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Pooling reputations
International Journal of Industrial Organization 20 (2002) 715–730 www.elsevier.com / locate / econbase
Pooling reputations Fredrik Andersson* Department of Economics, Lund University, P.O. Box 7082, S-220 07 Lund, Sweden Received 11 December 1998; received in revised form 1 January 2000; accepted 1 August 2000
Abstract It is shown that there are economies of scope in carrying a reputation, providing a rationale for multi-product firms in the absence of technological or organisational economies. It is also shown that a reputation for producing high quality of an old good may be necessary to introduce and maintain the production of a new good. 2002 Elsevier Science B.V. All rights reserved. Keywords: Reputation; Multi-product firms; New goods JEL classification: D21; L22
1. Introduction Reputations seem to be very important in a modern economy. One reason for this is presumably the abundance of variety as well as the abundance of information that consumers are faced with, and the accompanying need for sorting of information. Many markets for experience goods and experience services 1 seem to be cases in point: great variety is available, but most consumers economise on the costs of ascertaining quality by relying to a large extent on the reputations of
* Tel.: 146-46-222-8676; fax: 146-46-222-4118. E-mail address: [email protected] (F. Andersson). 1 A good is said to be an experience good if its quality cannot be ascertained (at reasonable cost) by the consumer prior to purchase. 0167-7187 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 00 )00101-6
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established products and brands rather than engaging in experimental consumption when making consumption decisions.2 The scope of the reputation transmitted by a brand name may be extensive. The Virgin brand name has, for example, been extended from being the trademark of records to also being the trademark of air services and soft drinks. The Virgin case, though extreme, seems to illustrate the potential for the credibility of a company (and its brand name) to be extended beyond a well-defined set of old activities to new activities that are unrelated to the old ones.3 We will come back to empirical evidence below. This paper deals with economies of scope in carrying a reputation and with the interaction among reputations in a multi-product firm. In precise terms, the paper is set out to make the comparison between the following two situations: (i) two goods are produced by separate firms each having a reputation for producing high quality; and (ii) the two goods are produced by the same firm which has a reputation for producing high quality. The question addressed is whether the latter arrangement may be beneficial in the sense of strictly improving profit opportunities. We will establish and elaborate on a simple result that provides an affirmative answer to this question: there may indeed be a rationale for multiproduct firms absent any economies of scope in production or organisation. It is also shown that a reputation for producing high quality of an old good may be necessary to introduce and to continue selling a new good.
1.1. Empirical background It seems that a significant body of empirical evidence regarding brand extensions and ‘umbrella branding’ has accumulated over the past decade. While most studies have used experimental data, the recent contribution by Erdem (1998) makes use of market data to assess the extent to which consumers’ quality perceptions regarding a brand in one product category are affected by their experiences with the same brand in another category. Erdem performs econometric analysis on a panel of data on purchases of oral-hygiene products. He builds a model with utility maximising consumers who consume two products from different categories within the oral-hygiene product market. Consumers have prior beliefs about the qualities of the two products that are normally distributed with a general (i.e., three-parameter) covariance matrix. When consuming a product,
2 The Internet seems to be a spectacular example of essentially the same phenomenon: huge amounts of information are available very easily, but most seekers of information face time constraints that are tight enough for them to rely mainly on sources with an established reputation for credibility. 3 The notion that the good reputation tied to a name carries over to new products is expressed as follows by Richard Branson, the founder of Virgin, ‘‘Consumers understand that all the values that apply to one product — good service, style, quality, value and fair dealing — apply to the others.’’ (Time Magazine, No. 26, June 1996.).
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consumers update their beliefs in a Bayesian fashion. Erdem estimates the model in its general form as well as with the restriction that prior quality beliefs not be correlated across products imposed. The restricted model is rejected, and the estimated correlation coefficient (of the prior beliefs) between the qualities of the two products of the same brand is 0.882; this is taken to support that ‘‘consumers expect the quality levels of products that are umbrella branded to be correlated highly’’.4 In addition, the estimates of the variances of prior perceptions as well as of the experience variability are positive. This corroborates the notion that uncertainty about product quality is a real concern for consumers. It also indicates that the quality of a product is not learned once and for all when the product is consumed. Moreover, the results point to perceptions about the quality of old products being affected by the quality of new products. These observations seem to lend some support to the existence of an underlying moral-hazard problem in the sense that this pattern is hard to reconcile with the notion that the qualityprovision problem is one of pure adverse selection. Sullivan (1990) also provides empirical evidence based on market data for the existence of image spillovers between products sold under the same name. She sets out to explore the consequences of two specific events: the ‘sudden acceleration’ incident and the ensuing bad news concerning one of Audi’s cars in 1986; and, Jaguar’s introduction of the first significantly new model for a long time in 1988, hypothesised to be good news for consumers. Sullivan employed used-car price data to estimate depreciation rates for three Audi models, two Jaguar models, and a number of competing models. By means of event dummy variables, she estimated the effect of the events on depreciation rates. She found that the Audi ‘sudden acceleration’ incident lead to significant increases in the depreciation rates for all three Audi models (the incident involved only one of them), while it had no significant effect on depreciation rates of other brands. In the same vein, Jaguar’s introduction of a new model lead to a significant decrease in the depreciation rate of Jaguars. In light of the negative record for Audi, Sullivan stresses the importance of firms’ managing their ‘brand portfolios,’ in order to, among other things, avoid uncontrollable risks. John et al. (1995) provide experimental evidence of image spillovers from new products to old ones. An experimental study focussing on the ‘extendability’ of a brand name is Rangaswamy et al. (1993). Rangaswamy et al. employ a utility-maximisation framework to explore variation in the extendability of brand names. The underlying idea is that the ‘fit’ of an extension — i.e., the similarity perceived by consumers between the new product and old products sold under a brand — which has been found to be important for the success of a brand extension 5 cannot fully explain the pattern of successes and failures of extensions. Rather, according to
4 5
Erdem, ibid., p. 346. See, e.g., Aaker and Keller (1990).
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Rangaswamy et al., a fuller explanation needs to consider also the ‘brand association’ of a brand name; some brands are presumed to be more powerful at sending high-quality signals (e.g., due to being associated with higher quality). Specifically, Rangaswamy et al. assume that the utility enjoyed by a consumer consuming a branded product can be decomposed into three components: one depending only on the product, one depending only on the brand, and one depending on the association of the brand with the product. By pairing each of four brand names (three well-known and one unfamiliar) with a number of configurations of attributes and estimating the benefit enjoyed by means of conjoint analysis (subjects were asked to report purchase intentions), the components of the decomposition described above were identified.6 Subjects were then asked to evaluate four brand extensions, ranging from extension within the same category to extension to a distant category. The authors hypothesised that there would be variation in the extendability of brands: brands associated with a high consumer utility from the brand itself (the second component of utility described above), and a low utility from the association of the brand with the product (the third component) were hypothesised to be more easily extended than brands for which the opposite pattern applied. The results obtained supported this hypothesis. Results pointing in the same direction — i.e., that ‘‘high-quality brands stretch farther than average quality brands’’ — were found by Keller and Aaker (1992) in a study of sequential extensions.7 As to more informal evidence of the importance of brand extensions, Tauber (1988) forcefully argues that brand extensions constitute a means of reducing costs of introducing new products. Tauber also discusses the importance of establishing a link between a new product and old ones in order that consumers perceive the extension as credible; he argues that this can be achieved either by means of fit — the new product being logically related to the old one — or by means of leverage — the original reputation being strong enough to make consumers willing to pay premium price for a new product if the name is attached to it. Tauber suggests Porsche sunglasses and Ferrari watches as examples of the latter kind.
