Prominence in Search Markets: Competitive Pricing and Central Pricing∗ Jidong Zhou Department of Economics University College London April 2009

Abstract This paper examines the implications of prominence in search markets. We model prominence by supposing that prominent products are sampled first by consumers. We find that prominence has contrasting impact on price and welfare between different market structures. If there is no systematic quality difference among products, prominent products are cheaper than non-prominent ones in the competitive-pricing case where different products are supplied by different firms, but they are more expensive in the central-pricing case where a multiproduct firm sells all products. Moreover, in the competitive-pricing case, making some products prominent tends to enhance industry profit but lower consumer surplus and total welfare, while in the central-pricing case it can boost all players’ surplus. Keywords: consumer search, prominence, oligopoly, multiproduct monopoly, product differentiation JEL classification: D11, D43, L13

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Introduction

Consumers often face many options in the market and need to search to find a satisfactory one. In many circumstances, some options are more prominent than others in the sense that they are more likely to be considered first by consumers. For example, ∗

This paper benefits from the discussions with Mark Armstrong and John Vickers. I also thank Syngjoo Choi, Antonio Guarino, Steffen Huck, Ran Spiegler, Michael Waterson, and seminar participants at Zurich for their comments. Financial support from the Economic and Social Research Council (UK) and the British Academy is gratefully acknowledged. Contact information: [email protected].

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when using the online search engine, people might first click through the sponsor links which are displayed prominently; when people come to a supermarket or a bookstore, those products displayed at the entrance or other prominent positions might catch their attention first; in a restaurant, those dishes recommended by the waiter or offered in a special menu might also be considered first by customers. The order in which people consider options is an important determinant factor of people’s final choices. Lots of evidence has shown that the options in the prominent positions could be favored disproportionately. For example, Madrian and Shea (2001) identify the default effect in 401(k) participation and saving behavior. They find that participation is significantly higher under automatic enrolment and a substantial fraction of participants hired under automatic enrolment stick to both the default contribution rate and the default fund allocation. Ho and Imai (2006) and Meredith and Salant (2007) both point out that ballot order affects election outcomes: being listed first can significantly increase vote shares. Einav and Yariv (2006) present evidence that economists with surname initials earlier in the alphabet have more successful professional careers.1 Sellers in the market also realize the importance of prominence in affecting buyers’ choices, and they are willing to pay for their products being displayed prominently. For example, search engines make money through selling sponsor links, the yellow page charges more for prominent adverts, manufacturers pay supermarkets for access to prominent display positions, and eBay charges sellers who want to make their lists more visible. The above discussion suggests that prominence plays an important role in the market, and its impact on market performance deserves investigation. Arbatskaya (2007), and Armstrong, Vickers, and Zhou (2007) (AVZ thereafter) have made progress in this direction. Arbatskaya considers a search model with a homogeneous product in which consumers search in an exogenously specified order. Since consumers only care about prices, in equilibrium the prices should decline with the rank of products. Otherwise, no consumer will bother to visit products in unfavored positions. AVZ consider a search model with horizontally differentiated products which is built on Wolinsky (1986), and Anderson and Renault (1999). AVZ introduce a prominent product in the market and suppose that all consumers will consider it first. They find that the prominent product will be charged a lower price than other non-prominent products, and making a product prominent usually increases industry profit but lower consumer surplus and total 1

Lohse (1997) experimentally investigates the influence of yellow page advertisement characteristics on consumer information processing behaviour. By tracing subjects’ eye movements, he finds that ads which are colourful, with graphics, with larger sizes, or near the beginning of a heading, are more likely to catch subjects’ attention. For example, subjects noticed over 93% of the large display ads but only 26% of the plain listings.

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welfare.2 The contribution of this paper is twofold. First, we extend AVZ by considering multiple prominent products. This allows us not only to examine how price and welfare vary with the number of prominent products but also to discuss the endogenous number of prominent products (e.g., in the case where a platform, say, a search engine can choose how many prominent positions to sell). Secondly and more importantly, we compare the implications of prominence between different market structures. Both Arbatskaya (2007) and AVZ consider the competitivepricing scenario where each firm only sells one product. Nevertheless, in the market, there often exist multiproduct firms, each supplying several differentiated variants or brands of the same product and can control their prices directly. For example, a restaurant supplies various dishes (even in the same category) and sets all prices by itself; a supermarket usually sells several brands of a product and has some discretion to influence the retail prices. In such cases, consumers also need to pay (in-store) search costs to find a satisfactory product, and we also often see prominent products such as the dishes recommended in a special menu and the brands displayed on the gondola ends. We find that in the central-pricing case with a multiproduct monopoly, the impact of prominence is almost opposite to that in the competitive-pricing case. Specifically, prominence in the central-pricing case can benefit both consumers and firms, and so improve total welfare. Section 2 analyzes the competitive-pricing model with multiple prominent products. We suppose consumers will sample among prominent products first, and if they are not satisfied with these products, they will continue on to search among non-prominent products. We find that prominent products are always cheaper than non-prominent ones. This generalizes the price result in AVZ. However, making several products prominent may raise all products’ prices, which cannot happen in the single-prominentproduct case where making one product prominent always lowers its price. We also find that the relationship between welfare and the number of prominent products is nonmonotonic. This is easy to understand since the case without prominent products is the same as the case where all products are prominent. We further show that, in the case with a relatively small search cost, industry profit will first increase and then decrease with the number of prominent products, and it will reach its maximum when about half of products become prominent; while consumer surplus and total welfare will vary in the opposite way. 2

