Product Quality, Reputation, and Market Structure

Transcription

1 Northwestern University From the SelectedWorks of Yuk-Fai Fong 2008 Product Quality, Reputation, and Market Structure James D Dana Yuk-Fai Fong, Northwestern University Available at:

2 Product Quality, Reputation, and Market Structure James D. Dana Jr. Department of Economics and CBA Northeastern University Yuk-fai Fong Kellogg School of Management Northwestern University January 12, 2008 Abstract Firms in an oligopoly market can more easily maintain a reputation for a high quality experience good than a monopolist or firms in a competitive market. Intuitively, selling an experience good of unknown quality is like selling a primary good of known quality and a secondary upgrade of unknown quality. When a monopolist or a competitive firm deviates in the price or quality of its upgrade, they can anticipate that consumers will no longer buy the upgrade, but the profit they earn from their primary good is unchanged. On the other hand, when an oligopoly firm deviates in the price or quality of its upgrade, the firm can anticipate not only that consumers will no longer buy its upgrade but also that the price it can charge for its primary good will fall. We also find that for a wide range of parameter values consumer surplus is higher in any low quality equilibrium than in any high quality equilibrium, even when it is socially efficient to produce high quality. We would like to thank Heski Bar-Isaac and Kathryn Spier for helpful comments. 1

3 1 Introduction The price, market structure, and product quality of experience goods are clearly linked. Theoretically, higher margins give stronger incentives to sustain a reputation for a high quality and they encourage firms to increase product quality in order to steal business from rivals. This is also true empirically. In the airline industry, deregulation lead to lower prices and a reduction in service quality. 1 Similarly, increased competition encourages firms to protect their market share by competing in product quality. In general, monopolists have higher margins but face less of a threat from competition, while firms in competitive markets have lower margins and face a greater threat from competition. In between are the oligopoly markets. Firms in oligopoly markets may enjoy high margins (because of tacit collusion) and face a strong threat from competition, which suggests product quality might be highest in imperfectly competitive markets. This paper considers a repeated game model of pricing and product quality choice in which market structure has a nonmonotone impact on firms ability to maintain reputation for high quality; high quality is more likely to be an equilibrium in oligopoly markets than in either monopoly or competitive markets. Empirical evidence on the relationship between market structure and quality is mixed. Mazzeo (2003) finds that on-time performance increases dramatically when a second non-stop carrier serves a route. Domberger and Sherr (1989) find that the British government s liberalization of the conveyancing monopoly in 1984 led to improvement in quality of conveyancing services in England and Wales. These papers are consistent with our model in that they emphasize some competition increases quality relative to monopoly. Another empirical paper, McMaster (1995) finds that introducing competitive bidding for some health services in the United Kingdom led to lower quality of these services. This is consistent with our prediction that within an oligopoly market, quality should fall as the number of firms rises, or more generally, as tacit collusion becomes more difficult. We consider an oligopoly model in which firms sell experience goods, that is goods whose quality is unobserved until after the purchase decision. High quality can be sustained more easily by oligopoly firms than by either a monopoly firm or by firms in a competitive market. More precisely, we consider a model in which firms can choose either to sell a high quality and or low quality good and find that a high quality good can be supported as a subgame perfect equilibrium (SPE) outcome for a larger range of discount factors in an oligopoly market. The intuition for our result can be seen by considering the analogous problem 1 Graham, et. al, (1983) show that the frequency of departures declined following deregulation. 2

