who posts the reputational bond? advertising and cobranding in vertical relationships

WHO POSTS THE REPUTATIONAL BOND? ADVERTISINGAND COBRANDING IN VERTICAL RELATIONSHIPS*

JUSTIN P. JOHNSON†

I identify and explore the relationship between two views of brands andadvertising, one emphasizing their role in assuring quality and theother emphasizing their role in shifting rents across firms in the supplychain. I show that in the presence of moral hazard, the identity of thereputational bondposter matters, and that both the upstream and thedownstream prefer to be the bondposter. I determine the welfare costsof bondposter identity, and who would pay more (or be willing toadvertise more) to become the bondposter.

I. INTRODUCTION

IT HAS LONG BEEN ARGUED THAT AN IMPORTANT ROLE OF BRANDS is to resolveasymmetric information problems involving product quality (Fogg-Meade[1901, p. 234], Shaw [1912, pp. 742–746] and Klein and Leffler [1981]). InKlein and Leffler’s extremely influential analysis of this possibility, firmsthat are active over a long horizon sell goods whose quality cannot beascertained before consumption. They show that despite an assumed lackof formal contracts to guarantee quality to consumers, there may nonethe-less exist an equilibrium in which a firm posts its brand (that is, its reputa-tion) as a bond, thereby providing incentives for itself to supply highquality products in each period; a firm that succumbs to the temptation todeceive the market today is never trusted again.

Because Klein and Leffler do not distinguish between different layers ofthe supply chain, their argument about the role of brands is seeminglydistinct from another venerable one put forth by Kaldor [1950], Steiner[1973, 1978, 1993], and Farris and Albion [1980], who all claim that adver-tising is a competitive weapon used by manufacturers to wrest rents fromdownstream retailers or wholesalers. For example, Kaldor argues thatwholesalers historically resisted efforts by manufacturers to affix brandnames to their products, facilitating a period he refers to as ‘wholesalers’domination,’ but that the success of some manufacturers in so affixing theirbrand names combined with ‘modern’ and ‘large-scale’ advertising led to

*I thank Heski Bar-Issac, Michael Waldman, two referees and the Editor for helpfulcomments.

†Author’s affiliation: Johnson Graduate School of Management, Cornell UniversityIthaca, New York, U.S.A.email: [email protected].

THE JOURNAL OF INDUSTRIAL ECONOMICS 0022-1821Volume LXI March 2013 No. 1

© 2013 Blackwell Publishing Ltd and the Editorial Board of The Journal of Industrial Economics

28

the ‘manufacturers’ domination’ of industry. Steiner points to a number ofcase and empirical studies in support of his contention that manufactureradvertising permits wholesale price increases with relatively modest conse-quent retail price increases, and his basic rent-shifting argument is alsoimplicit in the resistance of some major original equipment manufacturersto the end-user branding campaign begun by Intel in 1991.1

Interestingly, just as Klein and Leffler do not discuss the competition forrents within the supply chain, neither Steiner nor Farris and Albion makemention of the role of advertising in resolving asymmetric information.2

Thus, a potential connection between rent-seeking in the supply chain andquality assurance has for the most part been either ignored or unidentified.

In this paper I explore the connection between these two classic views ofbrands and advertising by analyzing long-run upstream/downstream rela-tionships in the presence of asymmetric information regarding productquality. In such a situation, either the upstream firm or the downstreamfirm might stake its brand or reputation as a bond for product quality. Forexample, consumers might look primarily to the brand of a manufacturerwhen seeking quality assurances or instead simply trust that the retailer willonly carry goods of a certain quality.

I ask whether the identity of the bondposter matters. The answer is thatit has important welfare and distributional consequences. The socialwelfare effects of having the manufacturer rather than the retailer be thebondposter depend on two distinct forces and can be either positive ornegative. Nonetheless, these forces are highly intuitive and moreover thereis a simple consideration that readily indicates their net welfare effect.

The positive effect of having the manufacturer post the bond is that itmakes it easier to guarantee high quality to consumers, meaning that the setof parameters where quality can be assured is larger. To understand themechanism behind this, consider the simple case of a single upstreammanufacturer capable of producing high quality goods who sells to adownstream retailer. When consumers look to the retailer’s brand forassurance, both it and the manufacturer have the option of cheating themarket. The manufacturer can do this by producing low quality goods, ofcourse. But even if it produces high quality goods, the retailer can insteadprocure inferior ones from elsewhere and pass them off on the market,thereby ripping it off. Thus, providing high quality goods requires partici-pation by both the manufacturer and the retailer—there are two non-trivialincentive compatibility conditions.

In contrast, transferring the posting of the bond to the manufacturereliminates the possibility of the retailer’s engaging in morally hazardous

1 See Section 6 for more detail.2 See Steiner [1993] and Farris and Albion [1980, pp. 27–30] for the clearest explanation of

the underlying mechanism envisioned by them.

ADVERTISING AND COBRANDING IN VERTICAL RELATIONSHIPS 29


activity and so requires only participation by the manufacturer to ensurehigh quality. The reason is that if consumers always look for the manufac-turer’s brand name before buying, then the retailer does little more thanpass the product through to the final consumer; an attempt to substitute aninferior good will be detected because it will not have the correct manufac-turer’s brand name on it. This makes it is easier to maintain a high qualityequilibrium.

This same mechanism shifts rents across parties in the supply chain. Thelogic is as follows. Because having the manufacturer post the bond removesthe need to maintain the retailer’s incentive compatibility constraint, themanufacturer has greater leeway in raising wholesale prices, allowing it toextract more of the available surplus for itself.

Thus, bondposter identity has distributional consequences, therebyuniting the arguments of those who argue that a main role of brands is toguarantee quality with those who argue that a main role is to seize rentsfrom others in the supply chain. In other words, beginning with the asym-metric information considerations of Klein and Leffler leads naturally tothe rent-shifting role of advertising emphasized by Kaldor, Steiner andFarris and Albion; asymmetric information simultaneously explains bothfunctions.

The intuition for the simple case just discussed generalizes substantially;with unobservable investments by both firms and general bargaining,bondposter identity influences both equilibrium existence and the distribu-tion of rents in the supply chain.

The identity of the bondposter also has welfare consequences. If themanufacturer posts the bond then retail prices tend to go up becausewholesale prices are higher. The consequent reduction in total output is badfor welfare if a high quality equilibrium could have been sustained withoutthe manufacturer posting the bond, for in this case the net effect is simplyto reduce consumption.

Therefore, whether having the manufacturer control the brand is good orbad for welfare reduces to a simple consideration. Namely, if it would havebeen possible to maintain a high quality equilibrium using the retailer’sreputation, then welfare falls when bondposter identity changes, whereas ifit would not have been possible to maintain a high quality equilibrium, thenwelfare increases through such a reputational transfer.

I also investigate the strength of the incentives for manufacturersand retailers to fight to be the bondposter. This is relevant because (inline with Kaldor, Steiner and Farris and Albion) firms may be able toinfluence through advertising whether consumers ascribe quality to themanufacturer or retailer. That is, firms may engage in an advertisingand brand-building battle for the ‘minds and attention’ of consumers.Assuming this to be so, it is interesting to identify which party wouldbe willing to expend more resources in such a struggle. I show that

JUSTIN P. JOHNSON30


whether there is downstream competition or not is an importantdeterminant.

My analysis also pertains to circumstances in which the retailer must becomplicit in convincing consumers that they should look to the manufac-turer for quality assurance. In the marketing literature, such cooperation tobuild up the manufacturer’s brand is referred to as cobranding or ingredi-ent branding. A classic example of this is the Intel Inside campaign, whichinvolves PC and laptop original equipment manufacturers (OEM’s) puttingthe Intel logo visibly on the outside of their machines and also in theiradvertising.

Below, I describe the relevant literature. Section III presents the basicmodel and intuition, and Section IV generalizes those results. Later sec-tions provide extensions to variable output and competition within a layerof production, and answer the question of which party would be willing topay more to become the reputational bondposter.

II. RELATED LITERATURE

Here I summarize the relevant literature, beginning with empirical workthat supports Klein and Leffler’s basic premise.3 Png and Reitman [1995]present evidence that products whose quality is more difficult for consum-ers to evaluate in advance of consumption are more likely to be branded.Smith and Brynjolfsson [2001] and Chevalier and Goolsbee [2003] showthat in the online book market, branded websites may possess marketpower relative to lesser known sites even when consumers have access toprice comparison websites, suggesting uncertainty in the minds of the endconsumer about the performance of these sites. Waldfogel and Chen [2006]argue that non-price information about retailers’ past performanceweakens the importance of brands.