1.2. Related literature The formal analysis of this paper lends heavily from that of Bernheim and Whinston (1990), who consider multimarket contact in an oligopoly model. When firms are involved in price competition in more than one market, it is sometimes
6
There was pre-testing to select products and attributes. Keller and Aaker (1992) also found, essentially, that one extension affected another extension only if the former violated prior expectations tied to the parent brand. 7
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strictly easier to sustain collusion in the two markets combined than it would be for separate sets of firms in the different markets. There are a number of papers dealing with brand extensions and ‘umbrella branding’ in an adverse-selection framework. The logic of the basic adverseselection model is that a firm develops a product which turns out to be of either high or low quality, and a reputation equilibrium is essentially one where a ‘high-quality firm’ — i.e., a firm having a high-quality product — behaves differently compared to a ‘low-quality’ firm. Wernerfelt (1988) and Choi (1998) explore adverse-selection models of brand extensions with signalling. Wernerfelt considers a static model where the umbrella branding of a new product with an old high-quality product sends a signal about the quality of the new product. He assumes the existence of a cost of selling the new product under the old brand — not incurred if it is sold under a new brand — which makes signalling effective. Choi explores a similar framework but does not assume that a brand extension carries a cost; instead, he constructs a ‘bootstrap equilibrium’ (i.e., an equilibrium sustained solely by self-fulfilling expectations). In the equilibrium devised, a new product may be introduced as a brand extension — which is generally cheaper in terms of signalling distortions of the price — as long as the ‘parent brand’ has never been extended to a low-quality product previously. A somewhat different kind of model — viz. a competitive adverse-selection model — is employed by Tadelis (1999) and Cabral (1998a).8 In Tadelis’s model, names are tradable, and an active firm makes in each period the choice among: retaining its name, buying a name from a retiring firm, and creating a new name. Assuming that the identity of the owner of a name is unobservable he shows circumstances when names are valuable due to their being associated with a reputation. Tadelis’s model captures nicely the feature that the reputation of a name may improve or deteriorate in response to performance; it also points out that a necessary condition for this to be true (in an adverse-selection model) is that ‘good’ names sometimes be bought by ‘bad’ firms in equilibrium. Cabral (1998a) uses a similar model to explore cross-reputational links between products. The equilibrium outcome of his model has the property that the likelihood that a firm introduces a new product under the same brand is increasing in the quality of the product as well as the in the strength of the firm’s reputation.9 Although we consider the basic structure of the adverse-selection models cited above very useful, it seems important to pursue similar inquiries in a moral-hazard
8
In this model, there are ‘good’ and ‘bad’ firms, the former type being more likely to be successful in the provision of a good / service. 9 Mailath and Samuelson (1998) discuss name trading in a similar framework with moral-hazard elements. Cabral (1998b) develops a moral-hazard model with an extension to quality provision where more efficient equilibria are sustained under umbrella branding due to equilibrium punishments being less frequent.
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framework. One reason for this is that an important incentive aspect of a reputation is ignored in the adverse-selection framework (since once a product is introduced consumers know its future quality). In the Section 2 we develop a simple reputation model for the one-good case, and in Section 3 we formalise the notion of pooled reputations and connect the model to product development. Section 4 concludes.
2. A reputation model We will consider a very simple reputation model: a monopolist (she) produces one or two experience goods and tries to maintain a reputation for producing high quality under the threat from consumers that they will never buy from her again if she defects. The model is an instance where a high price serves to assure high quality; it is set in a moral-hazard framework.10
2.1. Basic structure There are (at most) two goods, i 5 1, 2, and each good may be either of low or high quality. They are all produced with technologies that are constant returns to scale except for fixed costs k i that are independent of quality; the marginal unit cost of producing good i is ]c i for low quality, and ]c i for high quality (where ]c .c . 0). i ]i The model is set in discrete time, and the horizon is infinite; the discount factor is d. There are a large number of identical short-lived consumers in each period. The goods are non-durable and last for one period; demand is time independent. Demand for high quality is x i ( pi ) where pi is the price of good i, while demand for low quality, for simplicity, is assumed to be zero; x i ( ? ) is twice continuously differentiable. Demand for good i is decreasing in pi , i.e., x i9 , 0, and to guarantee that the monopolist’s problem has a unique solution, we assume that x i99 < 0. We confine ourselves to the case where demand is completely separable among the goods; i.e., where we have x i ( pi ). This is for simplicity; demand inter-dependencies would bring no substantive benefits. The above specification essentially implies that the underlying preferences are separable and quasi-linear in money; such preferences must be concave in consumption 11 and consumers are thus, importantly, averse to randomness in consumption. 10 The model can be seen as a development of the non-game-theoretic analyses of Klein and Leffler (1981) and Shapiro (1983). There is also a literature on price signalling of quality in adverse-selection environments, focussing on the uniqueness of equilibrium outcomes; see Ellingsen (1997) for a recent contribution and an overview. 11 Since if utility is u(x) 2 px, x9( p) 5 1 /u0.
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2.2. The one-good case Consider now a monopolist producing only one good, x, selling it at price pt in ] if she period t. The monopolist will make per-period profit pt 5 x( pt ) ? ( pt 2c) produces high quality, and the expected discounted future profit over the horizon is then
O d ? x( p ) ? ( p 2c).] `
P5
t
t
(1)
t
t 50
We assume that profits are unverifiable; i.e., that the firm’s profits cannot be specified in an enforceable contract.12 We will assume quality to be observable only by consumption, and we assume it to be unverifiable. We assume the existence of a cumulative statistic that informs the consumers in each period about the record of the monopolist; this record need only contain information about whether the monopolist has produced low quality in the past. We will prove the existence of the simplest reputational equilibrium possible, that where the monopolist maintains a reputation for producing high quality by actually doing so, and where consumers switch to the ‘bad’ equilibrium — i.e., the equilibrium with low expectations, zero demand, and no scope for building a reputation — if she ever defects. We will comment on the credibility of the consumers’ strategy below. In order for consumers to purchase the good, they must believe that the monopolist will produce high quality. Since quality is observed only afterwards, it is clear that the monopolist could get away with letting consumers down once; i.e., that she could achieve the same sales, x( p), at the anticipated price p no matter her choice of quality. Let the profit from producing low quality in such a situation be denoted pˆ 5 x( p) ? ( p 2c). If consumers expect high quality, the gain from a ] deviation is ] ] Dp 5 pˆ 2 p 5 x( p) ? ( p 2c) ] 2 x( p) ? ( p 2c) 5 x( p) ? (c 2c). ]
(2)
We define the monopoly solution as the price and quality that maximise the monopolist’s profit subject to the constraint that she be credible in producing high quality. It is clear that the monopoly solution must have high quality being produced in every period. The gain from defecting is Dp, and the loss is future profits from the next period on; the constraint is thus
Od x( p )( p 2c).] `
x( p0 )(c] 2c) ] <
t
t
t
(3)
t51
12
The reason for this may be that any enforceable contract on profits would be subject to cooking-the-books problems; this issue is discussed extensively by Hart (1995).
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Let us first formulate the constraint for a stationary path of prices; it will be clear that this is in fact without loss of generality. Computing the sum, (3) may then be rewritten as 12d ] > ]] x( p)( p 2c) x( p)(c] 2c). ] d
(4)
We will refer to this constraint as the (one-good) credibility constraint. Note that even though there may exist different views about how convincing our argument for a particular equilibrium is, it is clear that the credibility constraint is a minimum necessary condition for a firm to be credible; if it were violated, a firm would gain by producing low quality no matter how consumers would react. The monopoly solution is thus defined by the following problem
O d x( p )( p 2c),] ] x( p )(c] 2c) ] < O d x( p )( p 2c). `
max p
t
t
t
t50
`
s.t.