4 in which experience-good sellers each sell two products, a primary product with observable quality and a secondary upgrade with unobservable quality. The upgrade is either high or low quality and the value of the upgrade to consumers is zero when the quality is low. 2 Now imagine that the firms produce and sell only the upgrade. If a price exists at which a monopolist can sustain a reputation for a high quality upgrade, it follows that firms in an oligopoly and competitive markets can sustain a reputation for a high quality upgrade at the same price. Quality is sustained by giving each firm a fixed share of the market and having consumers punish each firm with zero sales and zero profits if it ever produced low quality, so the ability to sustain a reputation for high quality is independent of market structure. Now suppose instead that firms produce and sell both products. A monopolist earns its monopoly profit from the primary good, and firms in a competitive market earn zero profit from the primary good, and these profits are independent of whether or not the firms sell a high-quality or a low-quality upgrade. In contrast, the profit that firms in an oligopoly earn on the primary product can be anything ranging from the competitive profit to the monopoly profit; the profit depends on the discount factor and on the firms equilibrium strategies. This means that oligopolists using history-dependent strategies can tie the profits they earn on the primary product to their reputations for selling a high quality upgrade. The ability of firms to punish each other through a reduction in the price of the primary product means that the punishment for a deviation in the product quality is larger and the firms have a stronger incentive to produce high quality. We also explore the impact of allowing quality to be unobservable on firms ability to charge prices above the competitive price. We find that firms selling experience goods are able to charge prices above the competitive price more easily than firms selling goods with observable quality if the number of firms is sufficiently large or the high quality product is sufficiently more efficient than the low quality product. On the other hand, when high quality is not sustainable, firms ability to charge supranormalpricesisunaffected, but product quality deteriorates so the highest sustainable price falls. Since higher quality may only be feasible when the market is sufficiently concentrated our theory also suggests a potential benefit from imperfect competition. Despite this social benefit frommarketconcentration,wefind that for a wide range of parameter values for which both low quality and high quality equilibria exist, con- 2 Making an analogy between selling a primary product of known quality and a upgrade of unknown quality and selling a single product of unknown quality also requires that we assume that the upgrade can only be sold when it is bundled with the primary product. However, our intuition is valid whether or not we make this assumption. 3

5 sumers strictly prefer any low quality equilibrium to all of the high quality equilibria. 2 Related Literature Our paper is at the intersection of two literatures: the literature of reputations for product quality and the literature on tacit collusion. 3 Klein and Leffler (1981) and Shapiro (1983) consider models in which reputations are a mechanism to support high quality in a repeated moral hazard model. They showed that for any discount factor there exists a minimum price premium (and equivalently for any price premium, a minimum discount factor) required for high quality to be sustainable. Comparing the price premium with consumers willingness to pay for a high quality product determines the minimum discount factor needed to sustain high quality. As Stiglitz (1989) observes, the existence of a price premium implies that firms must earn positive profits and that competition may place limits on the level of quality that can be supported. In this spirit, Kranton (2003) shows that competition may cause firms to bid the market price down to a level that high quality cannot be supported as a subgame perfect Nash equilibrium outcome. However, Kranton considers only equilibria in which consumers beliefs about a firm s quality depend only on the firm s past quality and not on the firm s prices. Two other papers also look at the relationship between market structure and product quality in a repeated game. Under a similar restriction on consumer beliefs, Bar-Isaac (2005) provides an example in which there is a non-monotone relationship between competition and quality with a pattern that is opposite to ours. 4 In his example, reputation for high quality is the hardest to sustain under intermediate level of competition. And Hörner (2002) shows that competition promotes quality when quality is noisily observed because it allows dissatisfied consumers to easily and credibly punish any firm by switching suppliers whenever it fails to produce high quality. The literature has not studied tacit collusion among experience good sellers. Within the tacit collusion literature, our work is most closely related to Bernheim and Whinston s (1990) work on multimarket contact. They show that competing in 3 An excellent survey of the tacit collusion literature, written largely for policy makers, is Ivaldi et. al. (2003). An excellent early survey of the reputation literature is Stiglitz (1989). Mailath and Samuelson (2006) survey the more recent contributions to this literature. 4 In Bar-Isaac (2005), firms choose quantity and quality instead of price and quality. His assumption that consumers do not infer quality change from change in quanity is in the same spirit of Kranton s assumption. 4

6 multiple markets can facilitate tacit collusion, but only when the markets are asymmetric. 5 In our paper, we argue that it can be easier for firms to simultaneously tacitly collude on prices and maintain reputations of high product quality than to do either of these activities alone. These two activities are naturally asymmetric, so in that sense, our insights are consistent with Bernheim and Whinston s observation that increasing the dimensions of contact between the firms can increase profitability. In a similar way, our work is also related to repeated moral hazard models in the literature on brand extensions. Several papers (Wernerfelt, 1988, Choi, 1998, Cabral, 2003, and Andersson, 2002) show that it is can be easier for a monopolist to maintain a reputation for high quality when using a single umbrella brand on multiple products rather than using a single brand on each product. 6 This literature has generally not looked at the impact of competition on the incentives for brand extensions. 3 The Model We assume there are n>1 symmetric firms and a unit mass of homogeneous consumers. Firms are infinitely lived. Consumers live only one period and are replaced each period by a new generation of consumers. 7 Each consumer has valuation v h for a single unit of a high quality good. Each consumer has valuation v l <v h for a single unit of a low quality good. Each period every firm simultaneously chooses its product quality, either q l or q h,anditsprice,p, both of which are constrained to be the same across all the consumers. Consumers then choose whether or not to consume and from which firm to purchase. Consumers observe prices before they make their purchase decisions, but they do not observe firms product quality decisions until after making their purchase decision. We assume perfect public monitoring ex post, that is, we assume that firms price and product quality decisions become common knowledge to all consumers and 5 Dana and Fong (2006) show that firms offering multi-period subscription contracts can endogenously create multimarket contact. Although these markets are symmetric, tacit collusion still becomes easier because these markets take turn to open sequentially. 6 In a related paper, Dana and Spier (2006) show that product bundling helps firms to maintain a reputation for high quality when consumers are small, have heterogeneous preferences, and privately observe product quality. In their model, consumers will free ride and not punish optimally unless products are bundled. 7 Equivalently, consumers are long-lived, but are arbitrarily small and anonymous, so they maximize their period payoffs. 5