There are a number of papers in the marketing literature that exploreaspects of cobranding. For example, Ghosh and John [2008] provide atransactions cost economics approach, and Venkatesh and Mahajan [1997],Desai and Keller [2002] and Park, Jun and Shocker [1996] use labexperiments to study how consumers may react to ‘combined’ brands.González-Diaz et al. [undated] argue that in the Spanish fresh meatmarket, branded meats have begun emerging and butchers are less impor-tant in guaranteeing quality; they examine this phenomenon, includingcobranded meats, empirically. Choi and Jeon [2007] describe conditionsunder which a firm with an established reputation can use cobranding to

3 There are many theoretical papers that use the basic argument about reputational bondposting that Klein and Leffler suggest, including Rasmussen [1989] and Rasmussen and Perri[2001].



make it easier for an unproven firm in a new and different sector to signalits quality.4

Blackett and Boad [1999] and Keller [1998, pp. 283–294] also provideextensive discussion of cobranding from a marketing perspective, notingbenefits but also risks of such relationships, where the risk is that thesupplier of the input may gain too much power. They point to examplesinvolving firms or brands such as Intel, Nutrasweet, Teflon, Dolby, Recaroand Gore-Tex. It should be noted that there are many cases where cobrand-ing does not occur, although in principle it might. For example, many firmssell products under their own brand name although they do not manufac-ture the product themselves.5 Also, as discussed above, the conflict forthe right of manufacturers to have their brand names on the finishedproducts was an element in the historical struggle between manufacturersand wholesalers.

There are a number of empirical studies in the marketing literature on theinfluence of manufacturer advertising on retailer and manufacturermargins. See Farris and Albion [1980] and Lal and Narasimahan [1996] fordiscussions of them. Lal and Narasimhan also provide a theoretical modelthat predicts an inverse relationship between manufacturer and retailermargins, and Sethuraman and Tellis [2002] provide both a theoretical andan empirical investigation of the influence of manufacturer advertising onretail price promotions.

Biglaiser [1993] also examines the role of intermediaries in ensuringquality.6 He shows that an intermediary improves welfare when it is activein a market for longer than individual sellers are, because it has higherreputational incentives. Biglaiser and Friedman [1994] argue that the pos-sibility of middlemen carrying multiple brands is key to enhancing eco-nomic efficiency.7 Such differences in discounting and product lines play norole in my model.8

The literature on umbrella branding is also concerned with how brandinginfluences quality assurance. A series of papers beginning with Wernerfelt

4 See Bar-Issac and Tadelis [2008] for a useful survey of the literature on reputationbuilding.

5 Contract manufacturing is particularly common in electronics goods but the same phe-nomenon is at play with store brands in grocery stores and elsewhere.

6 Rubinstein and Wolinsky [1987] also consider an efficiency role of middlemen. However,in their analysis the middleman essentially serves to decrease search frictions not based inasymmetric information.

7 Also see Li [1998] for an assessment in which agents choose between engaging in produc-tion and specializing in identifying quality goods and serving as middlemen.

8 As a further contrast, in my model the elimination of a middleman is closest in spirit tohaving the manufacturer post the reputational bond and this expands, not contracts, the setof parameters on which high quality equilibria can be supported. Finally, as mentionedabove, there may also be negative social welfare consequences of the manufacturer postingthe bond, so that the overall welfare consequences are more complex in my model.

JUSTIN P. JOHNSON32


[1988] and including Choi [1998], Cabral [2000] and Hakenes and Peitz[2008] show that multiproduct firms may choose to use the same brandname on more than one product so as to provide assurances of quality. Incontrast to these papers, there is but a single product in my model and oneof the main goals of controlling the brand is to seize rents from otherplayers.

I close with a more detailed assessment of Kaldor’s argument and theextent to which he suggests a connection between the resolution of asym-metric information and rent-seeking in supply chains. Kaldor argues thatmanufacturers striving for efficiency in production were often limited bywholesalers. For example, an investment in a more scale-intensive facilitywould only pay off if enough wholesalers could be convinced to carry(sufficient quantities of) the product. Kaldor suggests that this processcould be inefficient and time-consuming, thereby reducing incentives toinvest. However, if manufacturers could establish themselves in the mindsof consumers, then they could be certain that there would be sufficientdemand for their products, thereby encouraging the best manufacturers tomake more investments in efficient production.

Kaldor also suggests that the shift from wholesaler to manufacturerdomination involved something called ‘goodwill,’ writing that (p. 19)

[I]ndependent wholesalers were either eliminated or reduced to the func-tion of mere distributing agents, and suppliers of credit to the retailers,with no ‘goodwill’ of their own and no power of initiative.

It is not entirely clear what Kaldor means by ‘goodwill.’ At one point(pp. 15–16) he refers to ‘goodwill’ as ‘the reliance of the buyer on thepersonal reputation of the seller. . ..,’ seemingly hinting at asymmetricinformation concerns. However, at other times, including in the text actu-ally discussing the two ‘domination’ regimes, it appears that Kaldor ismostly referring to ‘goodwill’ generated through advertising as simplymaking consumers brand-conscious per se.

III. A BASIC MODEL OF COMPETING BONDPOSTERS

Here I model a two-stage vertical market in which each stage is monopo-lized and in which there is a moral hazard problem affecting productquality. The interpretation is that the upstream firm U makes a productthat is either an input used by the downstream firm D or a finished pro-duct resold by D (to ease explication I shall typically write as if D were aretailer).

Although in Section 4 I shall accommodate the possibility that both thedownstream firm D and the upstream firm U may engage in morally haz-ardous activity, here I suppose that the quality of U’s product is not in



question. Rather, it is D who may engage in moral hazard by choosing topass off low quality substitute products on consumers.9 In addition to Dand U, there is a third player C representing the end consumer.

III(i). The Model

Time t is discrete and the horizon infinite, with the payoffs of D and U beingthe discounted value of the series of payoffs from the stage game describedjust below, with discounting according to d ∈ (0, 1). C represents asequence of short-run players.

In each period the following stage game is played. First, U offers awholesale price wt to D. Second, D observes wt and chooses action dt ∈ {n,y} where y represents retailing the good of U and n represents not using itand instead selling one produced internally that is presumed to be lowquality. Third, if dt = y, then U produces a unit and bears cost c > 0 andreceives payment wt from D, but if dt = n then U bears no costs and receivesno payment. Fourth, the market price is determined and C buys the goodfrom D, where the market price is taken to be the expected benefit toC given C’s beliefs. C’s actual (ex-post) valuation of the good is q(dt)P,where P > 0 is a constant and q(dt) ∈ {0, 1} is the quality of the good,0 = q(n) < q(y) = 1. Letting μt

C represent the probability assigned by C todt = y, the price paid is taken as μt

C P.In other words, D must choose whether to use U’s product or not. Doing

so ensures high quality, whereas not doing so ensures low quality thatgenerates no consumer value. Also, the market price that consumers pay isalways given by their expected valuation of the good.

I impose the following informational assumptions. In period t, C doesnot observe wt. I will consider separately the cases in which consumersobserve whether D is using U’s product or not (that is, observe dt or not);the interpretation of these possibilities is described below. Also, in period tall players including C observe all actions from all periods t < t; this ensuresthat each period t starts a proper subgame.

Summarizing elements of the above, and suppressing time subscripts,payoffs within a given period are denoted by vi, for i ∈ {C, D, U}, and areas follows (where I( )d is the indicator function which is equal to one if Dchooses d = y and zero otherwise).

v y w cU = −I( )( ),

v P y wD C= −μ I( ) ,

9 Note that this also corresponds to a situation in which, although the quality of U’sproduct is subject to moral hazard by U, D is able to inspect the product sufficiently well toensure high quality.

JUSTIN P. JOHNSON34


v y P PC C= −I( ) .μ

In words, this just says that U receives the wholesale price less productioncost, so long as D actually uses the product, whereas D is able to charge mCPto consumers but pays w if it chooses to use U’s product, and consumersreceive their actual valuations if D uses U’s product, and always pay theprice mCP to D.

Let Vi denote the equilibrium total discounted payoffs. Also, define thestate variable Wt:

Ωtd y t

== <⎧

⎨⎩

1

0

, ,

, .

if for all

otherwiseτ τ

That is, Wt = 1 if D has provided high quality goods to consumers in allearlier periods, and otherwise Wt = 0. Recall that μt

C is the belief assignedby C to the choice dt = y in period t, and that if dt is observed by C then μt

C

is determined directly by D’s choice of dt. Note that a complete specificationrequires that C has beliefs not just over dt but also over wt. However, inalmost all cases this plays no role and so for simplicity I do not discuss thisexcept where it is important; the assumption is that C has beliefs over w thatare determined by the strategy of U.

Throughout the entire paper I consider sequential equilibria, typicallywith some additional restrictions. One such restriction is the following.

Restriction (R1). Equilibria satisfy the following properties.

(1) If the decision dt is not observed by C, then μtC

t= Ω ,(2) wt is Markov in Wt.

Recall that by assumption in period t all moves from period t < t areobserved by all players. The primary role of the Markov assumption is insimplifying analysis of events that are off the equilibrium path, includingexpectations by D about what the future wholesale price will be if U chargesan out-of-equilibrium price today. In any such equilibrium in which high-quality production takes place, it is supported by the threat that consumersnever again believe quality is high if they receive low quality in some period.

The main question I address in this paper is whether it matters to whomconsumers look for quality assurance, U or D. Consumers might seek outmanufacturers’ brand names or instead trust that retailers only carry highquality merchandise. Realistically, the exact process determining to whomconsumers look is complex and not fully understood. I adopt the followingdefinition, which allows for clean game-theoretic analysis.

Definition. When dt is not observed prior to the formation of C’s period-tbeliefs μt

C , I say that ‘D posts the reputational bond.’ When dt is observed



prior to the formation of C’s period-t beliefs μtC , I say that ‘U posts the

reputational bond.’