(5)
t
0
t
t
t51
The profit implied by the monopoly solution is the above minus the fixed cost, k; we assume that this profit is strictly positive. Although simple, the following facts are important enough to be stated formally.13 Proposition 1. The monopoly solution leads to the static unconstrained monopoly price if the credibility constraint does not bind. If the constraint binds, the price is distorted upwards and profits are smaller. Proof. The concavity of the objective function and the linearity of the constraint (for a stationary price path) immediately imply that the optimal sequence of prices is time independent, and hence that we can express the credibility constraint as in (4). Exploiting the fact that x( p) cancels in (4) the constraint can be expressed as 12d p >c] 1 ]] (c] 2c). ] d
(6)
This proves the direction of the distortion; the last part is obvious from the fact that the choice set is made smaller by the constraint. h We will now prove the existence of a simple trigger-strategy equilibrium. The
13 The upward distortion derived here is similar in structure to the upward distortion of wages in the efficiency-wage model (see, e.g., Shapiro and Stiglitz, 1984); there, the distortion serves to ascertain that workers be keen enough to keep their jobs in order that they not shirk.
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offer to sell the good in accordance with the monopoly solution is called the monopoly contract. Proposition 2. The following is a subgame perfect Nash equilibrium. The monopolist offers the monopoly contract in each period and produces high quality. The consumers buy at any price less than or equal to the monopoly price in the first period, and continue to do so in future periods if and only if the monopolist has provided high quality in the past. Proof. See Appendix A. This is not a paper about equilibrium selection, and we will hence not go deeply into the issue of the multiplicity of equilibria. The equilibrium is a bootstrap equilibrium; i.e., best responses are determined, essentially completely, by expectations about the opponent’s behaviour. In an informal sense, it seems that the equilibrium we pick is the natural one if the monopolist is strong. Moreover, Fudenberg and Levine (1989) provide foundations for this notion by considering a game that is perturbed by the introduction of a small amount of incomplete information.14 The long-run player in the perturbed game is a ‘Stackelberg type’ (a type for whom it is a dominant strategy to play the desired strategy) with some probability. They show that the long-run player can attain, essentially, his ‘Stackelberg payoff’ if he is patient enough in any simultaneous-move game; in the sequential-move game considered here, an additional perturbation is required to ascertain that the game not be stuck in an equilibrium where the monopolist never gets the opportunity to produce in the first place.15
3. Pooling reputations We now consider a monopolist who is active in two markets. We will start by defining the joint monopoly solution, and then go on to characterising a subgame perfect equilibrium. The two goods, i 5 1, 2, are demanded in quantities x i ( pi ); we will maintain the ] assumption that x 99 i ( ? ) < 0. Further, let Dc i 5c i 2c ] i . The pooled credibility constraint (for a stationary price path; the subscript refers to the good) is 12d x 1 ( p1 )( p1 2c] 1 ) 1 x 2 ( p2 )( p2 2c] 2 ) > ]] [x 1 ( p1 ) Dc 1 1 x 2 ( p2 ) Dc 2 ], d 14
(7)
I am grateful to Joseph Harrington for suggesting this development. In our setting with many consumers, very simple such perturbations are possible (e.g., a small fraction of consumers always buying). 15
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and the joint monopoly solution now maximises
O d [x ( p )( p 2c] ) 1 x ( p )( p 2c] )], `
t
1
1
1
1
2
2
2
2
(8)
t50
subject to (7). The above is true for the case of a stationary optimal path. Given our previous assumptions, this is without loss of generality as long as the constraint defines a convex admissible set; this is guaranteed by x 99 i not being too large in absolute value, which we assume without further ado.
3.1. Profits It is obvious that profits from the pooled monopoly solution are no smaller than the sum of the profits of producing each good under their separate credibility constraints since the latter is possible in the pooled case as well. Profit opportunities are, however, improved. Let us say that ‘the constraint on good 1 binds’ if it binds in the one-good problem. Obviously, if the constraint on one of the goods binds, while the constraint on the other good is strictly non-binding (i.e., satisfied with strict inequality in the one-good problem), profits are strictly increased.16 If both constraints bind, it is not equally obvious that pooling is valuable for the monopolist. However, by considering the Kuhn-Tucker conditions for the onegood problems, it is seen that the Lagrange multipliers on the constraints are in general not equal; or, more precisely: if they are equal, an arbitrarily small perturbation of some of the parameters, (c] i , ]c i , x i ( ? )), i 5 1, 2, will make the Lagrange multipliers non-equal, and pooling will be strictly valuable (where a small perturbation of x i ( ? ) is to be understood as a perturbation at every point of the domain). We thus have. Proposition 3. If at least one of the constraints of the one-good problems binds strictly (i.e., with a positive Lagrange multiplier), then pooling is strictly valuable for the monopolist for almost all (c] i , ]c i , x i ( ? )), i 5 1, 2. Thus, pooling is strictly valuable unless, essentially, both constraints are (at least weakly) slack at the one-good solutions.
3.2. Equilibrium We will close this section by formally stating and proving the existence of a subgame perfect equilibrium in which the monopolist realises her monopoly profit. 16 Although we will return to this issue, it may be noted in passing that if in such a case the pooled problem has the pooled constraint slack, the distortion is removed, which is unambiguously favourable for the monopolist as well as for social welfare.
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Proposition 4. The following is a subgame perfect Nash equilibrium. The monopolist offers the monopoly contract in each period and produces high quality of each good. The consumers buy at any price less than or equal to the monopoly price in the first period, and continue to do so in future periods if and only if the monopolist has provided high quality in the past. Proof. The proof is identical to that of Proposition 2. The argument is that the equilibrium only requires us to construct beliefs that are consistent and create the right incentives; since we can re-define the good as the pair of goods in the proportion consumed at the monopoly solution, the argument is the same. h The fact that there are gains to pooling reputations is simple but important.17 In terms of the vast set of possible equilibria of the game, we have proved that the upper bound on profits over this set is pushed upwards and that pooling reputations makes playing a Pareto dominant equilibrium possible. Thus, the result is substantive no matter whether one considers the equilibrium selected the uniquely plausible one or not.
3.3. New goods and reputation extensions So far, we have assumed that the fixed costs are covered in all cases. We will now relax this and consider the introduction of new goods. Consider a product, good 2, that would be profitable to introduce and sell at the unconstrained monopoly price; i.e., a product that would be introduced if there were no credibility problem. It is, however, not profitable to produce and sell the product alone because the credibility constraint is restrictive enough for the resulting profits not to cover k 2 (by distorting price above the monopoly level, profits are reduced). Suppose now that the introduction may be made either by a firm that is inactive from the outset, or by a firm that already sells good 1 at the monopoly price. Suppose further that the credibility constraint does not bind too strongly for good 1. Obviously, there is a range of parameter values for which the active firm would introduce good 2, while the inactive firm would not. We have proved: Proposition 5. There are situations where the production and marketing of an old product is necessary for the introduction of a new product to be possible. It is worth noting that this result, though quite similar, is stronger than the results of Choi (1998) and Cabral (1998a), and, in fact, stronger than would be any 17
The argument follows closely the market-linkage logic identified by Bernheim and Whinston (1990).