7 firmsatthestartofthenextperiod. Production exhibits constant returns to scale. Each unit of the high quality product costs c h to produce and each unit of the low quality product costs c l to produce, where c l <c h. We assume v l >c l, so equilibrium sales are strictly positive even if consumers believe that only the low quality product is supplied. We also assume that a social planner would produce only the high quality good. In other words, we assume that v h c h >v l c l. (1) The common discount factor is [0, 1]. Before solving the general model, we consider several important benchmarks. Benchmark 1: Tacit Collusion and Observable Quality Consider any finite number of competing firms, n>1, that each sell a product whose quality is observable. The Nash equilibrium of the stage game is high quality at a price of c h. This is also an equilibrium of the infinitely repeated game. However, in the infinitely repeated game, firms may be able to support higher prices in a subgame-perfect- Nash equilibrium using the threat of static Nash reversion as a response to any deviation. Specifically, any price p in the interval [c h,v h ] can be supported as an equilibrium price as long as 1 p c h n 1 (p c h). (2) or equivalently, P 0 (n) 1 1 n, (3) where P 0 (n) is the critical value of above which any price can be supported, and the subscript 0 indicates that this is a critical value in one of our benchmark models. Intuitively, condition (3) states that firms would prefer to earn 1/n of the industry profit by charging p forever rather than cut their price and capture the entire market for a single period and then earn zero in ever period thereafter. This can be summarized as follows: 8 8 For high enough, tacit collusion on low quality and any price p (c l,v l ] can also be sustained by the threat punishment of static Nash reversion. Lemma 1 ignores these Pareto dominated equilibria and considers only equilibria in which firms sell high quality. 6

8 Lemma 1 Tacit Collusion (Friedman, 1971) When quality is observable, then for any n if < P 0 (n), then the unique subgame perfect equilibrium price is p = c h, and if P 0 (n), then any price in the interval [c h,v h ] can be supported as a subgame perfect equilibrium price. Benchmark 2: Competition and Unobservable Quality Suppose that quality is unobservable, but that the number of firms is very large. Clearly this implies tacit collusion is impossible, that is, (3) is not satisfied. However, it may nevertheless be possible to support the provision of a high quality product in equilibrium. As long as firms make positive profits and consumers punish firms that shirk on quality by purchasing from different firms in the future, high quality can be supported if firms are sufficiently patient. Consider the following equilibrium strategies. On the equilibrium path, every firm produces high quality and charges a price p every period. Consumers expect high quality as long as the firm s price is p or higher. Off the equilibrium path, consumers expect each firm to offer low quality if 1) that firm announces a price below p, or2)thatfirm has offered either a lower price or a low quality product in the past. If a firm deviates in either price or quality, then in all future periods, consumers expect that firm to offer low quality. Following any deviation, every other firm continues to play their equilibrium strategies. Note that when the number of firms selling high quality is very large, it follows that v h p v l c l or p v h v l + c l. Otherwise a firm could offer a price greater than c l and capture the entire demand even when consumers expect low quality. Also,notethatsincep v h v l + c l,ifafirm shirks on quality, its profits are zero every period thereafter. It cannot profitably sell a low quality good. So an equilibrium in which firms produce high quality products exists using the above strategies if and only if p c h 1 p c l +0 (4) for some price p v h v l + c l. This implies: Lemma 2 Competitive Reputation (Klein-Leffler, 1981, Shapiro, 1983, Allen, 1984): When quality is unobservable and there are a continuum of firms, there exists a subgame perfect equilibrium in which firms offer high quality if and only if there exists a price p v h v l + c l such that (4) holds, or equivalently, if and only if Q 0 = c h c l. (5) v h v l 7