The rationale for this definition is as follows. When dt is not observed,consumers cannot know directly whose product D is reselling and hencedepend on D for quality assurance. On the other hand, when dt is observedprior to the formation of C’s period-t beliefs, consumers know whether U’sproduct is being used.

Conceptually, for consumers to know whether U has provided theproduct or not, U’s brand name or logo must be visible (this is likely anecessary rather than sufficient condition, for reasons discussed below).For example, a consumer who sees a box of Kellogg’s cereal knows fromwhere the product came because of the design of the box, and whensomeone buys a PC with an Intel Inside label on it, they know it has an Intelmicroprocessor inside. (This assumes that D cannot or does not fraudu-lently alter its own product to deceive consumers as to its source, forexample by affixing a counterfeit brand label.)

In many cases, the identity of the bondposter is a (past) choice variable.Indeed, one of my main results is that each firm would prefer to be thebondposter, and hence would be willing to expend resources to be the partythat consumers look to for quality assurance.

One factor influencing the identity of the bondposter is how easy it is forU to display its brand to consumers; the nature of a given product maymake it easier or harder for U to do this. For example, it is easy for Kelloggto design its boxes in a distinctive manner that consumers may seek out,and illegal for a grocer to sell counterfeit Kellogg’s cereal—although Dmight simply refuse to carry products with such distinctive brands. Simi-larly, an automobile manufacturer may be able to design its cars to bedistinctive and prominently place its logo on them, and it would be difficultfor a car dealer to remove these or counterfeit them. On the other hand, itwould be difficult for an engine manufacturer unilaterally to have its brandclearly visible to consumers; a similar story is true for many manufacturedgoods. Indeed, in many cases U, taken as the supplier of an intermediateinput, may need some support from D for its brand to be visible, as whenPC manufacturers agree to affix Intel Inside labels on the exteriors of theirPCs.

Although the visibility of U’s brand is often important, I emphasize thatI do not mean to suggest that, in reality, the brand name’s being visible ona product necessarily means that the manufacturer is the bondposter,although this may often be a necessary condition. As suggested already, thesituation is likely more complex. It seems perfectly plausible that even ifbrand names are observed by consumers, they may simply ignore them orbe unaware of their histories, and instead focus on the retailer’s identity.And the extent to which consumers choose to focus on D or U’s brand

JUSTIN P. JOHNSON36


when both are visible is likely influenced by a variety of factors such asadvertising and past experiences, which I do not model.

Indeed, Kaldor himself emphasizes (p. 18) that there is more to estab-lishing the ‘manufacturer’s dominion’ than simply putting a label on some-thing; an additional component is advertising.

But the mere provision of a trade-mark—even when combined withdistinctive packaging, labelling, and colouring—is not a very effectivemethod of securing consumer ‘goodwill’. . . . [I]t is a difficult business toinduce [consumers] to adopt buying habits sufficiently firm to make themdemand a particular brand when purchasing a commodity from retailers.It is here that large-scale advertising has a vital role to play. Advertisingmakes the public ‘brand-conscious’; it is not so much a a question ofmaking the consumer buy things which he would not have bought oth-erwise; but of crystallising his routine habits, of making him consciousthat keeping to a certain routine in consumption means not only buyingthe same commodities. . . but sticking to the same brands.

III(ii). Analysis

Here I present analysis of the model presented above, beginning with thecase in which U posts the reputational bond (recall that this refers to thesituation in which dt is observed by C in period t). Intuitively, when dt isobserved by C the asymmetric information problem is fully resolved: anyattempt by D to cheat the market will be detected and D is thereby relegatedsimply to passing U’s product on to the end consumer.

A ‘high quality equilibrium’ is one in which dt = y in all periods along theequilibrium path.

Proposition 1. Suppose that U posts the reputational bond, and thatc ≤ P. There exists a high quality equilibrium satisfying R1. In any suchequilibrium, w = P on the equilibrium path, so that U extracts all availablesurplus:

VP c

VU D= −−

=1

0δ

, .and

Proof. All proofs are in the appendix. �

Because U extracts the entire industry surplus when it posts the bond, itclearly can’t do any better when instead D does. In fact, U does strictlyworse in such circumstances due to the need to maintain D’s incentivecompatibility constraint.

I now derive D’s incentive compatibility constraint given that it is thebondposter. If it ‘defects’ by choosing dt = n then its payoff is P today but



its continuation payoffs are zero under R1 (because μtC = 0 whenever

Wt = 0), whereas if it instead always chooses dt = y then it assures itself ofP - w in each period. Thus, the wholesale price along the equilibrium pathmust satisfy

P wP w P

−−

≥ ⇔ ≤1 δ

δ .

When D posts the reputational bond the most U can charge is strictly lessthan P. Hence, so long as a high quality equilibrium exists in either case, Uis worse off when D posts the bond whereas D is better off.

I introduce the notation DVi for i ∈ {D, U} to indicate the difference inpayoffs when U posts the reputational bond as opposed to D, subject to ahigh quality equilibrium satisfying R1 existing in either case. Observe thatDVU = -DVD, so that the identity of the bondposter only influences theallocation of total surplus, not its magnitude.

The following proposition formalizes the above discussion.

Proposition 2. Suppose that D posts the reputational bond, and thatc ≤ dP. There exists a high quality equilibrium satisfying R1. In any suchequilibrium, w = dP on the equilibrium path and payoffs are

VP c

V PU D= −−

=δδ1

, .and

Thus, both U and D prefer to be the one who posts the reputational bond:DVU > 0 > DVD.

Propositions 1 and 2 explain how changing the identity of the bondpostershifts rents across the parties in the supply chain. Thus, if advertising andbrand-building activities influence whom consumers look to for qualityassurance, then it follows that asymmetric information can provide a rolefor these activities not only to guarantee product quality but also to claimrents in the supply chain.

Another view is as follows. If one takes the product quality concernsemphasized by Klein and Leffler seriously, then a version of the rent-shifting view of Kaldor and Steiner pops out immediately once multipleparties in the supply chain are introduced.

Observe, however, that this rent-shifting argument presumes that a highquality equilibrium exists whether U or D posts the bond but in fact theconditions for existence differ in these two cases so that the identity ofthe bondposter also influences whether high quality can be maintained. Thefollowing result clarifies this by showing that it’s easier to maintain highquality when U posts the bond and also emphasizes that restriction R1 isnot a crucial element for the argument.

JUSTIN P. JOHNSON38


Corollary 1. High quality equilibria exist on a strictly larger subset of theparameters when U posts the reputational bond. Precisely:

(1) For c ∈ [0,dP] there exists a high quality equilibrium satisfying R1,whether D or U posts the reputational bond.

(2) For c ∈ (dP, P] there exists a high quality equilibrium satisfying R1 if Uposts the reputational bond. However, if D posts the bond, then theredoes not exist a high quality equilibrium (regardless of R1).

(3) For c > P there exists no high quality equilibrium, whether D or U poststhe bond (regardless of R1).

The reason that it is easier to maintain a high quality equilibrium when Uposts the reputational bond is that so doing eliminates the possibility for Dto engage in moral hazard. In other words, when consumers look to U forquality assurance, D can no longer cheat the market and consequently thereis no meaningful incentive compatibility constraint for D that must bemaintained.

The literature on umbrella branding also considers how branding deci-sions influence the provision of high quality to the market; see for exampleWernerfelt [1988], Choi [1998], Cabral [2000] and Hakenes and Peitz [2008].One main conceptual difference between the literature on umbrella brand-ing and my work is that I consider the ramifications of the brandingdecision for a single product, whereas the umbrella branding literatureaddresses the question of how a multiproduct firm may link consumerexpectations across its entire portfolio of products so that quality isassured.

Another important conceptual difference is that the literature onumbrella branding focuses almost exclusively on the idea that linking dis-tinct products via branding may indeed make it easier to assure quality. Incontrast, the branding decision serves an additional important role in myanalysis, namely to redistribute rents across the supply chain.

A potential criticism of the results in this section is that only D canengage in moral hazard. For example, one might wonder whether alsogiving U an opportunity to cheat the market would overturn Proposition 1.However, in the next section I allow for both U and D to engage in moralhazard and show that this does not meaningfully change how the marketworks (in later sections I also allow for variable output and the possibilityof competition within a layer of production).

IV. A GENERAL MODEL

Here I generalize the model presented above in two ways. First, I allow forboth D and U to make investments that influence the quality of the finalproduct, in addition to allowing D to choose whether or not to use the input



produced by U. Second, I allow for a more general bargaining structure, asopposed to assuming that U makes take-it-or-leave-it offers to D.

Extending the model in these ways leads to essentially the same intuitionsand results, thereby further emphasizing the role that the identity of thereputational bondposter plays.

Formally, the game is the same as before except for the followingchanges. First, the wholesale price is determined according to the followingprocedure. There is some exogenously given value b ∈ (0, 1) such that ineach period U receives a share b of the total profits generated, so long as theresulting wholesale price satisfies all the incentive constraints (providedbelow). If the resulting wholesale price does not satisfy all of the incentiveconstraints, then instead the equilibrium value of w is that which is closestto the original value but does satisfy the constraints. If no such value exists,then there is of course no high quality equilibrium. I discuss the specifics ofthis rule in more detail below, after presenting the incentive constraints.