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similar result in an adverse-selection framework; in an adverse-selection model, a monopolist can always introduce a new good by giving it away for free in the first period, and this strategy will, moreover, be profitable whenever the monopolist is patient enough. Here, the old good and its reputation may be necessary for production also in the long run; the reason being that incentives for producing high quality need be maintained.
3.4. Remarks on welfare analysis We have already noted that the objectives of the monopolist are somewhat aligned with efficiency objectives because prices are distorted upwards by credibility considerations. The simplest example is that with two goods, one credibility constraint binding and the other sufficiently lax for the pooled credibility constraint to be non-binding; then, moving from good-specific reputations to a pooled one increases profits and decreases one of the prices, while the other price is unchanged. An obvious question to ask is whether the welfare properties are that favourable generally. The answer is no, however, in the absence of free slack; the following result for Consumer Surplus (CS) shows that the misalignment of consumer and producer objectives is significant. Proposition 6. If both credibility constraints bind individually, the pricing induced by pooling reputations leaves CS no greater than pricing induced by separate reputations. Proof. See Appendix A. The intuition hinges on the fact that CS is a convex function of price, leading to price dispersion being beneficial in this sense, and the fact that the pooling of two reputations leads to a reduction in price dispersion. At the optimum with pooled reputations the prices of the two goods can be traded off marginally against each other at a rate that keeps CS constant; for larger changes (at the same rate), dispersion increases CS. Note that the welfare benefits of price dispersion are real, although consumer surplus is a somewhat dubious measure of welfare.18
4. Conclusion The main point of this paper is simple: there are economies of scope in carrying a reputation. A firm carrying a pooled reputation for producing high quality of two goods will, under reasonable conditions, do strictly better than would ‘the sum’ of 18
See, e.g., Stennek (1999) for a recent discussion of consumer surplus and random prices.
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two firms producing one good each and carrying the respective reputations. This advantage is reinforced in the context of the introduction of new goods — it may be necessary to support the introduction and the ongoing selling of a new good by means of an established reputation. So far, we have deferred the question of what reputations can reasonably be tied together. Proposition 4 tells us that tying any reputations is consistent with equilibrium. Some readers may worry that consumers are unlikely to perceive the link between products necessary for such an equilibrium. Here, we provide an example where our result applies to a case where no such arbitrariness is introduced. Formally, our example is one where a firm producing two goods is constrained by the technology to either produce both goods of low quality at costs (c] 1 ,c] 2 ), or produce both goods of high quality at cost (c] 1 ,c] 2 ). In such a case, the analysis from the one-good case goes through unchanged, and the arguments for the efficient equilibrium in the one-good model apply to the two-good model as well.19 In sum, our model predicts that technological and organisational choices be made with the complementarity of reputations in mind. A number of important questions are ignored by the current framework. In our view, the paramount one is the foundation of the reputation of a firm. Certainly, it would be desirable to derive the mechanisms for sustaining reputations of firms and brands from basic assumptions about individual incentives within firms. Apart from the obvious benefits, any progress along such lines would likely throw light on questions regarding the virtues of different organisational forms as bearers of reputation.20 Another issue which we have not addressed at all is that of the interaction between our results and competition. For example, intuition suggests that any commitment to producing high quality is an advantage for an incumbent; this seems worth further analysis.
Acknowledgements The paper was conceived and started while the author was visiting the Department of Economics, Harvard University, and early discussions with Oliver ¨ were very useful. I have received valuable comments Hart and Bengt Holmstrom 19
The example seems consistent with empirical evidence that consumers put more confidence in brand extensions where there is a perceived fit between the new product and the old one (Aaker and Keller, 1990). 20 Although the notion of collective reputation has received little attention within economic theory, Kandori (1992) and Tirole (1996) are recent contributions. The results of Tirole (1996) show that high enough rents are important for the sustainability of a group reputation, indicating that something similar to the credibility constraint of our model would have to hold in a model with a collective reputation as well.
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from Joseph Harrington and two anonymous referees as well as from Marcus ¨ Asplund, Hans Carlsson, Jorgen Weibull and seminar participants at The Industrial Institute for Economic and Social Research, Stockholm. Financial support from the Bank of Sweden Tercentenary Foundation is gratefully acknowledged.
Appendix A Proof of Proposition 2 It is clear by definition that the profit from the monopoly contract, p, is an upper bound on profits absent randomisation. The monopolist might in principle be able to do better by randomising, but not in this model since demand is concave. Hence, p is a strict upper bound on payoffs in each period, and it is clear that it is attainable as a Nash equilibrium if the monopolist cannot gain by defecting; i.e., if the credibility constraint is satisfied. To verify that the equilibrium is subgame perfect, we need only check that there are no profitable one-time deviations upon any history (Fudenberg and Tirole, 1991, Theorem 4.2). But this is obvious for the buyers, and once this is clear it is equally obvious for the seller since she is credible by construction. h Proof of Proposition 6 First, note that both credibility constraints’ binding separately implies that the pooled credibility constraint binds (suppose the pooled constraint were slack; then one of the prices would be above the level implied by the one-good credibility constraint which, in turn, exceeds the monopoly price; since credibility does not constrain the price, this cannot be optimal; a contradiction). Let CS denote Consumer Surplus; `
`
E
E
p1
p2
CS 5 x 1 ( j ) dj 1 x 2 ( j ) dj . Consider a price change from prices ( p1 , p2 ) that are optimal given two separate, binding, credibility constraints, to prices ( p 19 , p 92 ) that are optimal given the pooled credibility constraint. Let Dpi 5 p i9 2 pi , and assume, without loss of generality, that p 19 . p1 and p 29 , p2 . We have `
`
pi
E
E
E
p i9
pi
p 9i
DCSi 5 x i ( j ) dj 2 x i ( j ) dj 5 x i ( j ) dj < 2 Dpi x i ( p 9i ), but from the individual credibility constraints
(A.1)
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12d pi 5c] i 1 ]] (c] i 2c] i ), d which inserted into the pooled credibility constraint (7) gives x 1 ( p 19 ) Dp1 1 x 2 ( p 29 ) Dp2 5 0;
(A.2)
thus, an upper bound on the change in consumer surplus, DCS1 1 DCS2 , is zero. h
References Aaker, D., Keller, K., 1990. Consumer evaluations of brand extensions. Journal of Marketing 54, 27–41. Bernheim, D., Whinston, M., 1990. Multi-market contact and collusive behavior. RAND Journal of Economics 21, 1–26. Cabral, L., 1998a. Stretching firm and brand reputation. Mimeo, London Business School. Cabral, L., 1998b. Mulitmarket contact under imperfect observability, with an application to umbrella branding. Mimeo, London Business School. Choi, J.P., 1998. Brand extension as informational leverage. Review of Economic Studies 65, 655–669. Ellingsen, T., 1997. Price signals quality: The case of perfectly inelastic demand. International Journal of Industrial Organization 16, 43–61. Erdem, T., 1998. An empirical analysis of umbrella branding. Journal of Marketing Research 35, 339–351. Fudenberg, D., Levine, D., 1989. Reputation and equilibrium selection in games with a patient player. Econometrica 57, 759–778. Fudenberg, D., Tirole, J., 1991. In: Game Theory. MIT Press, Cambridge. Hart, O., 1995. In: Firms, Contracts, and Financial Structure. Oxford University Press, New York. John, D., Loken, B., Joiner, C., 1995. Spillover effects of brand extensions: can they spread to a firm’s established products. Working Paper 9503, Center for Research in Marketing, Carlson School of Management, University of Minnesota. Kandori, M., 1992. Social norms and community enforcement. Review of Economic Studies 59, 63–80. Keller, K., Aaker, D., 1992. The effects of sequential introduction of brand extensions. Journal of Marketing Research 29, 35–50. Klein, B., Leffler, K., 1981. The role of market forces in assuring contractual performance. Journal of Political Economy 89, 615–641. Mailath, G., Samuelson, L., 1998. Who wants a good reputation? CARESS Working Paper 98-12, University of Pennsylvania. Rangaswamy, A., Burke, R., Oliva, T., 1993. Brand equity and the extendability of brand names. International Journal of Research in Marketing 10, 61–75. Shapiro, C., 1983. Premiums of high quality products as returns to reputations. Quarterly Journal of Economics 98, 659–679. Shapiro, C., Stiglitz, J., 1984. Equilibrium unemployment as a worker discipline device. American Economic Review 74, 433–444. Stennek, J., 1999. The expected consumer’s surplus as a welfare measure. Journal of Public Economics 73, 265–288. Sullivan, M., 1990. Measuring image spillovers in umbrella-branded products. Journal of Business 63, 309–329.
