advertising under the constraint that a max[0 ;a ( p )]. This is equivalent to maximize with resp ect to p the function 5( p ) = (1 + v 0 p ) p 0 a ( p )over the interval p in [0 ;p a ] where p a is the highest ro ot of 0 = (1 + v 0 p ) p 0 v . Since a ( p ) is monotone decreasing in p , and since 5 0 ( p ) > 0 the prot so written is increasing in price, so that a maximum obtains at p a with a ( p a )= 0. Saying it dieren tly, consider again the separation constraint (i) ab ove. Since advertising adds to the costs of a high qualit y monop oly as muc h as it adds to those of a low quality it is relatively easier to imitate than a p olicy of high price: the latter is more costly in terms of lost prot (unit margin times demand) for a monop oly of low qualit y , who pro duces at a low marginal cost, than for one of high qualit y, who pro duces at a high marginal cost. 7
3. Duop oly 3.1. The structure of comp etition under full information Before the study of the signaling game describ ed in the Intro duction ab ove, it is necessary to briey present the full information results of comp etition in duopoly. Assume that the cost conditions are the same as for the monop oly case, again without loss of generalit y, assume that c L = 0. Let the buyer's utilit y b e describ ed by the expressions (2.1) and (2.2) ab ove. The consumer that is indieren t bet ween buying qualit y H or L has taste parameter m ( p H ;p L )= p H 0 p L ; if 0 <p H 0 p L < 1. Then it is easy to show that the demand to the high qualit y rm is the continuous function d H ( p H ;p L ) describ ed by d H ( p H ;p L ) = min f 1 0 p H + min[ p L ;v ] ; 1 g ; if p H < 1 + min[ p L ;v ] (3.1) d H ( p H ;p L )= 0 otherwise. Note here that for anyvalue of p L , d H ( p H ;p L ) = 0 for p H 2. Similarly, demand to rm of typ e L is given by d L ( p H ;p L ) = min f p H 0 p L ; 1 g ; if p L <p H ; (3.2) and d L ( p H ;p L ) = 0 otherwise. The two demand functions are depicted in Figure 1. The reaction function for rm H is describ ed by the function ^ p H =(1 = 2)(1 + p L + c ) ; if max [ c 0 1 ; 0] p L v; (3.3) if by contrast p>v , then rm L has zero demand and rm H reaction function consists of its monop oly price, that is ^ p H =(1 = 2)(1 + v + c ) ; if p L >v: Finally, if rm L quotes a price lower than c 0 1 then rm H cannot quote a price equal to (1 = 2)(1 + p L + c ) as this is lower than its marginal cost, therefore we set ^ p H = c for c 0 1 p L . Similarly, the reaction function for rm L is ^ p L = p H 2 ; if p H 2 <v; (3.4) 8
of Figure 4 b elo w) and it is dened by 14 A ( p H )=( p H 0 c ) 1 0 p H 2 = a y ( p H ) ; (3.10) for p H < 2 c , and by A ( p H )= ( p H 0 c ) 1 0 p H 2 0 1 2 p H 2 0 c = a z ( p H ) ; (3.11) for p H > 2 c . Note that a z = a y at p H =2 c so that A ( p H ) is continuous 15 .Furthermore 2 c is also a maximum of A ( p H )if p H > 0 : 5. While for c< 0 : 5 the maximum is at the right of p H =2 c and it coincides with the maximum of a z ( p H ). The interplay of the curves a ( p H ) and A ( p H ) determines the regions in the space of ( p H ;a ) couples to whic h the separating strategy H ; in state (H,L) or (L,H), m ust necessarily b elong if a separating equilibrium of the game exists. Note, to start, that if v< 2 strategies involving a zero amount of advertising and that satisfy the constraint derived by condition (A) alwa ys exist. If and only if A ( p H ) intersects the horizontal axis to the right of v 16 ,howe ver, there are price-alone strategies that also satisfy constraint (B). For the purp oses of the present Section|namely to demonstrate that the p ossibility of advertising enlarges the set of parameter ranges for which separation ma y o ccur over and ab ove the range for whic h separation ma y obtain through prices only|it is sucient to show that, when v> min f z ( c ) ; 2 g , there exist ranges for the cost parameter c for whic h a strategy H with strictly p ositiv e advertising satises necessary conditions (A) and (B). Proposition 3. For c< 1 and v> min f z ( c ) ; 2 g the only non-trivial separating equilibria that ma y exist involve a strictly p ositiv e lev el of advertising in the states (L,H) and (H,L). Furthermore, for c < 1/2 the high qualit y rm has a strictly p ositiv e prot, while for c 1/2 its prots are null but its mark et share p ositive. 14 The prot to rm H if the equilibrium strategies are play ed is ( p 0 c ) d H ( p H ;p H = 2) 0 a =( p 0 c )(1 0 p H = 2) 0 a: Then condition B writes as ( p H 0 c ) 1 0 p H 2 0 a max 1 2 p H 2 0 c ; 0 : (3.9) The righ t hand term is zero if p H < 2 c , that is when rm H would mak e negativ e prots if it deviated to the price of its riv al, but just needs to mak e non-negativ e prots. 15 The function A coincides with the Min [ a z ;a y ]over the relevant range and so it can b e more easily retained. 16 The condition is that the largest ro ot of a z ( p H ), denoted z ( c )= 1 4 (3 + 2 c + p 9 0 4 c + c 2 ) is larger than v .(Note that for all c> 0, z ( c ) >c and that the ro ots of a y ( c ) are c and 2). 15