Second, both U and D make investments in quality. Specifically, Uchooses quality q l ht

U ∈{ , }, where this choice is not known to any otherplayers until the end of the period. If U chooses h (corresponding to highquality), it bears the cost cU > 0 if indeed D chooses to use it, but if U setsq lt

U = or D does not use U’s input then U bears no cost this period.D simultaneously makes two decisions in each period. First, it chooses

whether to use the product supplied by U, where this decision is denoted bydt ∈ {n, y}; choosing to do so results in it paying w to U. Second, it choosesquality q l ht

D ∈{ , } . If D chooses h (corresponding to high quality), it bearsthe cost cD > 0, but choosing l results in no investment costs’ being borne.Neither of these choices is observed by other players until the end of theperiod.

Investments are related to final product quality as follows, where thegeneral rule is that the final good only has a positive probability of beinghigh quality if at least one high quality input (that from U or D) is used, butthat high quality is assured if both inputs are high quality. In detail, if bothU and D make high quality investments and D uses U’s input (so thatq q ht

DtU= = and dt = y), then the final product quality is high with prob-

ability one, where the value of this product to consumers is denoted by P asin earlier analysis. If D invests in quality but U does not, or if D invests inquality but chooses not to use U’s input, then the final quality is high withprobability pD < 1. If D does not invest in quality, but uses U’s input and Uinvests in quality, then the final quality is high with probability pU < 1. Inall other circumstances, the final product is low quality with probabilityone, where these other circumstances correspond to the cases where neitherD nor U invest in high quality, and where D does not invest in quality andalso chooses not to use U’s input.

In this model, a ‘high quality equilibrium’ is one in which q q htD

tU= =

and dt = y in each period. I use the following equilibrium restriction, which

JUSTIN P. JOHNSON40


says that C believes quality is high if and only if it has been high in allprevious periods.

Restriction (R2). Equilibria satisfy the following properties.

(1) If the decision dt is not observed by C, then μtC

t= Ω ,(2) if the decision dt is observed by C, then μt

Ct= Ω unless dt = n, in which

case μtC = 0,

(3) wt is Markov in Wt.

The restriction is very similar to R1. The only difference is that in thepresent case consumers can never directly ascertain quality prior to pur-chase, whereas in earlier analysis, quality could be known with certaintywhenever U posted the bond (because U had no unobservable investmentto make). R2 specifies that consumers believe quality to be low with cer-tainty if U’s input is not used.

I impose several parametric restrictions. First,

c PU D< −( ) ,1 π

which simply says that it is efficient for U to invest in quality, given that Dis. That is, because D is investing in quality, there is a probability pD thatthe final product will be high if U does not invest in high quality, whichmeans that the marginal contribution of U in fact making a high qualityinvestment is (1 - pD)P - cU > 0. Second,

c PD U< −δ π( ) .1

This is a strengthening of the condition that says it is efficient for D to investin quality, given that U is. This condition is implied if it is assumed thatthere is no equilibrium in which U prefers D does not make investments inquality.10

I now present the incentive constraints associated with a high qualityequilibrium, beginning with U. U faces a single decision, whether or not itis the bondposter: it either invests in a high quality input to sell to D or doesnot, where it is optimal to do so if and only if

(ICU) cw c

UD U≤ − −−

δ πδ

( )( ).

11

The left-hand side measures the cost savings from skimping on U’s invest-ment, whereas the right-hand side measures the losses to U: if the final

10 More precisely, this condition would automatically be satisfied if there were no moralhazard involving U, and the parameters were such that U always preferred equilibria in whichD in fact made investments in quality, as opposed to equilibria in which D never made suchinvestments.



product is low quality, which happens with probability 1 - pD if U does notinvest in a quality input (assuming that D is so investing), then consumerslose faith in the quality of the product and so U loses the ability to capturethe margin w - cU in all future periods. This condition is easier to satisfywhen w is larger.

Now consider D’s choices. To ensure a high quality end product (giventhat U is investing in quality), D must use U’s input and also make its owninvestment in quality. Because D could either individually or jointly defecton these two actions, there are potentially three conditions involving D thatmust be satisfied in a high quality equilibrium, where the exact number ofconditions depends on the identity of the bondposter.

The first of these three conditions ensures that D would not wish to useU’s input but not make its own investment in quality:

(ICD1) cP w c

DU D≤ − − −

−δ π

δ( )( )

.1

1

Such a defection saves cD today but places the discounted value ofP - w - cD at risk tomorrow. In particular, because (only) U’s input is stillbeing used in such a defection, there is a 1 - pU chance that the finalproduct will be low quality.

The second condition ensures that D would not choose to make its owninvestment in quality but not use U’s input, which saves it w today but alsorisks future margins:

(ICD2) wP w cD D≤ − − −−

δ πδ

( )( ).

11

The third of the three conditions involving D ensures that D would notchoose to both not make its own investment in quality and not use U’sinput. Defecting in such a manner saves cD + w today but ensures a lowquality final product and hence the loss of all future margins.

(ICD3) c wP w c

DD+ ≤ − −

−δ

δ( )

.1

There are two points to note about D’s incentive constraints, given by(ICD1)–(ICD3). First, they all become harder to satisfy when w is larger—they constrain the maximum wholesale price. Second, (ICD1) must besatisfied whether D or U posts the reputational bond, whereas (ICD2) and(ICD3) need only be satisfied when D posts the reputational bond. Thereason that these last two constraints need not be satisfied when U posts thebond is that both of these constraints involve D’s not using U’s input, whichis not an option when U posts the reputational bond (because if this occurs,consumer beliefs are such that quality is assumed to be low this period).

JUSTIN P. JOHNSON42


With these constraints in hand, the bargaining rule can be explained inmore detail. Because a higher value of w always makes it easier to satisfyU’s constraint but harder to satisfy D’s constraints, the net effect of thebargaining rule can be stated as follows. If setting w so that U receives a bshare of the generated surplus satisfies all the incentive conditions, thenthat value of w is the equilibrium level. However, if (only) U’s constraint isviolated, w is instead raised to the lowest possible level that does satisfy U’sconstraint, so long as this level continues to satisfy D’s constraints. On theother hand, if only D’s constraints are violated, w is lowered to the largestpossible level that does satisfy these constraints, so long as this level con-tinues to satisfy U’s constraint. If this process does not yield a value wsatisfying all required constraints, then there is no high quality equilibrium.

From this discussion it is clear that when D posts the reputational bond,there are four constraints that must be satisfied in order for a high qualityequilibrium to exist, but only two must be satisfied when U posts the bond.Given this, it is not surprising that having U be the bondposter alwaysexpands the parameter set on which a high quality equilibrium can bemaintained, exactly as in earlier analysis.

To see that this is so, assume that there exists a high quality equilibriumwhen D posts the reputational bond, and denote the induced wholesaleprice by wD. Because wD satisfies (ICU) and (ICD1)–(ICD3), if instead Uposted the reputational bond, it would be possible to find a correspondingwholesale value using the bargaining process described above and denotedby wU that would satisfy (ICU) and (ICD1). This ensures that the set ofparameters on which a high quality equilibrium exists is at least weaklylarger when U posts the bond; details for why it is in fact strictly easier tosupport a high quality equilibrium when U is the bondposter are deferredto the proof of Proposition 3.

The remaining question is whether the identity of the bondposter influ-ences the profits of U and D, assuming that a high quality equilibrium infact exists when D posts the bond. That is, when is it the case that wD < wU,so that the wholesale price is higher when U posts the bond and, conse-quently, each party prefers to be the reputational bondposter?

Intuitively, when D is posting the reputational bond and it is the case thatawarding D only a 1 - b share of the surplus provides insufficient incentivesfor D, then the value wD must equilibrate downwards. Alternatively, Umight instead be the bondposter, which would relax D’s incentive con-straints so that the original value of w might feasibly support a high qualityequilibrium. That is, having U post the bond in such a situation wouldallow for a higher wholesale price to emerge, so that wU > wD.

Therefore, it is to be expected that the identity of the bondposter influ-ences the distribution of profits whenever b is such that D would be mosttempted to cheat the market, given that it could do so by secretly not usingU’s input (or by both not using U’s input and not making its own invest-



ment). Not surprisingly, this happens whenever b is sufficiently large, sothat (absent D’s incentive constraints) U could command a large share ofthe total surplus.

The following proposition summarizes the discussion above. Recall thatthe notation DVi, for i ∈ {D, U}, indicates the difference in payoffs whenU posts the reputational bond as opposed to D, and that as beforeDVU = -DVD, so that the identity of the bondposter only influences theallocation of total surplus (contingent on a high quality equilibrium’s exist-ing in either case).

Proposition 3. In the model with generalized investments and bargainingin which U’s bargaining power is indexed by b ∈ (0, 1), the followingstatements are true under R2.

(1) High quality equilibria exist on a strictly larger set of parameters whenU posts the reputational bond.