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Tadelis, S., 1999. What’s in a name? Reputation as a tradeable asset. American Economic Review 89, 548–563. Tauber, E., 1988. Strategy for growth in cost-control world. Journal of Advertising Research 28, 26–30. Tirole, J., 1996. A theory of collective reputations (with applications to the persistence of corruption and to firm quality). Review of Economic Studies 63, 1–22. Wernerfelt, B., 1988. Umbrella branding as a signal of new product quality: an example of signalling by posting a bond. RAND Journal of Economics 19, 458–466.
Pooling reputations Fredrik Andersson* Department of Economics, Lund University, P.O. Box 7082, S-220 07 Lund, Sweden Received 11 December 1998; received in revised form 1 January 2000; accepted 1 August 2000
Abstract It is shown that there are economies of scope in carrying a reputation, providing a rationale for multi-product firms in the absence of technological or organisational economies. It is also shown that a reputation for producing high quality of an old good may be necessary to introduce and maintain the production of a new good. 2002 Elsevier Science B.V. All rights reserved. Keywords: Reputation; Multi-product firms; New goods JEL classification: D21; L22
1. Introduction Reputations seem to be very important in a modern economy. One reason for this is presumably the abundance of variety as well as the abundance of information that consumers are faced with, and the accompanying need for sorting of information. Many markets for experience goods and experience services 1 seem to be cases in point: great variety is available, but most consumers economise on the costs of ascertaining quality by relying to a large extent on the reputations of
* Tel.: 146-46-222-8676; fax: 146-46-222-4118. E-mail address: [email protected] (F. Andersson). 1 A good is said to be an experience good if its quality cannot be ascertained (at reasonable cost) by the consumer prior to purchase. 0167-7187 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 00 )00101-6
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established products and brands rather than engaging in experimental consumption when making consumption decisions.2 The scope of the reputation transmitted by a brand name may be extensive. The Virgin brand name has, for example, been extended from being the trademark of records to also being the trademark of air services and soft drinks. The Virgin case, though extreme, seems to illustrate the potential for the credibility of a company (and its brand name) to be extended beyond a well-defined set of old activities to new activities that are unrelated to the old ones.3 We will come back to empirical evidence below. This paper deals with economies of scope in carrying a reputation and with the interaction among reputations in a multi-product firm. In precise terms, the paper is set out to make the comparison between the following two situations: (i) two goods are produced by separate firms each having a reputation for producing high quality; and (ii) the two goods are produced by the same firm which has a reputation for producing high quality. The question addressed is whether the latter arrangement may be beneficial in the sense of strictly improving profit opportunities. We will establish and elaborate on a simple result that provides an affirmative answer to this question: there may indeed be a rationale for multiproduct firms absent any economies of scope in production or organisation. It is also shown that a reputation for producing high quality of an old good may be necessary to introduce and to continue selling a new good.
1.1. Empirical background It seems that a significant body of empirical evidence regarding brand extensions and ‘umbrella branding’ has accumulated over the past decade. While most studies have used experimental data, the recent contribution by Erdem (1998) makes use of market data to assess the extent to which consumers’ quality perceptions regarding a brand in one product category are affected by their experiences with the same brand in another category. Erdem performs econometric analysis on a panel of data on purchases of oral-hygiene products. He builds a model with utility maximising consumers who consume two products from different categories within the oral-hygiene product market. Consumers have prior beliefs about the qualities of the two products that are normally distributed with a general (i.e., three-parameter) covariance matrix. When consuming a product,
2 The Internet seems to be a spectacular example of essentially the same phenomenon: huge amounts of information are available very easily, but most seekers of information face time constraints that are tight enough for them to rely mainly on sources with an established reputation for credibility. 3 The notion that the good reputation tied to a name carries over to new products is expressed as follows by Richard Branson, the founder of Virgin, ‘‘Consumers understand that all the values that apply to one product — good service, style, quality, value and fair dealing — apply to the others.’’ (Time Magazine, No. 26, June 1996.).
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consumers update their beliefs in a Bayesian fashion. Erdem estimates the model in its general form as well as with the restriction that prior quality beliefs not be correlated across products imposed. The restricted model is rejected, and the estimated correlation coefficient (of the prior beliefs) between the qualities of the two products of the same brand is 0.882; this is taken to support that ‘‘consumers expect the quality levels of products that are umbrella branded to be correlated highly’’.4 In addition, the estimates of the variances of prior perceptions as well as of the experience variability are positive. This corroborates the notion that uncertainty about product quality is a real concern for consumers. It also indicates that the quality of a product is not learned once and for all when the product is consumed. Moreover, the results point to perceptions about the quality of old products being affected by the quality of new products. These observations seem to lend some support to the existence of an underlying moral-hazard problem in the sense that this pattern is hard to reconcile with the notion that the qualityprovision problem is one of pure adverse selection. Sullivan (1990) also provides empirical evidence based on market data for the existence of image spillovers between products sold under the same name. She sets out to explore the consequences of two specific events: the ‘sudden acceleration’ incident and the ensuing bad news concerning one of Audi’s cars in 1986; and, Jaguar’s introduction of the first significantly new model for a long time in 1988, hypothesised to be good news for consumers. Sullivan employed used-car price data to estimate depreciation rates for three Audi models, two Jaguar models, and a number of competing models. By means of event dummy variables, she estimated the effect of the events on depreciation rates. She found that the Audi ‘sudden acceleration’ incident lead to significant increases in the depreciation rates for all three Audi models (the incident involved only one of them), while it had no significant effect on depreciation rates of other brands. In the same vein, Jaguar’s introduction of a new model lead to a significant decrease in the depreciation rate of Jaguars. In light of the negative record for Audi, Sullivan stresses the importance of firms’ managing their ‘brand portfolios,’ in order to, among other things, avoid uncontrollable risks. John et al. (1995) provide experimental evidence of image spillovers from new products to old ones. An experimental study focussing on the ‘extendability’ of a brand name is Rangaswamy et al. (1993). Rangaswamy et al. employ a utility-maximisation framework to explore variation in the extendability of brand names. The underlying idea is that the ‘fit’ of an extension — i.e., the similarity perceived by consumers between the new product and old products sold under a brand — which has been found to be important for the success of a brand extension 5 cannot fully explain the pattern of successes and failures of extensions. Rather, according to
4 5
Erdem, ibid., p. 346. See, e.g., Aaker and Keller (1990).