As an informal proof for the case c< 0 : 5 consider the graph represented in the left part of Figure 4, whic h has b een drawn for a value of v> 2, and of c =0 : 25: the curv e a ( p ) is recognized as starting from the origin, and A ( p ) starts from the p oint c , where a y ( p H ) = 0. The two constraints there cross at the p oint where p H =2 c , and at the p oint where p H = 1. It can b e shown that for c< 1 = 2 these crossings o ccur in the same way as depicted in that graph 17 , i.e. one has that for p H in the range [2 c; 1] the inequalit y A ( p ) >a holds, while outside that range the opposite inequality holds (the right hand graph in Figure 4 has b een drawn for a value of c = 0, the valid region shrinks in size as c is increased form zero to 0.5). It follows that in general, for c< 1 = 2, the region to which a separating strategy H must b elong is formed by (i) a non-empt y region where advertising is strictly p ositive; (ii) a (p ossibly empt y) region consisting of all p oints on the abscissa lying in the in terval [ v; z ( c )]. This proves the rst part of the Proposition. (To prove the part of the proposition regarding the case c> 1 = 2 consider Figure 5, whic h has b een drawn under the hyp othesis that c =0 : 7. It is apparent from Figure 5 that if v> 2, then a separating equilibrium if it exists is given by the p oint of tangency of A ( p H ) and a ( p H ). The same situation arises for all values of c 0 : 5, b ecause for these values one can easily check that A ( p H ) has a unique maximum at the point where p H =2 c , and that at p H =2 c one has a ( p H )= A ( p H ), so that the equilibrium H is unique in these cases 18 ). 2 We will nally note that a price couple equal to the full information prices for the high and low qualit y may be used at a separating equilibrium if the high qualit y rm accompanies the full information price by an adequate exp enditure in advertising. For instance, for c =0 : 25 one has that p 3 H =5 = 6 and a = a s (5 = 6) ma y constitute a separating strategy H for H. The imp ortant feature of the results so far obtained is that they, in the same line as for the monop oly case, establish a characterization of equilibria, preceding a complete sp ecication of b eliefs. Existence is discussed in App endix 2. 3.4. Persistence As it is clear, the plausibility that advertising must b e used in a one-shot set-up, implies that it can b e used also in situations where rep eat purchase is not present. For instance in the case of the restaurants quoted in the Intro duction. The luxurious setting of one of two restaurants can be interpreted as an ostentation 17 In particular, p H =2 c is the p oin t where a s ;a y ;a z ; all cross; p H = 1 is always one of the ro ots of the equation a s = a z , and it is the largest ro ot for c< 1 = 2. 18 When c = 1 then 2 c = 2 and the p oint of tangency of the two constrain ts implies that p H =2. For c> 1 the two constraints do not touch any more since A ( p H ) < 0 for c> 1, so that the separating equilibria with adv ertising do not exist for these v alues of c . 16
of "waste" that p ersists over time as it must signal to new consumers at eac h p erio d. Similarly, the rep etition of promotion campaigns on television by some brands ma y have the same function. Furthermore, as it shall b e shown b elo w p ersistence can occur when renown brands ma y b e induced to advertise in order to deter the en try of other rms. 4. Advertising as an Entry Barrier Assume there is a third rm in addition to the two previously considered. This rm is a producer of lowest qualit y, in the sense that it can b e one of two typ es: L or 0, but not of typ e H. If a buyer purchases the goo d 0 at price p 0 she gets a utility u 0 = 0 p 0 .To simplify matters assume that a op can never b e mistak en for a high qualit y