(2) Suppose that a high quality equilibrium exists regardless of the bond-poster. There exists a value b* < 1 such that if b > b*, both U and Dprefer to be the one who posts the reputational bond: DVU > 0 > DVD.For b ≤ b*, the identity of the reputational bondposter has no impacton the split of surplus between U and D.

Proposition 3 emphasizes that the insights from the simple model of Section3 are robust to substantial generalization concerning the types of invest-ments that players make in quality, and also to the process whereby w isdetermined. Indeed, the intuition is very similar to that from the basicmodel, and as discussed just above: because U’s being the reputationalbondposter makes it more difficult for D to cheat the market, it is easier toensure the existence of a high quality equilibrium, and it is possible for w torise as a result.

Proposition 3 also shows, however, that if U has low bargaining power,so that b < b*, bondposter identity no longer influences the distribution ofrents. It is important to note, however, that the result on profit-shifting isonly neutralized in these cases, but never reversed: having U be the bond-poster never lowers U’s profits.

Also note that shifting the identity of the bondposter from D to U onlyeliminates constraints. That is, it does not become easier for U to cheat themarket when it becomes harder for D to cheat the market. Hence, there isno incentive tradeoff that occurs when U becomes the bondposter, butinstead there is a global improvement in incentives.

This observation confirms that it is not a question as such of whether Dor U has stronger incentives to cheat the market, or whether they discountfuture payoffs differently; such matters are central to the analysis of mid-dlemen in Biglaiser [1993] and Biglaiser and Friedman [1994]. Here, insteadof the issue’s being which incentive compatibility constraint is easier to

JUSTIN P. JOHNSON44


satisfy, U’s or D’s, the issue is how many incentive compatibility constraintsmust be satisfied.

V. VARIABLE OUTPUT

Here I extend the analysis by incorporating a quantity decision. By sodoing, I identify a third impact of bondposter identity, one which influencestotal social welfare even conditional on a high quality equilibrium’s exist-ing.11 Extending the analysis in this direction also is useful because in thenext section, competition between quantity-setting firms is introduced.

For convenience, I return to the basic model of Section 3 (where only Dmay engage in moral hazard by not using U’s input), except as noted here.The first change is that simultaneous to choosing dt ∈ {n, y}, D sets anoutput level Xt that is the number of units sold to C and also the number ofunits purchased from U if dt = y. (If dt = n then zero units are purchasedfrom U and U produces no units.) The second change is that the marketprice is μt

CtP X( ), where P(X) is strictly decreasing with P′ + XP″ < 0 and

3P″(X) + XP�(X) ≤ 0.12 I use the equilibrium restriction R1 in this section.Within-period payoffs are as follows (as earlier, I suppress time sub-

scripts and let II(d) be the indicator function which is equal to one if Dchooses d = y and zero otherwise).

v y w c XU = −I( )( ) ,

v XP X y XwD C= −μ ( ) ( ) ,I

v y P X P X dXC CX= −∫ [ ( ) ( ) ( )] .I � �μ

0

I first assess the case where U posts the bond, then the case where D does,and afterwards provide comparison and discussion.

V(i). The Upstream Firm Posts the Reputational Bond

X w X P X w w X w w cX w

* and * *( ) arg max ( ( ) ), arg max ( )( ).= − = −

These are the retail quantity schedule and equilibrium wholesale pricethat would persist in a static model with linear prices in the absence of

11 Recall that in the earlier analysis, if a high quality equilibrium exists regardless of whoposts the bond, then the identity of the bondposter serves only to shift rents between Uand D.

12 The last assumption ensures that in the absence of asymmetric information U faces aconcave optimization problem.



asymmetric information. They are also the equilibrium objects in therepeated game, as stated in the following proposition.

Proposition 4. Suppose that D chooses an output level Xt in addition todt ∈ {n, y}, that only D may engage in moral hazard, and that U posts thereputational bond. If c < P(0), then there exists a high quality equilibriumwith positive output satisfying R1. In it, the wholesale price and output aregiven by w* and X*(w*) on the equilibrium path.

I defer discussion of this result until after analysis of the market outcomewhen D posts the reputational bond.

V(ii). The Downstream Firm Posts the Reputational Bond

Now suppose that D posts the reputational bond and consider a proposedequilibrium value w. In any period in which only high quality products havebeen sold to C previously, the incentive compatibility condition for D tofaithfully resell U’s product is

(1)max ( ( ) )

max ( ).X

X

X P X wXP X

−−

≥1 δ

There exists a unique value w > 0 such that this condition holds preciselywhen w ≤ w.13 Hence, in any high quality equilibrium, the wholesale pricesatisfies w ≤ w and U maximizes its per-period profits subject to this con-straint. That is, U’s maximization program is

max * , s.t.w

X w w c w w( ) −( ) ≤ ˆ.

These observations are stated formally in the following proposition.

Proposition 5. Suppose that D chooses an output level Xt in addition todt ∈ {n, y}, that only D may engage in moral hazard, and that D poststhe reputational bond. In any high quality equilibrium satisfying R1, thewholesale price and output are given by w = min[w*, w] and X*(w) on theequilibrium path.

V(iii). Comparison and Discussion of the Two Regimes

Comparing Proposition 4 to Proposition 5, it is apparent that the equilib-rium wholesale price must be (weakly) higher when U posts the bond,

13 The reason this condition is correct is that I am focusing on equilibria satisfying R2, sothat μt

C depends only on Wt, not Xt. However, note that the construction of a high qualityequilibrium does not rely on this assumption. That is, if the beliefs of the consumer μt

C canalso depend on Xt, it is certainly still possible to construct an equilibrium.

JUSTIN P. JOHNSON46


leading to higher profits for U. In addition to influencing the payoffs of Dand U, however, the final market output may change due to the change inthe wholesale price. The following corollary clarifies.

Corollary 2. Suppose that D chooses an output level Xt in addition todt ∈ {n, y}, that only D may engage in moral hazard (by not using U’sinput), and that c < P(0). Then, all else fixed, there exist d1 and d2 with0 < d1 < d2 < 1 such that for all d > d1 the following hold.

(1) There exists a high quality equilibrium with positive output satisfyingR1, whether D or U posts the reputational bond.

(2) Both U and D prefer to post the reputational bond under R1:

Δ ΔV VU D≥ ≥0 ,

where these inequalities are strict if d ∈ (d1, d2) and hold with equalityfor d ≥ d2.

(3) When U posts the reputational bond rather than D, equilibrium outputgoes down and so does social welfare, under R1:

Δ Δ ΔV V VC D U+ + ≤ 0,

where this inequality is strict if d ∈ (d1, d2) and holds with equality ford ≥ d2.

Also, if d < d1, a high quality equilibrium only exists if U posts thereputational bond.

Although Corollary 2 confirms the earlier intuition that both U and Dwould prefer to be the poster of the reputational bond (conditional on ahigh quality equilibrium’s existing irrespective of who the bondposter is),an important difference between earlier results exists. In particular, whenoutput is variable, having U post the reputational bond leads to loweroutput and lower social welfare, whereas when output is not variable,having U post the bond does not have any negative welfare consequences.

The intuition for this additional distortion follows readily from thatalready developed; when U posts the bond, it raises the wholesale pricewhich leads to an increase in the retail price, thereby hurting C and indeedsocial welfare as a whole.

A related point is that the gains to U from becoming the bondposter arenot exactly offset by the losses to D—DVU + DVD � 0, unlike in previousanalysis in which there was no quantity distortion associated with bond-poster identity. Instead, the losses to D outweigh the gains to U, so thatindustry surplus as well as social surplus declines when U becomes thebondposter, despite the fact that U privately gains: DVU + DVD < 0. This isa simple consequence of the fact that when U raises w, D buys fewer unitswhich moderates the profit gain to U. In particular, this moderating force



has a first-order effect on U’s profits, whereas the envelope theorem impliesthat this has zero first-order effect on D’s profits.

Note that neither the decline in social welfare nor that in industry profitsarises when firms are sufficiently patient. In fact, Corollary 2 shows thatwhen output is variable and firms are sufficiently patient, the identity of thebondposter has neither a distributional nor a welfare impact; neitherwholesale nor retail terms of trade depend on who the poster is. The reasonis that when output is variable it is eventually the case (even under sym-metric information) that further increases in w lower U’s profits due to thedouble markup problem. Thus, although the range of incentive-compatibleprices increases with d, it is not optimal for U to take advantage of this pasta certain level. This is different from the case in which a single unit istransacted, for in that case U always wishes to raise w to squeeze moresurplus from D’s trade with C.

Note, however, that if I were to introduce two-part pricing schemesbetween U and D then the distributional role of bondposter identity wouldreturn even if firms were very patient. The reason is as follows. U wouldalways prefer to provide goods to D at marginal cost and extract surplusthrough the fixed fee. But this means that the total surplus extractable fromC per period can simply be considered a given value �P , where

�P X P X cX

= −max ( ( ) ).

Both D and U wish to claim as much of this fixed value �P as possible,and the analysis from Section 3 applies by simply interpreting the value wtthere as the per-period fixed fee (given that the variable input price is setat c).