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Rangaswamy et al., a fuller explanation needs to consider also the ‘brand association’ of a brand name; some brands are presumed to be more powerful at sending high-quality signals (e.g., due to being associated with higher quality). Specifically, Rangaswamy et al. assume that the utility enjoyed by a consumer consuming a branded product can be decomposed into three components: one depending only on the product, one depending only on the brand, and one depending on the association of the brand with the product. By pairing each of four brand names (three well-known and one unfamiliar) with a number of configurations of attributes and estimating the benefit enjoyed by means of conjoint analysis (subjects were asked to report purchase intentions), the components of the decomposition described above were identified.6 Subjects were then asked to evaluate four brand extensions, ranging from extension within the same category to extension to a distant category. The authors hypothesised that there would be variation in the extendability of brands: brands associated with a high consumer utility from the brand itself (the second component of utility described above), and a low utility from the association of the brand with the product (the third component) were hypothesised to be more easily extended than brands for which the opposite pattern applied. The results obtained supported this hypothesis. Results pointing in the same direction — i.e., that ‘‘high-quality brands stretch farther than average quality brands’’ — were found by Keller and Aaker (1992) in a study of sequential extensions.7 As to more informal evidence of the importance of brand extensions, Tauber (1988) forcefully argues that brand extensions constitute a means of reducing costs of introducing new products. Tauber also discusses the importance of establishing a link between a new product and old ones in order that consumers perceive the extension as credible; he argues that this can be achieved either by means of fit — the new product being logically related to the old one — or by means of leverage — the original reputation being strong enough to make consumers willing to pay premium price for a new product if the name is attached to it. Tauber suggests Porsche sunglasses and Ferrari watches as examples of the latter kind.
1.2. Related literature The formal analysis of this paper lends heavily from that of Bernheim and Whinston (1990), who consider multimarket contact in an oligopoly model. When firms are involved in price competition in more than one market, it is sometimes
6
There was pre-testing to select products and attributes. Keller and Aaker (1992) also found, essentially, that one extension affected another extension only if the former violated prior expectations tied to the parent brand. 7
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strictly easier to sustain collusion in the two markets combined than it would be for separate sets of firms in the different markets. There are a number of papers dealing with brand extensions and ‘umbrella branding’ in an adverse-selection framework. The logic of the basic adverseselection model is that a firm develops a product which turns out to be of either high or low quality, and a reputation equilibrium is essentially one where a ‘high-quality firm’ — i.e., a firm having a high-quality product — behaves differently compared to a ‘low-quality’ firm. Wernerfelt (1988) and Choi (1998) explore adverse-selection models of brand extensions with signalling. Wernerfelt considers a static model where the umbrella branding of a new product with an old high-quality product sends a signal about the quality of the new product. He assumes the existence of a cost of selling the new product under the old brand — not incurred if it is sold under a new brand — which makes signalling effective. Choi explores a similar framework but does not assume that a brand extension carries a cost; instead, he constructs a ‘bootstrap equilibrium’ (i.e., an equilibrium sustained solely by self-fulfilling expectations). In the equilibrium devised, a new product may be introduced as a brand extension — which is generally cheaper in terms of signalling distortions of the price — as long as the ‘parent brand’ has never been extended to a low-quality product previously. A somewhat different kind of model — viz. a competitive adverse-selection model — is employed by Tadelis (1999) and Cabral (1998a).8 In Tadelis’s model, names are tradable, and an active firm makes in each period the choice among: retaining its name, buying a name from a retiring firm, and creating a new name. Assuming that the identity of the owner of a name is unobservable he shows circumstances when names are valuable due to their being associated with a reputation. Tadelis’s model captures nicely the feature that the reputation of a name may improve or deteriorate in response to performance; it also points out that a necessary condition for this to be true (in an adverse-selection model) is that ‘good’ names sometimes be bought by ‘bad’ firms in equilibrium. Cabral (1998a) uses a similar model to explore cross-reputational links between products. The equilibrium outcome of his model has the property that the likelihood that a firm introduces a new product under the same brand is increasing in the quality of the product as well as the in the strength of the firm’s reputation.9 Although we consider the basic structure of the adverse-selection models cited above very useful, it seems important to pursue similar inquiries in a moral-hazard
8
In this model, there are ‘good’ and ‘bad’ firms, the former type being more likely to be successful in the provision of a good / service. 9 Mailath and Samuelson (1998) discuss name trading in a similar framework with moral-hazard elements. Cabral (1998b) develops a moral-hazard model with an extension to quality provision where more efficient equilibria are sustained under umbrella branding due to equilibrium punishments being less frequent.
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framework. One reason for this is that an important incentive aspect of a reputation is ignored in the adverse-selection framework (since once a product is introduced consumers know its future quality). In the Section 2 we develop a simple reputation model for the one-good case, and in Section 3 we formalise the notion of pooled reputations and connect the model to product development. Section 4 concludes.
2. A reputation model We will consider a very simple reputation model: a monopolist (she) produces one or two experience goods and tries to maintain a reputation for producing high quality under the threat from consumers that they will never buy from her again if she defects. The model is an instance where a high price serves to assure high quality; it is set in a moral-hazard framework.10
2.1. Basic structure There are (at most) two goods, i 5 1, 2, and each good may be either of low or high quality. They are all produced with technologies that are constant returns to scale except for fixed costs k i that are independent of quality; the marginal unit cost of producing good i is ]c i for low quality, and ]c i for high quality (where ]c .c . 0). i ]i The model is set in discrete time, and the horizon is infinite; the discount factor is d. There are a large number of identical short-lived consumers in each period. The goods are non-durable and last for one period; demand is time independent. Demand for high quality is x i ( pi ) where pi is the price of good i, while demand for low quality, for simplicity, is assumed to be zero; x i ( ? ) is twice continuously differentiable. Demand for good i is decreasing in pi , i.e., x i9 , 0, and to guarantee that the monopolist’s problem has a unique solution, we assume that x i99 < 0. We confine ourselves to the case where demand is completely separable among the goods; i.e., where we have x i ( pi ). This is for simplicity; demand inter-dependencies would bring no substantive benefits. The above specification essentially implies that the underlying preferences are separable and quasi-linear in money; such preferences must be concave in consumption 11 and consumers are thus, importantly, averse to randomness in consumption. 10 The model can be seen as a development of the non-game-theoretic analyses of Klein and Leffler (1981) and Shapiro (1983). There is also a literature on price signalling of quality in adverse-selection environments, focussing on the uniqueness of equilibrium outcomes; see Ellingsen (1997) for a recent contribution and an overview. 11 Since if utility is u(x) 2 px, x9( p) 5 1 /u0.
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2.2. The one-good case Consider now a monopolist producing only one good, x, selling it at price pt in ] if she period t. The monopolist will make per-period profit pt 5 x( pt ) ? ( pt 2c) produces high quality, and the expected discounted future profit over the horizon is then
O d ? x( p ) ? ( p 2c).] `
P5
t
t
(1)
t
t 50
We assume that profits are unverifiable; i.e., that the firm’s profits cannot be specified in an enforceable contract.12 We will assume quality to be observable only by consumption, and we assume it to be unverifiable. We assume the existence of a cumulative statistic that informs the consumers in each period about the record of the monopolist; this record need only contain information about whether the monopolist has produced low quality in the past. We will prove the existence of the simplest reputational equilibrium possible, that where the monopolist maintains a reputation for producing high quality by actually doing so, and where consumers switch to the ‘bad’ equilibrium — i.e., the equilibrium with low expectations, zero demand, and no scope for building a reputation — if she ever defects. We will comment on the credibility of the consumers’ strategy below. In order for consumers to purchase the good, they must believe that the monopolist will produce high quality. Since quality is observed only afterwards, it is clear that the monopolist could get away with letting consumers down once; i.e., that she could achieve the same sales, x( p), at the anticipated price p no matter her choice of quality. Let the profit from producing low quality in such a situation be denoted pˆ 5 x( p) ? ( p 2c). If consumers expect high quality, the gain from a ] deviation is ] ] Dp 5 pˆ 2 p 5 x( p) ? ( p 2c) ] 2 x( p) ? ( p 2c) 5 x( p) ? (c 2c). ]
(2)
We define the monopoly solution as the price and quality that maximise the monopolist’s profit subject to the constraint that she be credible in producing high quality. It is clear that the monopoly solution must have high quality being produced in every period. The gain from defecting is Dp, and the loss is future profits from the next period on; the constraint is thus
Od x( p )( p 2c).] `
x( p0 )(c] 2c) ] <
t
t
t
(3)
t51
12
The reason for this may be that any enforceable contract on profits would be subject to cooking-the-books problems; this issue is discussed extensively by Hart (1995).