An earlier paper on ordered consumer search is Perry and Wigderson (1986). There is two-sided asymmetric information in their model: the product is homogenous but each seller has an uncertain cost, and consumers differ in their willingness-to-pay for the product. They also assume no scope for going back to a previous offer. They argue that in equilibrium the observed prices, on average, could be non-monotonic in the order of sellers.

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Section 3 analyzes the central-pricing model. In this setting, we find that prominent products are more expensive than others. This is because, due to consumers’ search order, raising the prices of prominent products will mainly force consumers to buy nonprominent products, while raising the prices of non-prominent products will mainly drive consumers to leave the market. Relative to the case without prominent products, the firm raises the prices of prominent products but lowers the prices of non-prominent ones. As far as welfare implications are concerned, the firm always earns a higher profit by making some products prominent, and both consumer surplus and total welfare can also be enhanced. The main reason is that in the central-pricing case, making some products prominent can increase total output. While in the competition case, total output usually go down after some products become prominent. This paper draws on the rich literature on search in markets. In particular, our competitive-pricing model is related to the branch on search with differentiated products, which is initiated by Wolinsky (1986) and developed further by Anderson and Renault (1999).3 Both of them consider a random sequential search process, while we introduce non-random search order to explore the impact of prominence on market performance. Our central-pricing model is related to Salop (1977). That paper explores how a (multi-store) monopoly can use dispersed prices among its multiple sublets as a sorting device to discriminate over consumers with heterogenous search costs. Our paper also relates with the literature on advertising and search. Indeed, a major purpose of advertising is to make a product more “prominent”. In particular, Robert and Stahl (1993), and Bagwell and Ramey (1994) provide similar price prediction as our competitive-pricing model: the firm which advertises more heavily will charge a lower price, though for very different reasons. More recently, and closer in spirit to our approach, Hann and Moraga-Gonzalez (2007) propose a model of search and advertising where the search model involves product differentiation as in Wolinsky (1986). They assume that a consumer’s likelihood of sampling a firm is proportional to that firm’s advertising intensity. In symmetric equilibrium, all firms advertise with the same intensity (so are equally prominent) and set the same prices, and consumers end up searching randomly. Finally, our work is related to the work on auctions for being listed prominently on online search engines. The two papers by Chen and He (2006) and Athey and Ellison (2007) are especially relevant, since they include a model of the consumer side of the market, and consumers search sequentially through the suggested links to find a good match for their needs.4 In equilibrium, high-quality sellers will buy top links, 3

Weitzman (1979) is an earlier paper which studies the general optimal search among options with stochastic match values. But there is no supply side in his model. 4 Borgers et al. (2007), Edelman et al. (2007), and Varian (2007) also study online paid-placement auctions, but they do not have a formal search model in consumer side.

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and consumers will rationally click through those links first. Therefore, prominence can improve overall efficiency. Nevertheless, there is no price competition in their models, and so they do not discuss the impact of prominence on market prices, which, however, is our focus.5

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Competitive Pricing

Our model generalizes AVZ to allow for more than one prominent product. There are n ≥ 2 firms, each of them supplying a single product at a constant unit cost which we normalize to zero. There are a large number of consumers with measure normalized to one. Each consumer has a unit demand, and the value of a firm’s product is idiosyncratic to consumers. Specifically, (u1 , u2, · · · , un ) are the values attached by a consumer to different products, and ui is assumed to be independently drawn from a common distribution F (u) on [umin , umax ] which has a positive and differentiable density function f (u). We also assume that all match utilities are realized independently across consumers. The surplus from buying one unit of firm i’s product at price pi is ui − pi . If all match utilities and prices are known, a consumer will choose the product providing the highest surplus. If ui − pi < 0 for all i, she will leave the market without buying anything. Initially, however, we assume consumers have imperfect information about the actual price and match utility of each product, but they can gather information through a sequential search process: a consumer can find out a product’s price and match utility by incurring a search cost s > 0, and she can stop searching whenever she wants. Following the tradition in the search literature, we assume that the sampling process is without replacement and there is costless recall (i.e., a consumer can return to any option she has sampled without extra cost). Although there are no systematic quality differences among products, some products are assumed to be more prominent than others. Without loss of generality, let A = {1, · · · , m} be the set of prominent products and B = {m + 1, · · · , n} be the set of non-prominent products. The effect of prominence on consumer behavior is reflected through consumers’ search order: consumers will always sample those prominent products first.6 But either among prominent products or among non-prominent ones, 5