VI. BATTLE OF THE BRANDS AND THE ROLE OFDOWNSTREAM COMPETITION

In this section I build on Kaldor, Steiner and Farris and Albion by assum-ing that advertising and other branding activities are tools to influencewhether U or D is in the forefront of consumers’ minds and consequentlywho the reputational bondposter is. As earlier results have already made itclear that in many cases both U and D would prefer to be the bondposter,my goal here is to ascertain who would be willing to pay more to achievethat goal.

That is, if there were a battle for the attention of consumers (with thevictor being the bondposter), who would win it? To the extent that awillingness to expend resources increases the likelihood of securing one’sfavored outcome, answering this question helps predict who the bond-poster will be.

JUSTIN P. JOHNSON48


I do not provide a formal model of the competition to become thebondposter, although that may be a useful direction for future research.One possibility is that such conflicts are similar to patent races in that oncea firm reaches a certain lead (in terms of brand-recognition) the other firmstops advertising. Similarly, it may be that having a head start is a signifi-cant advantage in such cases.

It may also be that there is a connection between innovation and the abilityto establish a brand. For example, suppose that advertising by U is moreeffective when U’s product is higher quality relative to outside options. Insuch a case it may be easier for U to establish a reputation, and hence increaseits own profits, when it has recently innovated. This predicts a relationshipbetween advertising and innovation that is driven primarily by the desire toshift rents in the vertical chain as opposed to driving new demand.

The main results here indicate that the competitiveness of the down-stream segment plays a crucial role in this determination. I begin with aresult on bilateral monopoly and then extend to the case of downstreamcompetition.

VI(i). Bilateral Monopoly

Suppose as in earlier analysis that both layers of the supply chain aremonopolized. Also recall that from earlier analysis we know thatDVU ≥ 0 ≥ DVD, and that this means that D is willing to pay more than U tobe the bondposter if and only if DVD + DVU < 0, which is in turn equivalentto the joint surplus of D and U being higher when D posts the bond.

Proposition 6. Suppose that D chooses an output level Xt in addition todt ∈ {n, y}, that only D may engage in moral hazard, and that a highquality equilibrium with positive output satisfying R1 exists whether D orU posts the reputational bond. The downstream firm is always willing topay more to post the reputational bond than the upstream firm is:DVD + DVU ≤ 0, where this inequality is strict for d in some interval (d1, d2),all else fixed.

Proposition 6 shows that D would pay more than U would for the rightto post the bond. The logic is that U’s posting the bond leads to an increasein the wholesale price, causing two effects. First, there is an increase inpayments from D to U on all units currently being sold; this is merely atransfer. Second, D responds by reducing total purchases from U. Thissecond effect causes the joint surplus of D and U to fall.

I do not mean to suggest that the downstream firm should be expectedalways to post the reputational bond in bilateral relationships. Rather, asmentioned above, who emerges as the bondposter is likely influenced by anumber of factors including but not limited to DVU and DVD. For example,one additional factor identified by Kaldor in the transition away from the



‘wholesalers’ dominion’ and towards the ‘manufacturers’ dominion’ is theease with which manufacturers became able to reach end customers withadvertising.

The exact outcomes will therefore depend on the precise underlyingmechanism and may vary across markets and time. Although I do notprovide a concise description of what this mechanism is, one importantforce among the many other factors that may influence the identity of thebondposter is the presence of competition within a layer of the supplychain. Consider for example the PC and laptop markets, in which manyconsumers associate end product quality with the presence of an Intelmicroprocessor. It is also the case, as discussed in more detail below, thatthe downstream market of original equipment makers (OEM’s) is muchless concentrated than the upstream market. I now investigate the connec-tion between these two observations.

VI(ii). The Influence of Downstream Competition

Here I introduce downstream competition and show that it is possible forU to value controlling the brand more than the downstream layer of thesupply chain (collectively) does. The model is as before with the followingchanges. There are now m downstream firms labeled i = 1, 2, . . . , m whocompete in quantities. In each period t, after U sets a common wholesaleprice wt for all m firms, each of the downstream firms simultaneouslychooses output and also whether to resell the product of U or instead use alow quality substitute. Thus, in each period each downstream firm chooses(Xti, dti), where dti ∈ {n, y}.

The terminology is as before: when the {dti} are visible to C each periodfor which I say that U posts the reputational bond, and when the {dti} arenot visible I say that the downstream firms post bonds. Define theexpanded state variable Wt as the vector in which the ith component equalsone if firm i has chosen y in all previous periods, and otherwise equals zero.Denote the i component of this vector by Wti.

Let μtiC be C’s belief that firm i in period t is choosing dti = y. I also take

this to be not just the belief of the end consumer but also of all firms j � i.Restricting attention to cases where μti

C ∈{ , }0 1 , adopting the conventionthat Xti = 0 for all firms with μti

C = 0, and also assuming linear demand forsimplicity, the market price in period t is

P Xt tjj tj

C

= −=

∑11{ : }

.μ

In other words, there is linear demand but only units produced by firmsthat consumers believe are producing high quality units (that is, those firmsj such that μtj

C =1 ) influence the market price.

JUSTIN P. JOHNSON50


I now present some additional notation that will make it easier to statethe main proposition below. In the equilibrium constructed there, down-stream firms use static Cournot strategies. When U posts the bond, thismeans that in period t all firms choose dti = y and choose Xti to maximizetheir static Cournot profits. Building on earlier notation, X wk*( ) is theequilibrium industry output of a static Cournot game with k firms facinglinear demand and input price w, and

w X w w ckw

k* arg max *( )( )= −

is the input price U would charge those k firms in the absence of asymmetricinformation.

When the downstream firms post bonds, all equilibria I consider are suchthat the μti

C are determined at the beginning of the period, both on and offthe equilibrium path, so that consumer beliefs do not depend on contem-poraneous output. That is, consumers assume any given firm is producinghigh quality units today so long as it has always done so in the past. Thismeans that the static objective function of a firm that has never cheated canbe written as follows (maintaining the convention that Xtj = 0 for thosefirms with μtj

C = 0):

πμ

μ

ti

ti tjj t ti

ti tjj

X X w d y

X X

tjC

tjC

=− −( ) =

−( )=

=

∑

∑

1

1

1

1

{ : }

{ : }

, ;if

,, .if d nti =

⎧

⎨⎪

⎩⎪

In other words, within each period, firms act as Cournot competitors, buta firm may choose to defect from a high quality equilibrium and in so doingsave the per-unit wholesale input price w.

Of course, if a firm chooses to defect and thereby save input costs today,it loses all future profits. To find the highest w such that no firm would wishto defect, define wk such that

X wk

X w wX

kk

X w X

kk k

Xk

**

max *

ˆˆ ˆ )

ˆ .

( ) − ( ) −[ ]−

= − − ( )−⎡⎣⎢

⎤⎦⎥

1

11

1δ

The left-hand side of this expression gives the present discounted value ofa single downstream firm’s Cournot profits, for given wholesale prices, andthe right-hand side gives the maximum profit a firm can make by defectingfrom a high quality equilibrium in which each other firm is producing theequilibrium per-firm Cournot output X*(wk)/k. The value wk that equalizesthese two terms gives the maximum value that U can charge and still inducefirms to use its input.



Building on earlier notation, agree that DVD is the change in the payoffto a single downstream firm from U’s becoming the bondposter in a highquality equilibrium, and that as before DVU is the corresponding change toU’s profits.

Proposition 7. In the model with m > 2 downstream firms that compete inquantities there exist d1 and d2 > d1 such that, whether D or U posts thereputational bond, if d > d1 then there exists a high quality equilibriumsatisfying the following properties.

(1) If U posts the bond, then w wt m= * along the equilibrium path.(2) If D posts the bond, then w w wt m m= min[ *, ]ˆ along the equilibrium path.(3) The upstream firm is willing to pay more to post the reputational bond

than all downstream firms combined. That is, DVU + mDVD ≥ 0, wherethis inequality is strict for d ∈ (d1, d2).

Comparing Proposition 6 to Proposition 7 shows that controlling thereputational bond becomes relatively more valuable to U as the down-stream becomes more competitive. The intuition for why competition mayoverturn Proposition 6 is as follows. Because individual downstream firmsdo not internalize the impact of their output on the profits of other down-stream firms, there is the typical negative externality associated with theiroutput. An increase in the wholesale price is like imposing a tax on outputand partially mitigates this externality, thereby reducing the total profit lossexperienced by these firms when U becomes the bondposter. Of course, thiseffect is only present when there is downstream competition. (Also notethat this effect need not always be strong enough that U would pay more tobe the bondposter, although as shown this is the case when there is lineardemand.)

This does not imply that the downstream is better off when U becomesthe bondposter; with linear demand, it is never the case that an increase ininput costs raises Cournot profits. Nonetheless, this beneficial strategiceffect partially mitigates the loss from heightened wholesale prices conse-quent to U’s becoming the bondposter; the net effect is that U stands togain more than the downstream collectively loses.14

Intel provides a potential example of an upstream firm willing to pay tobecome the reputational bondposter. In 1991, Intel introduced the ‘IntelInside’ marketing campaign. One component of this campaign involvedconvincing OEM’s to put the Intel logo on the exterior of their products.

14 Note that U might potentially benefit if it could change the number of active downstreamfirms. For example, if m is very large, U will only be able to charge slightly above marginalcost and so it would prefer a smaller number of retailers, even if overall output were todecline. Nonetheless, Proposition 7 is correct as stated, because it merely states that thereexists some equilibrium in which the stated results hold.