9 Benchmark 3: Monopoly and Unobservable Quality Next consider a monopolist (n =1) selling a product whose quality is unobservable. Or equivalently, consider the case in which the n firms each have a monopoly over a fraction 1/n of the consumers. IntheuniqueNashequilibriumofthestagegameeachfirm sells a low quality product at a price v l. This is also an equilibrium of the infinitely repeated game. However, in the infinitely repeated game a monopolist may be able to support higher quality in a subgame perfect equilibrium using the threat of static Nash reversion. Specifically, suppose consumers equilibrium expectations are that the firm will produce high quality as long as the price is p or higher and the firm has only produced high quality in the past, but they expect low quality forever whenever the price is below p or they observed the firm produce low quality in the past. These represent consumers optimal punishment strategies. Given these off-the-equilibrium-path strategies, high quality can be supported in a subgame-perfect equilibrium as long as the present discounted value of all future profit on the equilibrium path exceeds the profit associated with shirking on quality and thereafter selling a low quality product at a price of v l. The present discounted value of all future profits on the equilibrium path must also exceed the profit associated with a deviation in price or a deviation in both price and quality. However since consumers expect low quality immediately after seeing a price deviation, the payoff from any other deviation is no higher, and in most cases strictly lower, than the payoff from deviating in quality alone. So, for a given price p, high quality can be supported as a subgame perfect equilibrium if and only if p c h 1 (p c l)+ v l c l 1. (6) It follows that for a given price, high quality can be supported as a subgame prefect Nash equilibrium for all c h c l. (7) p v l Moreover, since the critical value is decreasing in p, it follows that if high quality can be supported at any price, it must be supportable at p = v h.thisimplies: Lemma 3 Monopoly Reputation: When a single firm sells a product with unobservable quality, if Q 0 = c h c l, (8) v h v l 8

10 then subgame perfect Nash equilibria exist in which the firm produces high quality, and otherwise the unique equilibrium outcome is low quality at a price of v l. This implies the following corollary: Corollary 4 High quality can be supported as a subgame perfect Nash equilibrium outcome by firms in a competitive market if and only if high quality can be supported as a subgame perfect Nash equilibrium outcome by a monopolist. Anintuitivewaytoseewhythisistrueistothinkofthefirmsassellingtwo goods, a primary good and a secondary upgrade, where the upgrade can be either high or low quality. The value of the primary good is v l to all consumers and its cost is c l. The low quality upgrade is worth 0 and costs the firm 0 and the high quality upgrade is worth v h v l and costs the firm c h c l. However, the quality of the upgrade is unobservable. For both a monopolist and a competitive firm, the profit earned from the primary product is independent of its reputation for the quality of its upgrade. In the case of a monopolist, that profit is the monopoly profit fora low quality good and in the case of a competitive firm that profit iszero. Sothese firms have the same ability to sustain a reputation for a high quality upgrade. That is, both types of firm are able to sustain a reputation for a high quality upgrade if and only if the present value of the profits earned on producing the genuine upgrade exceed the one shot profits from selling a inferior upgrade, that is, if (v h v l ) (c h c l ) v h v l, (9) 1 or Q 0. The crucial assumption is that consumers have homogeneous valuations for the upgrade and most importantly, that their valuations for the upgrade are independent of the price they paid for primary good. Note that the result still holds when consumers have heterogeneous valuations for the primary good as long as they have homogeneous valuations for the upgrade conditional on purchasing the primary good. 4 Oligopoly and Unobservable Quality We now consider the general model. First, notice that selling low quality at a price of c l is the unique Nash equilibrium of the one-shot game. This is because offering low quality is a dominant strategy and Bertrand price competition among homogeneous 9