product, but it is indistinguishable from a low qualit y product, an assumption that could b e relaxed in a more complete version of this game. To keep with the approach of short term interaction, we assume that the entry, price, and advertising decisions are all sim ultaneously taken. If we had assumed rep eat purc hase, and a multi-perio d framework, it would b e p ossible to mo dify the example here in order to consider the b ehavior of incum b en ts against p otential entrants. In this game it is common knowledge that there can b e such a pro ducer, called a "yer-by-the-night", in the sense that everyb ody knows that if three rms are on the market one could b e a op and must leav e the mark et after having deceived consumers once. We shall concen trate on the asymmetric states (H,L,0) and those obtained p erm uting the order of the entries. Since qualit y H cannot by hyp othesis b e imitated by the op, in these states the op must imitate the low quality if it wan ts to enter. Then if the state (H,L,0) realizes rm L has to prevent the op from entering 19 . If the typ e 0 rm en ters and replicates the strategy of rm L then consumers cannot distinguish whic h rm is L and which is the op. Firm H, by contrast ma y separate from rm L using a strategy that can b e describ ed analogously to what has b een done ab ove so as to prevent rm L from imitating|for brevity we do not re-state the conditions (A) and (B) for this game. Note that if the op en ters and imitates rm L, then this rm and the op are b oth b eliev ed to b e ops with probability 0.5 and will share the demand addressed to the corresp onding exp ected qualit y as it shall b e briey shown. The consumers know that there is at most one op, hence their exp ected utilit y from buying from one of the two rms that uses the strategy L =( p L ;a L )is 19 Under the assumption that a high qualit y cannot be mistaken with a op, when the state is (H,H,0) the yer{by-the-night cannot enter. If the state is (L,L,0) , under revelation one would observe advertising from b oth lo w quality rms, as it is briey explained in the follo wing fo otnote. Finally, if the state is (L,L,L) all rms pla y the Bertrand equilibrium with a price equal to marginal cost (here zero) and no adv ertising. 17
u f =0 : 5[ v 0 p L ]. The consumer indierent from either rm playing L and rm His m 3 = p H 0 p L 0 (0 : 5) v . The total demand addressed to the two rms L and 0 is therefore equal to m 3 . Assume then that at state (L,H,0) rm L m ust deter the op with a (separating) strategy L =( p L ;a L ). A necessary condition for this strategy to deter the y er-by-the-night is that if this enters and plays exactly L it makes a loss. The no-jamming constraint prev enting a op from entering and imitate rm L is: p L 2 ( p H 0 p L 0 v 2 ) 0 a L 0 : (4.1) The R.H.S. in the inequalit y ab ove is justied by the fact that the full information price and prot of a op is zero. The L.H.S. is simply the prot of a op that enters and imitates a rm of typ e L that is playing ( p L ;a L ) against a rm H that is playing ( p H ;a H ). If a L = 0 the yer-by-the-night always nds it protable to en ter so that advertising is necessary for rm L to k eep the op out 20 . Obviously, a necessary condition for the low qualit y rm to separate from the op through advertising is that by so doing it mak es a prot higher than if it accommo dates the en try of the yer-by-the-night. The rm L prot after accommo dation is p L 2 ( p H 0 p L 0 v 2 ). And the price p L that maximizes this prot is equal to p ` (1 = 2)( p H 0 v= 2). A deviation from the entry prev enting price p L that b elongs to L =( p L ;a L ), to p ` entails a prot equal to (1 = 4)( p H 0 v= 2) 2 . Therefore a condition that L =( p L ;a L ) must satisfy is that p L ( p H 0 p L ) 0 a L > (1 = 4)( p H 0 v= 2) 2 : (4.2) Finally, the b ehavior of rm H m ust assure that rm L do es not wantto imitate rm H in a duopoly, i.e. that p L ( p H 0 p L ) 0 a H >p L ( p H 0 p L ) 0 a L (this again is the no-jamming condition). The lesson from this second example is that the theory here exposedcan account for (i) low quality rms advertising together with high quality rms, (2) persistenceof both rms advertising over time. Note that the existence region for high-price and no advertising for rm H shrinks further if the low qualit y rm advertises. In fact the L.H.S. of all conditions (A) and (B) is lowered by the xed amount a L , so that the incentive constraint a z ( p ) is shifted upward, and the range of v -values that are larger than the ro ot z c shrinks accordingly as a L is increased. 20 When the state is (L,L,0) the two rms of typ e L can deter the entry of the third rm by using a price-advertising couple ( p LL ;a LL ) satisfying the no-jamming condition p LL 1 3 0 a LL 0 ; which ensures that entry is not protable. The two type L rms make nonnegativ e prots provided p LL 1 2 0 a LL 0. Clearly, there are man y such couples ( p LL ;a LL ), one example is ( p LL ;a LL )= ( v; v 3 ), at which b oth rms mak e zero prots. 18