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Let us first formulate the constraint for a stationary path of prices; it will be clear that this is in fact without loss of generality. Computing the sum, (3) may then be rewritten as 12d ] > ]] x( p)( p 2c) x( p)(c] 2c). ] d
(4)
We will refer to this constraint as the (one-good) credibility constraint. Note that even though there may exist different views about how convincing our argument for a particular equilibrium is, it is clear that the credibility constraint is a minimum necessary condition for a firm to be credible; if it were violated, a firm would gain by producing low quality no matter how consumers would react. The monopoly solution is thus defined by the following problem
O d x( p )( p 2c),] ] x( p )(c] 2c) ] < O d x( p )( p 2c). `
max p
t
t
t
t50
`
s.t.
(5)
t
0
t
t
t51
The profit implied by the monopoly solution is the above minus the fixed cost, k; we assume that this profit is strictly positive. Although simple, the following facts are important enough to be stated formally.13 Proposition 1. The monopoly solution leads to the static unconstrained monopoly price if the credibility constraint does not bind. If the constraint binds, the price is distorted upwards and profits are smaller. Proof. The concavity of the objective function and the linearity of the constraint (for a stationary price path) immediately imply that the optimal sequence of prices is time independent, and hence that we can express the credibility constraint as in (4). Exploiting the fact that x( p) cancels in (4) the constraint can be expressed as 12d p >c] 1 ]] (c] 2c). ] d
(6)
This proves the direction of the distortion; the last part is obvious from the fact that the choice set is made smaller by the constraint. h We will now prove the existence of a simple trigger-strategy equilibrium. The
13 The upward distortion derived here is similar in structure to the upward distortion of wages in the efficiency-wage model (see, e.g., Shapiro and Stiglitz, 1984); there, the distortion serves to ascertain that workers be keen enough to keep their jobs in order that they not shirk.
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offer to sell the good in accordance with the monopoly solution is called the monopoly contract. Proposition 2. The following is a subgame perfect Nash equilibrium. The monopolist offers the monopoly contract in each period and produces high quality. The consumers buy at any price less than or equal to the monopoly price in the first period, and continue to do so in future periods if and only if the monopolist has provided high quality in the past. Proof. See Appendix A. This is not a paper about equilibrium selection, and we will hence not go deeply into the issue of the multiplicity of equilibria. The equilibrium is a bootstrap equilibrium; i.e., best responses are determined, essentially completely, by expectations about the opponent’s behaviour. In an informal sense, it seems that the equilibrium we pick is the natural one if the monopolist is strong. Moreover, Fudenberg and Levine (1989) provide foundations for this notion by considering a game that is perturbed by the introduction of a small amount of incomplete information.14 The long-run player in the perturbed game is a ‘Stackelberg type’ (a type for whom it is a dominant strategy to play the desired strategy) with some probability. They show that the long-run player can attain, essentially, his ‘Stackelberg payoff’ if he is patient enough in any simultaneous-move game; in the sequential-move game considered here, an additional perturbation is required to ascertain that the game not be stuck in an equilibrium where the monopolist never gets the opportunity to produce in the first place.15
3. Pooling reputations We now consider a monopolist who is active in two markets. We will start by defining the joint monopoly solution, and then go on to characterising a subgame perfect equilibrium. The two goods, i 5 1, 2, are demanded in quantities x i ( pi ); we will maintain the ] assumption that x 99 i ( ? ) < 0. Further, let Dc i 5c i 2c ] i . The pooled credibility constraint (for a stationary price path; the subscript refers to the good) is 12d x 1 ( p1 )( p1 2c] 1 ) 1 x 2 ( p2 )( p2 2c] 2 ) > ]] [x 1 ( p1 ) Dc 1 1 x 2 ( p2 ) Dc 2 ], d 14
(7)
I am grateful to Joseph Harrington for suggesting this development. In our setting with many consumers, very simple such perturbations are possible (e.g., a small fraction of consumers always buying). 15
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and the joint monopoly solution now maximises
O d [x ( p )( p 2c] ) 1 x ( p )( p 2c] )], `
t
1
1
1
1
2
2
2
2
(8)
t50
subject to (7). The above is true for the case of a stationary optimal path. Given our previous assumptions, this is without loss of generality as long as the constraint defines a convex admissible set; this is guaranteed by x 99 i not being too large in absolute value, which we assume without further ado.
3.1. Profits It is obvious that profits from the pooled monopoly solution are no smaller than the sum of the profits of producing each good under their separate credibility constraints since the latter is possible in the pooled case as well. Profit opportunities are, however, improved. Let us say that ‘the constraint on good 1 binds’ if it binds in the one-good problem. Obviously, if the constraint on one of the goods binds, while the constraint on the other good is strictly non-binding (i.e., satisfied with strict inequality in the one-good problem), profits are strictly increased.16 If both constraints bind, it is not equally obvious that pooling is valuable for the monopolist. However, by considering the Kuhn-Tucker conditions for the onegood problems, it is seen that the Lagrange multipliers on the constraints are in general not equal; or, more precisely: if they are equal, an arbitrarily small perturbation of some of the parameters, (c] i , ]c i , x i ( ? )), i 5 1, 2, will make the Lagrange multipliers non-equal, and pooling will be strictly valuable (where a small perturbation of x i ( ? ) is to be understood as a perturbation at every point of the domain). We thus have. Proposition 3. If at least one of the constraints of the one-good problems binds strictly (i.e., with a positive Lagrange multiplier), then pooling is strictly valuable for the monopolist for almost all (c] i , ]c i , x i ( ? )), i 5 1, 2. Thus, pooling is strictly valuable unless, essentially, both constraints are (at least weakly) slack at the one-good solutions.
3.2. Equilibrium We will close this section by formally stating and proving the existence of a subgame perfect equilibrium in which the monopolist realises her monopoly profit. 16 Although we will return to this issue, it may be noted in passing that if in such a case the pooled problem has the pooled constraint slack, the distortion is removed, which is unambiguously favourable for the monopolist as well as for social welfare.
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Proposition 4. The following is a subgame perfect Nash equilibrium. The monopolist offers the monopoly contract in each period and produces high quality of each good. The consumers buy at any price less than or equal to the monopoly price in the first period, and continue to do so in future periods if and only if the monopolist has provided high quality in the past. Proof. The proof is identical to that of Proposition 2. The argument is that the equilibrium only requires us to construct beliefs that are consistent and create the right incentives; since we can re-define the good as the pair of goods in the proportion consumed at the monopoly solution, the argument is the same. h The fact that there are gains to pooling reputations is simple but important.17 In terms of the vast set of possible equilibria of the game, we have proved that the upper bound on profits over this set is pushed upwards and that pooling reputations makes playing a Pareto dominant equilibrium possible. Thus, the result is substantive no matter whether one considers the equilibrium selected the uniquely plausible one or not.