11 firms leads to marginal cost pricing. So it follows that selling low quality at a price of c l in every period is also an equilibrium of the repeated game. Now, consider the following equilibrium strategies in which firms punish rivals deviations. On the equilibrium path, firms produce high quality and sell at price p every period. Consumers expect high quality and 1 of them purchase from each n firm as long as v h p. Off the equilibrium path, if any firm deviates in either price or quality, then in all future periods, all firms revert to the static Nash equilibrium selling low quality at a price of c l andearnzeroprofits. Consumers have rational expectations, so all consumers and firms expect a firm to offer low quality if any firm has offered either a lower price or a low quality product in the past. In addition, consumers expect a firm to offer low quality in the current period whenever that firm announces a price below p. This belief is fully consistent with firms subsequent off-the-equilibrium path behavior. When a firm deviates in price, it anticipates zero profit in all future periods regardless of its current quality. Hence, a firm that deviates in price has no incentive to produce high quality in the current period. Also note that these are the optimal punishments. It is impossible to impose negative profits on the deviator, so these strategies impose the most severe punishment and hence characterize the highest sustainable quality. Consider the firm s incentive to shirk on quality. Given these strategies, the firm will not shirk on quality as long as p c h 1 p c l. (10) Let Q (p) be defined as the value of for which this constraint holds with equality. So (10) is satisfied as long as Q (p) c h c l p c l, (11) or equivalently p c h (1 ) c l. (12) Clearly Q (p) is decreasing in p, so supporting high quality is easier at higher prices. Next consider the firm s incentive to lower price. A firm that deviates in price is expected to produce low quality, so clearly it will produce low quality. Conditional on deviating, the firm will maximize its deviation profit, which is ½ p Π l (p 0,p)= 0 c l if v l p 0 v h p, 0 otherwise, 10

12 where p 0 is the deviating firm s price. It follows that the most profitable deviation is p 0 = p (v h v l ) if p (v h v l ) >c l and p 0 = c l otherwise. So if p v h v l + c l the firm has no incentive to deviate in price. If p>v h v l + c l,thenthefirm has no incentive to deviate in price as long as 9 1 (p c h ) n (1 ) p (v h v l ) c l, (13) or equivalently P (p, n) 1 1 (p c h ) n (p (v h v l ) c l ). (14) This condition can be satisfied if and only if there exists p v h such that p (1 ) n((v h v l )+c l ) c h. (15) (1 ) n 1 Finally note that we do not need to separately consider deviations in both price and quality. Since a firm that deviates in price always chooses low quality, our analysis of the firm s optimal price deviation is sufficient. This can be summarized as follows: Lemma 5 For any finite number of firms, n>1, high quality and the price p (c h,v h v l + c l ] can be supported as a subgame perfect Nash equilibrium outcome if and only if Q (p). For any finite number of firms, n>1, highqualityandthe price p (v h v l + c l,v h ] can be supported as a subgame perfect Nash equilibrium outcome if and only if P (p, n) and Q (p) are both satisfied. Lemma (5) characterizes the set of p, n, and for which high quality is sustainable as a subgame perfect equilibrium outcome. The following proposition characterizes the set of n and for which high quality is sustainable as a subgame perfect equilibriumoutcomeatsomepriceandspecifies the upper and lower bounds of the associated prices. 9 If consumers did not infer low quality from price cut, as modeled in Kranton (2003), then the deviation profit would have been p c l and the incentive constraint would have been 1 (p c h ) n (1 ) p c l. In this case, the incentive constraint would necessarily fail for sufficiently large n. In our analysis, given that firms reverts to low quality and marginal cost pricing following any deviation, no rational consumer will believe that a firm which deviates in price will produce high quality. 11

13 Proposition 1 For any finite number of firms, n>1, highqualitycanbesupported as a subgame perfect Nash equilibrium outcome if and only if or equivalently min max Q (p), P (p, n) ª. (16) p (v h v l +c l,v h ] ½ c h c l v h c l c h c l v h v l 1 1 n if n< v h c l if n v h c l v l c l, v l c l. The supportable equilibrium prices are ½ ¾ ch (1 ) c l (1 ) n((vh v l )+c l ) c h p, min,v h. (18) (1 ) n 1 Proof: It follows immediately from Lemma 5 that any finite number of firms, n>1, there exists a price p (v h v l + c l,v h ] such that high quality and the price p can be supported as a subgame perfect Nash equilibrium if and only if and (17) min max Q (p), P (p, n) ª. (19) p (v h v l +c l,v h ] Both P (p, n) and Q (p) are continuous on (v h v l + c l,v h ],and d P (p, n) dp d Q (p) dp = c h c l (p c l ) 2 < 0, = (v h v l ) (c h c l ) n (p c l v h + v l ) 2 > 0, so Q (p) is everywhere decreasing in p and P (p, n) is everywhere increasing in p. Also, near the lower bound of the interval (v h v l +c l,v h ], P (p, n) < 0 and Q (p) > 0, so clearly Q (p) > P (p, n). Note that P (v h,n) Q (v h ) if and only if c h c l 1 1 v h c h v h c l n v l c l or n v h c l. v l c l Suppose that Q (v h ) P (v h,n),orequivalently,n v h c l v l c l, so that the two functions cross somewhere in the interval (v h v l +c l,v h ]. It follows that max Q (p), P (p, n) ª 12