Finally, assume that the mark et size increases or decreases over time as in a cyclical behavior of demand. For instance assume that the mass of consumers is M t where the subscript t denotes a date. If advertising is used as an entry barrier, then it p ersists; however it m ust also vary according to demand conditions: the no-jamming constraint prev enting a op to enter and imitate rm L b ecomes: p L 2 ( p H 0 p L 0 v 2 ) M t a L : (4.3) As M t varies along the cycle so varies the minim um amount of advertising of rm L. As a conclusion we get that advertising varies pro-cyclical ly . 5. Concluding remarks on advertising, signaling, and price p olicy When advertising is used as an en try barrier, since in that case it is clear that a price-alone strategy can always b e mimic ked by an en trant of lower qualit y,it arises as a natural equilibrium b ehavior. When it is just used by a high quality to separate from a low qualit y its relative merits o ver a price-alone strategy should b e intuitively explained as they seem to apply for the duop oly and not for the monop oly case. Note rst that to obtain separation when one rm is of high qualit y and the other is of low quality the former m ust discourage imitation by visibly wasting some resources. This can b e done by an abnormal increase (for the case of a decrease in price see comments belo w) in price, or by adding the xed costs of an advertising campaign. A high price, however is painful in terms of lost customers that switch to the rival supplier. This eect is larger the more elastic is the rm's demand to the price dierence. For high enough prices if qualit y do es not command a high premium the high quality is out of the market and cannot separate. The qualit y premium for rm H in our mo del is higher (in p ercen tage terms) the lower is the parameter v . A high v induces a low p ercen tage dierence in utilit y ( u H 0 u L ) =u L =( m 0 p H + p L ) = ( v 0 p L ). This accounts in part for the diculty to obtain separation through a high price and no advertising when v is high. By using advertising and an appropriate price together, the high qualit y rm ma y succeed in discouraging imitation without raising its price to o m uch above that of the rival. Second, the price of the low quality rm at a separating equilibrium is a decreasing function of the price of the high quality rm (in monop oly this is not so). This means that the lower the price that is used by the latter for separation, the lower the margins that it can enjoy by imitating the low qualit y rm. This makes it easier for the high quality to be discouraged from mimic king the low qualit y. Also in this resp ect the use of advertising, since it allo ws a reduction in the signaling price of the high qualit y rm renders the separation easier. 19
More generally, the imp ortance of a low price in a comp etitive framew ork is quite obvious, while it is not so in the context of a monop oly. By fo cussing on the single-rm problem some authors have stressed the imp ortance of low intro ductory prices as a signaling p olicy (see Sc hmalensee[1978]), while others have attributed more imp ortance to high-price p olicies as signaling devices (see Bagwell and Riordan[1991]). The explanation we use here does not conict with either those views of low (or of high) intro ductory prices as signals, although we stress the imp ortance of advertising comp onents of a signaling strategy that al low a price p olicy to b e a signal 21 . In our example a price higher than the full information price|when revelation is sp ontaneous the full information price itself|may signal without advertising. But there are situations where advertising is necessary for prices higher than, equal to, or lower than the full information price to separate. The old idea that the entry of new rms may b e deterred through advertising nds its counterpart in our mo del in the idea that signaling through advertising allows a lower price than signaling through price alone and reduces the market share for the rivals. The low qualit y rm by advertising can use a price low enough to discourage entry of a rm with a still lo w er qualit y, while without advertising the same price cannot deter the entran ts. This typ e of advertising is most likely to contin ue over time and to vary in a pro-cyclical fashion, as it is directed not so muc h to separate one incum b ent from another incum b ent but to discourage, through time, the mimic king from p otential entrants. 