3.3. New goods and reputation extensions So far, we have assumed that the fixed costs are covered in all cases. We will now relax this and consider the introduction of new goods. Consider a product, good 2, that would be profitable to introduce and sell at the unconstrained monopoly price; i.e., a product that would be introduced if there were no credibility problem. It is, however, not profitable to produce and sell the product alone because the credibility constraint is restrictive enough for the resulting profits not to cover k 2 (by distorting price above the monopoly level, profits are reduced). Suppose now that the introduction may be made either by a firm that is inactive from the outset, or by a firm that already sells good 1 at the monopoly price. Suppose further that the credibility constraint does not bind too strongly for good 1. Obviously, there is a range of parameter values for which the active firm would introduce good 2, while the inactive firm would not. We have proved: Proposition 5. There are situations where the production and marketing of an old product is necessary for the introduction of a new product to be possible. It is worth noting that this result, though quite similar, is stronger than the results of Choi (1998) and Cabral (1998a), and, in fact, stronger than would be any 17
The argument follows closely the market-linkage logic identified by Bernheim and Whinston (1990).
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similar result in an adverse-selection framework; in an adverse-selection model, a monopolist can always introduce a new good by giving it away for free in the first period, and this strategy will, moreover, be profitable whenever the monopolist is patient enough. Here, the old good and its reputation may be necessary for production also in the long run; the reason being that incentives for producing high quality need be maintained.
3.4. Remarks on welfare analysis We have already noted that the objectives of the monopolist are somewhat aligned with efficiency objectives because prices are distorted upwards by credibility considerations. The simplest example is that with two goods, one credibility constraint binding and the other sufficiently lax for the pooled credibility constraint to be non-binding; then, moving from good-specific reputations to a pooled one increases profits and decreases one of the prices, while the other price is unchanged. An obvious question to ask is whether the welfare properties are that favourable generally. The answer is no, however, in the absence of free slack; the following result for Consumer Surplus (CS) shows that the misalignment of consumer and producer objectives is significant. Proposition 6. If both credibility constraints bind individually, the pricing induced by pooling reputations leaves CS no greater than pricing induced by separate reputations. Proof. See Appendix A. The intuition hinges on the fact that CS is a convex function of price, leading to price dispersion being beneficial in this sense, and the fact that the pooling of two reputations leads to a reduction in price dispersion. At the optimum with pooled reputations the prices of the two goods can be traded off marginally against each other at a rate that keeps CS constant; for larger changes (at the same rate), dispersion increases CS. Note that the welfare benefits of price dispersion are real, although consumer surplus is a somewhat dubious measure of welfare.18
4. Conclusion The main point of this paper is simple: there are economies of scope in carrying a reputation. A firm carrying a pooled reputation for producing high quality of two goods will, under reasonable conditions, do strictly better than would ‘the sum’ of 18
See, e.g., Stennek (1999) for a recent discussion of consumer surplus and random prices.
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two firms producing one good each and carrying the respective reputations. This advantage is reinforced in the context of the introduction of new goods — it may be necessary to support the introduction and the ongoing selling of a new good by means of an established reputation. So far, we have deferred the question of what reputations can reasonably be tied together. Proposition 4 tells us that tying any reputations is consistent with equilibrium. Some readers may worry that consumers are unlikely to perceive the link between products necessary for such an equilibrium. Here, we provide an example where our result applies to a case where no such arbitrariness is introduced. Formally, our example is one where a firm producing two goods is constrained by the technology to either produce both goods of low quality at costs (c] 1 ,c] 2 ), or produce both goods of high quality at cost (c] 1 ,c] 2 ). In such a case, the analysis from the one-good case goes through unchanged, and the arguments for the efficient equilibrium in the one-good model apply to the two-good model as well.19 In sum, our model predicts that technological and organisational choices be made with the complementarity of reputations in mind. A number of important questions are ignored by the current framework. In our view, the paramount one is the foundation of the reputation of a firm. Certainly, it would be desirable to derive the mechanisms for sustaining reputations of firms and brands from basic assumptions about individual incentives within firms. Apart from the obvious benefits, any progress along such lines would likely throw light on questions regarding the virtues of different organisational forms as bearers of reputation.20 Another issue which we have not addressed at all is that of the interaction between our results and competition. For example, intuition suggests that any commitment to producing high quality is an advantage for an incumbent; this seems worth further analysis.
Acknowledgements The paper was conceived and started while the author was visiting the Department of Economics, Harvard University, and early discussions with Oliver ¨ were very useful. I have received valuable comments Hart and Bengt Holmstrom 19
The example seems consistent with empirical evidence that consumers put more confidence in brand extensions where there is a perceived fit between the new product and the old one (Aaker and Keller, 1990). 20 Although the notion of collective reputation has received little attention within economic theory, Kandori (1992) and Tirole (1996) are recent contributions. The results of Tirole (1996) show that high enough rents are important for the sustainability of a group reputation, indicating that something similar to the credibility constraint of our model would have to hold in a model with a collective reputation as well.
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from Joseph Harrington and two anonymous referees as well as from Marcus ¨ Asplund, Hans Carlsson, Jorgen Weibull and seminar participants at The Industrial Institute for Economic and Social Research, Stockholm. Financial support from the Bank of Sweden Tercentenary Foundation is gratefully acknowledged.
Appendix A Proof of Proposition 2 It is clear by definition that the profit from the monopoly contract, p, is an upper bound on profits absent randomisation. The monopolist might in principle be able to do better by randomising, but not in this model since demand is concave. Hence, p is a strict upper bound on payoffs in each period, and it is clear that it is attainable as a Nash equilibrium if the monopolist cannot gain by defecting; i.e., if the credibility constraint is satisfied. To verify that the equilibrium is subgame perfect, we need only check that there are no profitable one-time deviations upon any history (Fudenberg and Tirole, 1991, Theorem 4.2). But this is obvious for the buyers, and once this is clear it is equally obvious for the seller since she is credible by construction. h Proof of Proposition 6 First, note that both credibility constraints’ binding separately implies that the pooled credibility constraint binds (suppose the pooled constraint were slack; then one of the prices would be above the level implied by the one-good credibility constraint which, in turn, exceeds the monopoly price; since credibility does not constrain the price, this cannot be optimal; a contradiction). Let CS denote Consumer Surplus; `
`
E
E
p1
p2
CS 5 x 1 ( j ) dj 1 x 2 ( j ) dj . Consider a price change from prices ( p1 , p2 ) that are optimal given two separate, binding, credibility constraints, to prices ( p 19 , p 92 ) that are optimal given the pooled credibility constraint. Let Dpi 5 p i9 2 pi , and assume, without loss of generality, that p 19 . p1 and p 29 , p2 . We have `
`
pi
E
E
E
p i9
pi
p 9i
DCSi 5 x i ( j ) dj 2 x i ( j ) dj 5 x i ( j ) dj < 2 Dpi x i ( p 9i ), but from the individual credibility constraints
(A.1)
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12d pi 5c] i 1 ]] (c] i 2c] i ), d which inserted into the pooled credibility constraint (7) gives x 1 ( p 19 ) Dp1 1 x 2 ( p 29 ) Dp2 5 0;
(A.2)
thus, an upper bound on the change in consumer surplus, DCS1 1 DCS2 , is zero. h
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