14 is minimized at the intersection. Let ˆp (n) denote the price at which the two functions cross, so added the left and right most equalities or So Q (ˆp (n)) = c h c l =1 1 (ˆp (n) c h ) ˆp (n) c l n (ˆp (n) (v h v l ) c l ) = P (ˆp (n),n), ˆp (n) = n n 1 (v h v l )+c l. min max Q (p), P (p, n) ª = Q (ˆp (n)) = P (ˆp (n),n) p (v h v l +c l,v h ] c h c l = n (v n 1 h v l )+c l c l = c µ h c l 1 1. v h v l n Now suppose that Q (v h ) > P (v h,n) so n< v h c l v l c l.inthiscase min max Q (p), P (p, n) ª = Q (v h )= c h c l. p (v h v l +c l,v h ] v h c l The lower bound on p follows (12) and upper bound on p follows (15) and p v h. This completes the proof. The solid line in Figure 1 shows the threshold value of, defined in (16). For all above this threshold, production of the high quality product is sustainable. As we can see from the figure and equation (17), the threshold value of is constant for n v h c l v l c l,butforn> v h c l v l c l, the threshold value of increases with the n. This is because c h c l v h v l 1 1 n increases in n. For comparison, Figure 1 also shows P 0 (n) and Q 0, which are, respectively, the critical threshold in the first benchmark model and the common critical threshold in the second and third benchmark models. 13

15 c = Q h l 0 vh vl c v h h P ( n) 1 c cl c l 0 p ( v v + c, v ] 1 = 1 n Q P { ( p) ( p n) } min max,, h l l h ch cl 1 1 v v n h l 0 2 v v h h cl c h v v h l cl c l n Figure 1: Comparison of critical values of We now show that an oligopoly with n>1 firms can more easily sustain high quality then a monopolist. Proposition 2 For any finite number of firms, n>1, therangeof for which high quality can be supported with unobservable quality is strictly greater than the range of for which high quality can be supported under monopoly or competition with unobservable quality. Specifically, min p (v h v l +c l,v h ] max Q (p), P (p, n) ª < Q 0 (20) Proof: Since Q 0 = c h c l, v h v l and since c h c l > c h c l, v h v l v h c l (21) and c h c l > c µ h c l 1 1, v h v l v h v l n (22) equation (20) follows immediately from Proposition 1. 14

16 Proposition 2 establishes that for any n>1, there exists a range of discount factorssuchthathighqualitycanbesustainedwhenafinite number of firms compete with one another, but high quality cannot be sustained when a single firm produces or arbitrarily many firms compete with one another. From (8) and (17), we can see that the range of discount factors for which high quality can be sustained in an oligopoly, but not in a monopoly, is [ c h c l v h c l, c h c l v h v l ) when the oligopoly is small, i.e.,, c h c l v h v l ) when the oligopoly is large, i.e., n> v h c l n v h c l v l c l,and[ c h c l v h v l 1 1 n From (8) and (17), we can also see that for sufficiently small, i.e., < c h c l v l c l. v h c l,high quality cannot be supported in any market structure. When is in an intermediate range, i.e., [ c h c l v h c l, c h c l v h v l ),thenhighqualitycanbesupportedonlyinanoligopoly of sufficiently small size. And finally, when is sufficiently large, i.e., [ c h c l v h v l, 1), high quality can be supported for any market structure. Thinking of the firms as selling a primary good and a secondary upgrade also helps understand the intuition for Proposition 2. In Corollary 4 we saw that local monopolists and competitive firms have the same incentive to sustain a reputation for a high quality upgrade because in both the monopoly and competitive models, the firms profits from selling the primary good are independent of their reputation for quality. In an oligopoly, however, firmscantietheprofits they earn from selling the primary product to the industry s reputation for quality. When a firm loses its reputation for high quality, the ensuing price war erodes its profit fromtheprimary product. Because of the risk of losing the profits from the primary good, firms are less tempted to shirk on quality, which makes a reputation for high quality easier to sustain. Next, we investigate how the observability of product quality impact firms ability to sustain prices above the competitive level. We find that above marginal cost prices are easier to sustain when product quality is unobservable only if the number of firms is sufficiently large or the high quality product is sufficiently more efficient than the low quality product. If the high quality product is only moderately more efficient than the low quality product, then when n is small, making quality unobservable can lower the highest sustainable equilibrium product quality and lower the highest sustainable equilibrium prices. Proposition 3 For any finite number of firms, n>1, therangeof for which prices above marginal cost can be sustained with unobservable quality is strictly greater than the range of for which prices above marginal costs can be sustained with observable quality if and only if n v h c l v h c h. (23) 15