21 The signaling role of prices is also the fo cus of W olinski [1983] and Co op er and Ross [1984]. In these works, however, some consumers are informed ab out pro duct qualities or can acquire information at a cost (i.e. the pro duct is a searc h go o d). The question there studied is then the extent to which equilibrium prices transmit information from informed to uninformed agents. It is high prices that have received the most attention in those works. 20
References [1] Bagwell, K. and G. Ramey [1990], "Advertising and Limit Pricing". Rand Journal of Economics , 19, 59-71. [2] Bagwell, K. and M. Riordan [1991],"High and Declining Prices Signal Pro duct Qualit y", American Economic Review 81, 224-239. [3] Coop er, R. and T. Ross [1984], "Prices, Product Qualities and Asymmetric Information", Review of Economic Studies 51, 197-208. [4] Dorfman, R. and Steiner, P. [1954]: "Optimal Adv ertising and Optimal Quality". American Economic Review , 44, 826-836. [5] Fudenb erg, D. and J. Tirole [1986], "A Signal-Jamming Theory of Predation", Rand Journal of Economics 17, 366-376. [6] Gabszewicz, J. and J-F. Thisse [1979]: " Price Comp etition, Qualit y , and Income Disparities". Journal of Economic Theory, 20, 340-359. [7] Kihlstrom, R. and M. Riordan [1984],"Advertising as a Signal", Journal of Political Econom y 94, 796-821. [8] Klein B. and Leer K. [1981]:" The role of Market Forces in Assuring Contractual Performance". Journal of Political Econom y , 81, pp.615-641. [9] Martin, S. [1993]: Advanced Industrial Economics. Cam bridge, MA, Blac kwell. [10] Matthews,S.A. and D. Fertig [1990],"Advertising Signals of Pro duct Quality" , Northwestern Univ ersity, CMSEMS D.P. 881. [11] Milgrom, P. and J. Rob erts [1986],"Prices and Advertising Signals of Pro duct Qualit y", Journal of Political Econom y 94, 796-821. [12] Nelson, P. [1974],"Advertising as Information", Journal of Political Econom y 81, 729-754. [13] Riordan, M. [1986]: "Monopolistic Comp etition with Experience Goo ds", Quarterly Journal of Economics , 90, pp.629-650. [14] Schmalensee, R. :[1972]: The Economics of Advertising . Amsterdam: North- Holland. 21
[15] Sc hmalensee, R. :[1978]:" A mo del of Adv ertising and Mark et Structure", Journal of Political Econom y , 86, pp. 485-503. [16] Shaked, A. and J. Sutton [1982]: "Relaxing Price Comp etition through Product Dieren tiation". Review of Economic Studies , 49, 3-13. [17] Shapiro C. [1982]"Consumer Information, Product Quality, and seller Reputation", Bell Journal of Economics, 13, pp. 20-35. [18] Shapiro C. [1983]:"Premiums for High Qualit y Pro ducts as Ren ts to Reputation", Quarterly Journal of Economics, 98, pp. 659-680. [19] Sp ence, M. [1973] "Job Market Signaling", Quarterly Journal of Economics 87, 355-374. [20] Tirole, J.[1989]: The Theory of Industrial Organization . Cam bridge, MA, MIT Press. [21] Wolinsky, A. [1983],"Prices as Signals of Pro duct Qualit y", Review of Economic Studies 50, 647-658. 22
6. App endix 1 Proof of Prop osition 1 Proof: Supp ose that ( p; a ) satises b oth (i) and (ii). Suppose further that ( p; 0) does not satisfy either one or b oth (i) and (ii). Since ( p; a ) satises (ii) (1 + v 0 p )( p 0 c ) 0 a 0 v + c 0 then, a fortiori (1 + v 0 p )( p 0 c ) 0 v + c 0 . The lo west value of a that can b e associated to p is therefore given by (i) and is (1 + v 0 p ) p 0 v a + . Then, assume =( p; a + ) . By continuity of the function (1 + v 0 p ) p there exists a price p 0 >p such that (1 + v 0 p 0 ) p 0 = v . Hence assume the strategy 0 =( p 0 ; 0) , which veries constraint (i), is used instead of . Constraint (ii) for 0 writes as (1 + v 0 p 0 )( p 0 0 c ) 0 v + c 0 . Since satises (ii), for this inequalit y to b e veried, it is sucien t that (1 + v 0 p 0 )( p 0 0 c ) 0 v + c (1 + v 0 p )( p 0 c ) 0 v + c 0 a + . But this writes as (1 + v 0 p 0 ) p 0 0 c (1 + v 0 p 0 ) 0 v 0 (1 + v 0 p ) c or (1 + v 0 p 0 ) (1 + v 0 p ) , which is true since p 0 >p and since b oth expressions in parentheses are non-negativ e. The argumen t applies also for all strategies (p,a) with a>v + and it is therefore complete. 