JUSTIN P. JOHNSON52


Intel also provided advertising allowances to OEM’s for their print adver-tising if it incorporated the Intel logo. Intel Inside is described by Intelthusly:15

Key to this strategy was gaining consumer’s [sic] confidence in Intel as abrand and demonstrating the value of buying a microprocessor from theindustry’s leading company, the pioneer of the microprocessor. . . .[A]ssociating Intel with ‘safety,’ ‘leading technology’ and ‘reliability,’ thecompany’s following—and consumer confidence—would hopefullysoar. That would create a new ‘pull’ for Intel-based PC’s.

Not all OEM’s were enthusiastic about the campaign. Compaq and IBM,in particular, strongly opposed it on the grounds that it reduced the brandequity of their completed products.16 Nonetheless, eventually these com-panies took part in the campaign.

The Intel Inside history is consistent with the theoretical results givenabove. First, the OEM market was almost surely more competitive thanthe x86-compatible microprocessor market in the 1990’s. For example, in1994, Compaq was the PC leader in sales with 13.6%, whereas in 1993Intel supplied 74% of the x86-compatible microprocessor market.17

Second, although it is difficult to assess precisely, the campaign is oftenconsidered a success for Intel that helped solidify its dominance of themarket; certainly the reluctance of some OEM’s to participate is consist-ent with this.

As described above, OEM participation was required to get the Intellogo on PC’s and in print advertising of OEM’s, ultimately leading Intel topay OEM’s to participate. Hence, as a theoretical matter it is possible that,despite the protests of certain large OEM’s, the overall downstreammarket as well as Intel benefitted; Proposition 7 does not provide guidanceas to how well off exactly the downstream market will be if U is able toseize the reputational bond by convincing downstream firms to assist it inso doing. Of course, it may also be that Intel played the downstream firmsagainst one another and ultimately made them worse off. In particular, itmay be that once Intel achieved a certain level of brand recognition withthe help of some downstream firms, not participating became an extremelyunpalatable alternative and this may have allowed Intel to transfer rela-tively meager rents to the downstream firms and yet seize the reputationalbond.

15 See www.intel.com/pressroom/intel_inside.htm for all the claims in this paragraph.16 ‘Why Compaq is Mad at Intel,’ Fortune, October 31, 1994.17 ‘Why Compaq is Mad at Intel,’ Fortune, October 31, 1994, and ‘Intel Market Share

Rises,’ New York Times, February 21, 1994.



VII. CONCLUSION

I have shown that the identity of the bondposter has important welfare anddistributional consequences. Incorporating two very standard economicideas, namely asymmetric information and a tension within the supplychain, readily reveals that a firm that puts itself in the forefront of consum-ers minds can shift rents to itself and away from others in the supply chain.My results therefore justify the common emphasis amongst business prac-titioners on the importance of ‘controlling the brand’ and (for manufac-turers) of establishing a connection directly with consumers rather thanrelying on retailers to boost sales.

In terms of the existing literature, I have shown that two seeminglydistinct arguments regarding the role of advertising are actually closelyintertwined; the presence of asymmetric information alone provides notonly a quality assurance role for brands but also a rent-shifting role. In thismanner the arguments of Klein and Leffler are extended to encompassthose of Farris and Albion, Kaldor and Steiner.

APPENDIX

Proof of Proposition 1. I first construct a high quality equilibrium. Let wt = P for anyvalue of Wt, and dt = y if and only if wt ≤ P. Note that (because dt is observable to C)μt

C =1 if dt = y and 0 otherwise. Given this, D has a zero continuation payoff in anyperiod given U’s strategy in the proposed equilibrium. Hence D’s proposed strategy isoptimal. Because U extracts the full surplus given D’s strategy, and because P ≥ c byassumption, its strategy is also optimal.

Now consider any other proposed high quality equilibrium that satisfies R1. I willshow that it is also the case that wt = P on the equilibrium path. Define w(i) to be thewholesale price given i = Wt ∈ {0, 1}. Suppose that w(0) < P. Then in any period t withWt = 0, U could set wt = (w(0) + P)/2 > w(0). Because D’s action will not change Wt fort > t given that Wt = 0, D’s action will not change future wholesale price offers of U,and hence D is best off accepting U’s offer in this period. Thus, w(0) = P. Finally,consider any period t with Wt = 1 and suppose that w(1) < P. If U instead offerswt = (w(1) + P)/2, then it is optimal for D to accept this offer, because not doing soleads to zero payoffs today and wt = P in all future periods (because Wt will equal zeroin such periods), whereas accepting the offer leads to positive payoffs. Hence, wt = Pin all periods. �

Proof of Proposition 2. First note that, as suggested in the text above, both D and Uhave zero continuation payoffs whenever D chooses n in some period. Thus, settingdt = n and wt = P for Wt = 0 constitutes equilibrium strategies (off the equilibriumpath).

Now suppose that Wt = 1. Under R1, if w(1) > dP then as shown above it is notoptimal for D to choose dt = y. Hence w(1) ≤ dP in any high quality equilibriumsatisfying R1. Suppose that w(1) < dP. Then U could set wt = (w(1) + dP)/2, and itwould be optimal for D to choose dt = y. Hence, an equilibrium exists so long as it isin fact profitable for U to supply the product at this price, that is so long as c ≤ dP. In

JUSTIN P. JOHNSON54


particular, for Wt = 1, set wt = dP and dt = y if and only if wt ≤ dP. Payoffs follow fromdirect computation. �

Proof of Corollary 1. Given Propositions 1 and 2, and that clearly a high qualityequilibrium cannot exist when c > P, it is sufficient to show that if c > dP and D poststhe reputational bond then there does not exist a high quality equilibrium (evenwithout R1).

Consider any high quality equilibrium, letting wt denote the equilibrium wholesaleprices. Note that for U to indeed supply the product to D it must be that

cwt t

t1 0−≤

=

∞

∑δδ .

Let VtD ≥ 0 represent the continuation payoffs to D if it chooses dt = n in period t,

given that Wt = 1. Then incentive compatibility for D requires that

P V P w wP c P

c PtD t

tt

tt

t

+ ≤ − ⇒ ≤−

⇒−

≤−

⇔ ≤=

∞

=

∞

∑ ∑δ δ δ δδ δ

δδ

δ( ) ,0 0 1 1 1

where I have used the inequalities on both VtD and c from just above. �

Proof of Proposition 3. I begin by showing that (ICD1) is strictly easier to satisfythan (ICD3), so that if for some w it were preferable for D to defect from a highquality equilibrium when U is posting the reputational bond, it would also find itoptimal to do so if it were posting the bond. Showing this will make the rest of theproof straightforward.

Algebra reveals that (ICD1) can be written as

w P cc

DD

U≤ − −

−−

( )( )

,11

δδ π

and (ICD3) can be written as

w P cD≤ −δ .

Now,

P cc

P c P cDD

UD U D− −

−−

> − ⇔ − >( )( )

( ) ,11

1δ

δ πδ δ π

which is true by assumption. Hence the result has been shown.Now consider the claim that high quality equilibria exist on a strictly larger subset

of parameters when U posts the bond. It was explained in the text that there must beat least a weakly larger equilibrium set when U posts the bond, and so it is sufficientto show that there is a vector of parameters that supports an equilibrium when Uposts the bond but not when D does. To this end, take any parameter vector that onlyweakly supports a high quality equilibrium when U posts the bond, so that there is buta single value of w that satisfies both (ICU) and (ICD1); such a configuration canalways be constructed by starting with any vector of parameters that supports a high



quality equilibrium and increasing cU until only a single value of w satisfies bothconstraints.

Now, if instead D posted the reputational bond, (ICD3) would also need to besatisfied. But because it was just shown that this constraint is strictly harder to satisfythan (ICD1), there can be no value of w that would satisfy all four required incentivecompatibility conditions, and the result follows.

Now consider the second claim of the proposition, supposing that a high qualityequilibrium in fact exists. Let w denote the highest value of w that satisfies all fourincentive constraints, and consider how wD changes with b. Clearly, for sufficientlylarge values of b, w wD = , which means that one of D’s incentive constraints is bindingat this level of w.

Let b* denote the smallest value of b such that w wD = , and note that b* < 1. Thereason that b* < 1 is that in a neighborhood around b = 1 the default bargainingposition is to give D close to zero profits, which is insufficient to secure D’s investmentbecause cD > 0. Thus, w wD = in some neighborhood of b = 1, so that b* < 1.

For b < b*, w wD < which means that all of D’s incentive constraints are slack atwD. Hence, having U post the bond instead of D would not change the equilibriumvalue of w, because doing so only removes incentive constraints involving D;wD = wU. Similarly, for b = b*, one of D’s constraints has only just begun to bind,and so the value of w that gives U exactly a share b* of the surplus still satisfies allthe constraints.