17 Equivalently, min max P (p, n), Q (p) ª P 0 (n) (24) p (v h v l +c l,v h ] if and only if (23), which implies (24) holds for all n if and only if v h 2c h c l. Proof: Since P 0 (n) =1 1 n > c µ h c l 1 1, v h v l n it follows from Proposition 1 that (24) holds when n v h c l v l c l.whenn< v h c l v l c l,then (24) holds if and only if 1 1 n c h c l v h c l or equivalently, if and only if (23) holds. Finally, note that (24) holds for all n if and only if (23) is satisfied for n =2,orequivalentlyv h 2c h c l. Condition (23) of Proposition 3 implies that making quality unobservable is more likely to increase the highest sustainable price when high quality is more efficient (i.e., v h c h is higher). This is quite intuitive because the cost of being punished with a change in expected quality is more severe when the low quality product is relatively less attractive or relatively more costly. Condition (23) of Proposition 3 also implies that making quality unobservable is more likely to increase price when there are more firms, which might seem counterintuitive. However increasing n does not make high prices easier to support, it only increases the impact of quality being unobservable. The reason it does this is that the harder it is to tacitly collude when quality is observable, the more likely it is that punishing firms with a change in expected quality will do better than punishing them with a price war. Note that when condition (23) is not satisfied, firms ability to charge supranormal h prices is unaffected by the observability of product quality. However, for 1 1, c h c l n v h c l i, unobservability of quality causes firms to produce only low quality products so the highest sustainable price falls. 5 Product Quality and Consumer Welfare Our analysis so far has focused on identifying conditions under which firms are able to maintain a reputation of high quality. Although by assumption production of 16

18 high quality good is socially efficient, it is interesting to ask whether consumers are always better off in high quality equilibria than in low quality equilibria when both types of equilibria exist. In general it is difficult to unambiguously compare consumer welfare in these two types of equilibria, however, in the following proposition we identify conditions under which consumers are unambiguously worse off in high quality equilibria than in low quality equilibria. Proposition 4 If ( ) (, n) Φ (, n) : [ c h c l, c h c l 1 ) and n ( v h c l v h v l 1, 1 1 v h v l, c h c l ] then high quality equilibria and low quality equilibria co-exist and consumers prefer any low quality equilibrium to every high quality equilibrium. Proof. Recall from Proposition 1 that when a high quality equilibrium exists, which happens for all c h c l 1 v h c l and n, the price range for the high quality 1 v h v l c h c l good is ½ ¾ ch (1 ) c l (1 ) n((vh v l )+c l ) c h p, min,v h. (1 ) n 1 For n> 1, since tacit collusion among firms selling low quality products is impossible, in any low quality equilibrium, the low quality good will be sold at marginal cost 1 c l. Consumers prefer any low quality equilibrium to every high quality equilibrium if v l c l >v h c h (1 )c l.notethat µ v l c l v h c h (1 ) c l = v µ h v l ch c l > 0 if and only if < c h c l. v h v l v h v l This completes the proof. The area of the set Φ is shaded in Figure 1. Proposition 4 implies that enhancing efficiency needn t increase consumer welfare and suggests that our finding that oligopoly interactions can increase quality need not be seen as an argument for relaxing anti-trust scrutiny. 17

19 6 Heterogenous Customers and Downward sloping Demands We believe our insights are quite robust to generalizations of our assumptions, particularly our assumption that consumers are homogeneous. One important difference when consumers vary in their willingness to pay is that firms can make it easier to sustain a reputation for high quality product by charging a price above the monopoly price. While this restricts sales of the product, it makes incentive constraint for high quality easier to satisfy. However, charging a higher price also makes the incentive constraint for price harder to satisfy. While this difference makes the comparison more subtle, it is fairly easy to see that even with heterogeneous consumers a monopolist is still more tempted to shirk on quality than a firm in an oligopoly. This is because after shirking a monopolist loses only the incremental profits associated with high quality and continues to earn the monopoly profit generated from the sale of a low-quality product, while an oligopolist loses both the incremental profits from selling a high quality good and its share of the low-quality monopoly profits. Consider a simple extension of our model in which consumers vary in their willingness to pay for the products but have the same willingness to pay for quality upgrade, denoted by (v h v l ). In such environment, the market demands for the high and low quality goods can be represented by downward sloping demand curves q h (p) and q l (p) which satisfy q h (p) =q l (p (v h v l )). (25) The incentive constraint for a monopolist to produce the high quality good is q h (p)(p c h ) q l (p 0 )(p 0 c l ) q h (p)(p c l )+max. 1 p 0 1 This incentive constraint is most easily satisfied when q h (p)(p c h ) q h (p)(p c l ) 1 is maximized. This term can be rewritten as q h (p)((p c h ) (1 )(p c l )) 1 = = = µ 1 q h (p) p c h (1 ) c l µ 1 q l (p (v h v l )) p c h (1 ) c l µ µ 1 q l (p 0 ) p 0 ch (1 ) c l (v h v l ), 18