2 Proof of Lemma 1: Proof: Supp ose that at an equilibrium rm L plays an action 0 dierent from L when the state is (H,L). By denition of a Separating Equilibrium rm L is p erceiv ed as L and its opp onentasH.However, by deviating to strategy L , if it is still p erceiv ed as L with probability one it will play according to its b est reply against H , and if it is p erceiv ed as L with probability less than one, it will receiv e a higher demand than if it is with probability one, and its prot will increase, therefore, in either case there is no strategy a vailable to rm L that dominates L : 2 7. App endix 2: Existence The necessary conditions for the existence of a separating equilibrium are suf- cien t to characterize the nature of the signal used, but are not sucien t to guarantee existence in general. Recall furthermore that the analysis has b een so far concerned only with the actions prescrib ed in states (H,L) and (L,H) , and the other actions have b een left unspecied. The presen t Section lls this gap and sho ws that existence is guaranteed, in one of the simplest b elief systems that can b e envisaged, if only an additional 23
condition is imp osed up on H . Of course the equilibria here found satisfy (as all equilibria must) the c haracterization in Section 3 above based up on conditions (A) and (B). To eliminate the inuence of the value taken by b ( H j H )upon the result that advertising ma y b e necessary, we assume that b ( H j H )=0, so as to render as large as p ossible the set of situations in which a price alone strategy of the t yp e H =( p; 0) can work as a signal. Assume that consumers beliefs have the following structure. (i) If they observe that no rm uses advertising and that prices are equal to c at b oth rms consumers b eliev e that the state is (H,H) . (ii) If only one rm plays H and if this satises (A) and (B) above, then they b elieve that this rm is H and the other is L, unless the other rm also plays either H ,or(0 ; 0) in which case they b eliev e that state is (L,L) . (iii) An y other strategy couple dierent from those contemplated by (i) and (ii) induces the belief that the state is (L,L) . Formally: (i) ( b i ( i j j ) ;b j ( i j j ))=(1 ; 1) if ( i ; j )=(( c; 0) ; ( c; 0)); (ii) ( b i ( i j j ) ;b j ( i j j )) = (1 ; 0) if ( i ; j )=( H ;x ) with x= 2f H ; (0 ; 0) g and with H satisfying conditions (A) and (B); (iii) ( b i ( i j j ) ;b j ( i j j ))=(0 ; 0) otherwise. Note that (iii) encompasses the symmetric couple ( H ; H ) so that these b eliefs imply that condition (A) is written with b ( H ; H )=0. It must b e shown now that the equilibrium strategy prescrib e that: if the state is (L,L) then i and j are (0 ; 0) at each rm; If the state is (H,L) they are H =( p H ;a ) by rm H and L =( p H = 2 ; 0) by rm L, with H satisfying condition 3.2 , 3.3 and a condition that shall b e dened b elo w; nally, if the state is (H,H) they are ( c; 0) by eac h rm. First, if the state is (H,L) or (L,H) the strategies played m ust b e H , and ( p H = 2 ; 0) resp ectiv ely. The b est deviations from equilibrium under the assumed system of b eiefs are H for rm L and ( p H = 2 ; 0) for rm H. But these deviations cannot b e protable since H satises conditions (A) and (B) above. This couple of actions is therefore a couple of mutual b est replies. Second, if the state is (L,L) then the play of a null price and of no advertising by b oth rms m ust constitute a couple of b est replies: if a rm deviates to an y other strategy with a p ositiv e price it shall still b e perceiv ed as L, therefore it cannot increase its prot above zero. Therefore the couple ((0 ; 0) ; (0 ; 0)) is a couple of m utual b est replies. It remains to be veried whether under the state (H,H) the candidate that the b eliefs prop ose, namely the couple (( c; 0) ; ( c; 0)) is a pair of mutual b est replies. It is immediate to see that the only p ossible deviation left to either rm by the b eliefs is the play of strategy H instead of ( c; 0). That deviation generates an observation of the kind listed in (ii) in the b elief system, and therefore aords 24