Now consider b > b*. Because w wD = in this case (by definition), it must be thatone of D’s constraints would be strictly violated if w granted U a b share of thesurplus, because w is the largest feasible value of w. Thus, U is receiving less thana b share of the profits, because this is the only way to ensure D does not defect. Ifthe binding constraint is either (ICD2) or (ICD3) instead of (ICD1), then having Ube the bondposter strictly relaxes the constraint on w, and hence it is the case thatwU > wD. But I had already shown at the start of the proof that (ICD3) was harderto satisfy that (ICD1), so that (ICD1) cannot be the binding constraint at w . Hence,the result follows. �

Proof of Proposition 4. As in (some) earlier analysis, because D’s decision isobserved by C, μt

C =1 if dt = y, and μtC = 0 if dt = n.

First consider subgames in which Wt = 0. I show that in such cases, U sets wt = w*and D plays X*(w) and y. To see this, first note that if D chooses dt = n, then becauseμt

C = 0, D earns zero that period. In contrast, choosing dt = y implies μtC =1 and

hence D earns X*(w)(P(X*(w)) - w) ≥ 0. Also, because (under R1) U is playing astrategy that is Markov in Wt, and because Wt = 0 implies Wt = 0 for t > t, D’s actionwhen Wt = 0 has no impact on future play, and it follows that it is indeed optimal forD to choose X*(w) and y. Given this, when Wt = 0, choosing w* is optimal for U, sothat output is X*(w*).

Now suppose that Wt = 1. I show that U sets wt = w* and D chooses X*(w) and y insuch subgames. Note that the equilibrium value of w in this case cannot exceed w*, forif it did U would prefer to set w = w*, which would continue to induce D to select y andconsequently raise profits today for U (and D). Similarly, for w < w*, if U raises w tow*, then D will still choose y because it anticipates w < w* in future periods by sodoing, as opposed to w* in future periods if it sets dt = n (leading to Wt+1 = 0).Moreover, raising w to w* raises profits today for U. Hence, under R1, w = w* when

JUSTIN P. JOHNSON56


Wt = 1. This ensures a high quality equilibrium, and to verify that there is positiveoutput, note that because c < P(0), it is the case that w* ∈ (c, P(0)) and hence X* ispositive. �

Proof of Proposition 5. Consider any high quality equilibrium satisfying R1. Con-sider Wt = 1, and note the equilibrium w must satisfy w ≤ w, for otherwise D wouldchoose n. Also, it must be that w ≤ w*, for otherwise U could lower w in any period tand earn higher profits without causing D to choose n. Hence, w ≤ min[w*, w]. Finally,note that the conditions imposed on P(X) ensure that (w - c)X*(w) is concave, ignor-ing the constraint w ≤ w, and hence concave in the region w ≤ [w*, w]. The resultfollows. �

Proof of Corollary 2. As is clear from Inequality (1), when D posts the reputationalbond, for any w that U might charge, there is a required size that d must exceed forthere to exist a high quality equilibrium. Define d1 as the lowest value of d for whicha high quality equilibrium exists if U charges c > 0, and define d2 as the lowest valuesuch that a high quality equilibrium exists when U charges w*. Because there is nomoral hazard when U posts the bond, and because d > d1 ensures that U can chargew > c and still ensure a high quality equilibrium, then by definition statement (1) of thecorollary follows, as does the final claim about no high quality equilibrium’s existingwhen d < d1 and D is posting the bond.

Now, for d > d2, U is not constrained in selecting the wholesale price regardless ofwho posts the bond, and so w = w* in either case, using Propositions 4 and 5.However, by definition, for d ∈ (d1, d2), when D posts the bond it must set w < w*. Thestatements in (2) follow.

To show (3), note that social welfare is simply the discounted value of the usualarea between the demand curve and marginal cost c. Now, for d > d2 there is nochange in w and hence no change in X depending on who posts the bond. However,for d ∈ (d1, d2), w increases from w to w* when U posts the bond, leading to a declinein X and social welfare. �

Proof of Proposition 6. Take d1 and d2 as defined in the proof of Proposition 2. Ford ∈ (d1, d2), U is constrained in the wholesale price it can set when D is the bondposterand to ascertain the effect of U’s becoming the bondposter one can consider the effectof relaxing slightly the constraint w ≤ w. From the envelope theorem, the change inper-period payoffs are

∂∂

= −∂∂

= + ′ −vw

X wvw

X w X w w cD U

ˆ( ˆ ),

ˆ( ˆ ) ( ˆ )( ˆ ).and

Summing gives

∂∂

+( ) = ′ − ≤ˆ

( ˆ )( ˆ ) ,w

v v X w w cD U 0

where the inequality is strict in the range w < w*, that is for d ∈ (d1, d2). Because U’sbecoming the bondposter is equivalent to eliminating the constraint w ≤ w, the resultfollows. �



Proof of Proposition 7. I begin by constructing an equilibrium when D posts thereputational bond. Let k(t) be the number of firms in period t with Wti = 1. Let �wt

be the price actually charged by U in period t, and wt the equilibrium value. Theproposed strategies are as follows. In period 1 U charges w w wm m1 = min[ *, ]ˆ . In anyperiod t > 1 U charges w w wt k t k t= ( ) ( )min[ * , ]ˆ if �w wτ τ= for all t < t, but otherwisecharges wt = P(0). Each downstream firm i with Wti = 1 chooses dti = y in any periodt in which �w wtτ = for all t ≤ t. Conditional on choosing dti = y, each such firm ichooses Xti = X*(wt)/k(t). In any period t in which �w wtτ ≠ for some t ≤ t, a firmwith Wti = 1 chooses dti = n and X X k tti k t= ( )* ( ) ( )0 / . (In any period t in whichfirm i has Wti = 0, then μti

C = 0 and by assumption this firm chooses dti = n andXti = 0.)

Consumer beliefs are as follows. In each period t, for each firm i, set μtiC

ti= Ω solong as �w wτ τ= for all t < t. Otherwise, μti

C = 0. Note that these consumer beliefsare indeed consistent with the proposed strategies, both on and off the equilibriumpath. That is, consumers expect high quality from all firms that have always deliv-ered it in the past, so long as the upstream firm has not deviated from the equilib-rium wholesale price in an earlier period, and this coincides with the actions takenby downstream firms.

To confirm that this is an equilibrium, first consider any period t in which�w wτ τ≠ for some t ≤ t. Because μTi

C = 0 for all T > t and i, any firm i must preferdti = n. Given that such a firm’s rivals j with Wtj = 1 are playing the static Cournotequilibrium quantities X k tk t( )* ( ) ( )0 / , i also finds it optimal to do so. In contrast, if�w wτ τ= for all t ≤ t, then given that U is expected to continue charging wk(t) in

future periods and that rivals with Wti = 1 are playing the static Cournot equilibriumquantities X w k tk t k t( ) ( )* ( ) ( )/ (and will not change their future play based on i’soutput choice in t), i also finds it optimal to do so.

Now consider U’s strategy. In any period t with �w wτ τ≠ for some t ≤ t, nodownstream firm will purchase from U no matter what price it charges, given theanticipation of P(0) in future periods. Hence charging P(0) is optimal. If instead�w wτ τ= for all t ≤ t, charging anything other than wk(t) leads to zero revenues as

described above, and so charging wk(t) is optimal (and indeed provides the highestpossible revenue in a static game subject to the constraint that the wholesale pricenot exceed wk(t)).

I now compute profits along the equilibrium path. To do so I begin by taking anarbitrary w and determine static cournot profits for U and downstream firms.Under linear demand, this equilibrium is unique and symmetric, with industrydemand X given by

Xm

mw=

+−

11( ).

Total per-period profit of a single downstream firm is

11

2−+

⎛⎝⎜

⎞⎠⎟

wm

.

To find w*, note that U ideally maximizes X(w)(w - c), which can be written (aftersubstituting in the expression for X above) as

JUSTIN P. JOHNSON58


mm

w w c+

− −1

1( )( ),

giving optimized value

wc

* =+12

.

This implies that whenever the participation constraint of the downstream can beignored, upstream per-period profits are

v wm

mcU ( ) .* =

+−⎛

⎝⎜⎞⎠⎟1

12

2

From w*, it also follows that

v wc

mD ( ) .* =

−+

⎛⎝⎜

⎞⎠⎟

14

11

2

I am now in position to complete the proof. If U is posting the bond, then as in earlieranalyses the potential for moral hazard by downstream firms is not an issue and theanalysis is a standard wholesale-pricing problem; U charges w* each period. Giventhis, note that for w ∈ [c, w*] it is the case that DVU = (1 - d)-1[vU(w*) - vU(w)] andDVD = (1 - d)-1[mvD(w*) - mvD(w)]. Consider

Δ ΔV Vc

w w cc

mw

mU D+ ≅

−⎛⎝⎜

⎞⎠⎟ − −( ) −( ) + −( )

+( )−

−( )+

12

11

4 11

1

2 2 2

ˆ ˆˆ

.

It is straightforward to verify the following properties of this equation when m > 2. Itis (i) positive and decreasing at c, (ii) zero and increasing at w*, and (iii) convex.Because U will never supply the product if w < c and never choose w > w*, it followsthat there is an interval (c, w*) such that if w lies in it, then DVU + DVD > 0. Becausew can be considered a function of d that maps (0, 1) onto (0, 1) in a monotonic fashion,the existence of d1 < d2 satisfying the properties claimed in the statement of theproposition follows. �

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who posts the reputational bond? advertising and cobranding in vertical relationships

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