20 where p 0 p (v h v l ). Note that profit is decreasing in cost. Therefore, µ µ max p 0 1 q l (p 0 ) p 0 ch (1 ) c l (v h v l ) 1 max p q l (p)(p c l ) if and only if µ ch (1 ) c l (v h v l ) c l or Q 0 = c h c l. v h v l In other words, the range of for which a monopolist can maintain a reputation for high quality remains unchanged even if consumers have heterogenous valuations (or equivalently, the the market demands are downward sloping). This is striking because the crucial necessary condition is independent of the functional forms of q h ( ) and q l ( ) as long as (25) is satisfied. When there are infinitely many firms, as in the case of homogenous consumers, high quality is sustainable only if p c h 1 p c l +0, so it is clear that high quality is sustainable among infinitely many firms if and only if Q 0 just as in the case of homogenous consumers. So Lemmas 2 and 3 continue to hold in this more general framework. Similarly, It is clear that a version of Proposition 2 will hold as well. We also conjecture that Proposition 3 holds even when consumers differ in their willingness to pay. That is, above marginal cost prices are easier to sustain when qualityisunobservableaslongaseithern is large or if the high-quality good is significantly more efficient than the low-quality good. Recall that when quality is unobservable, the incentive constraint for production of high quality is independent of the number of firms. Therefore, as the number of firms becomes sufficiently large, the incentive constraint associated with deviations in price will be the binding constraint. However, as in our model with homogeneous consumers, with heterogeneous consumers this constraint will be easier to satisfy when quality is unobservable. Therefore, for a large enough number firms, above marginal cost prices are easier to sustain when quality is unobservable. 19

21 7 Conclusion Using a repeated moral hazard model of experience goods, we show that firms in an oligopoly can more easily maintain a reputation for a high quality than a monopolist or firms in a competitive market. When firms in an oligopoly expect that shirking on quality will start a price war, the long-run cost of quality shirking is increased. Hence, it is easier to sustain a reputation for high quality in an oligopoly market. We also find that while producing high quality is socially efficient, consumers may prefer low quality, that is, consumer may capture more consumer surplus in any of the low quality equilibria then in all of the high quality equilibria. An important way that our analysis differs from previous work on competition and reputations is that we relax the assumption that consumers expectations of a firm s quality are invariant to the price that it charges (or the quantity it sells). Both Kranton (2003) and Bar-Isaac (2005) use this assumption to refine the set of equilibrium they consider. We show that relaxing this restriction dramatically increases the potential for oligopolists to sustain reputations for high quality products. We think that this restriction may not be appropriate, particularly when consumers are sophisticated. Specifically, we question whether it is reasonable to rule out equilibria with high quality products by assuming that a off-the-equilibrium-path price cut leads to a subgame in which the firm s equilibrium strategy is to continue to offer high quality. Nevertheless, the level of sophistication necessary for consumers to anticipate quality changes following a fall in prices is demanding, so we expect our model to be empirically relevant only when buyers are relatively sophisticated. References [1] Allen, Franklin (1984) Reputation and Product Quality, The RAND Journal of Economics, Vol. 15, No. 3. (Autumn), [2] Andersson, F. (2002) Pooling Reputations, International Journal of Industrial Organization, 20(5), [3] Bar-Isaac, Heski (2005), Imperfect competition and reputational commitment, Economics Letters, 89, [4] Bernheim, Douglas and Michael Whinston (1990) Multimarket Contact and Collusive Behavior, RAND Journal of Economics, 21, [5] Cabral, L. M. B. (2000) Stretching Firm and Brand Reputation, RAND Journal of Economics, 31(4),

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