Chen and He (2006) do have prices charged by advertisers, but the structure of consumer demand in their model means that the Diamond Paradox is present, and all firms set monopoly prices. 6 There are at least three ways to think about our assumption about prominence. First, consumers may be exposed to options in an exogenously restricted order, and they have no ability to avoid prominent products. For instance, if a consumer goes to a travel agent to buy airline tickets or a financial advisor to buy a savings product, the advisor may reveal some options prior to others. Second, consumers could suffer from bounded rationality of some form and be susceptible to manipulation by marketing ploys. Third, consumers could be fully rational: they choose to visit prominent firms first

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consumers sample products randomly. When A or B is empty, all products are equally prominent and our model degenerates to Wolinsky (1986); our model with m = 1 is just the case considered by AVZ. Firms maximize their profit by setting prices simultaneously, given their relative prominence and their expectations of consumer search behavior.

2.1

The demand system

Since all prominent products and all non-prominent products are symmetric, we focus on the equilibrium where they are charged at pA and pB , respectively. Denote by ∆ = pB − pA the price difference (if any) between them. We first consider consumers’ optimal stopping rule. Let a solve Z umax (u − a)dF (u) = s. a

Thus, if there is no price difference among products and if a consumer has found a product with utility a, she is indifferent between buying this product and sampling one more product. As long as the search cost is not too high, a exists uniquely and decreases with s. Throughout this paper, we assume the search cost is relatively small such that both pA and pB are no greater than a in equilibrium and the search market is active.7 When m ≥ 2, the optimal stopping rule crucially depends on whether consumers expect pA < pB or pA > pB . If pA < pB , as we shall show below, the stopping rule is actually stationary within each product group (but not across groups). Nevertheless, if pA > pB , the stopping rule in the prominent group is nonstationary. This is because, the more a consumer approaches to the end of the prominent group, the more attractive the low price in the non-prominent group is, and so the less willing she is to stop searching. As a result, when m ≥ 2 we may have multiple equilibria depending on consumers’ expectation of prices. However, as we shall show below, in the uniform-distribution setting which most of our following analysis will focus on, pA > pB cannot be an equilibrium outcome. Therefore, from now on we focus on consumers’ expectation of pA ≤ pB . Let zA ≡ a − pA ≥ zB ≡ a − pB . because they expect these firms to make the best offers, and this expectation is correct in equilibrium. Our approach is largely neutral with respect to these R u three possibilities. 7 When consumers expect pA ≤ a, we have pAmax (u − pA )dF (u) ≥ s, and so they are willing to participate in the market. When consumers expect pB ≤ a, there also exist some consumers who will search beyond prominent firms. However, as usual in search models, there are uninteresting equilibria where consumers expect all firms to set very high prices such that participating in the market is not worthwhile at all, or consumers expect non-prominent firms to set too high prices such that they will never search beyond prominent firms. We do not consider these equilibria further.

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They are interpreted as the cutoff reservation surplus levels in group A and B, respectively. The Optimal Stopping Rule: Phase 1: In the prominent group A, stop searching if the surplus of the best offering so far has been no less than zA ; otherwise, search on whenever there are prominent products remained unsampled. Phase 2: After sampling all prominent products, if the highest available surplus has been no less than zB , then buy the best prominent product. Otherwise, keep searching in non-prominent group B. Phase 3: In the group B, stop searching whenever the highest surplus so far has been no less than zB . Otherwise, search on if there are non-prominent products remained unsampled. Phase 4: After searching all products, if the highest surplus is non-negative, then go back to buy the best product. Otherwise, leave the market without buying anything. The stopping rule among non-prominent products is standard, and here we explain the stopping rule among prominent products. Denote by vi the highest net surplus after sampling i ≤ m products in A. If a consumer comes to the last product in A and finds out vm < zB , then entering B is always worthwhile because the benefit from searching one more product in group B is larger than the unit search cost. (Recall the definition of a.) If vm ≥ zB , she should not enter B according to her stopping rule in B. Thus, the consumer should enter group B if and only if vm < zB . Now consider the situation when the consumer comes to the penultimate product in A. If she finds out vm−1 < zA , sampling the last product in A is always desirable. Otherwise, she should stop searching now, because even if she searched on, she would not enter B since zA ≥ zB . This argument can go backward further and explain the stopping rule in A. We now derive demand functions. We claim that a prominent firm’s demand, if it deviates to a price p while other firms keep charging their equilibrium prices, is qA (p) = hA · [1 − F (a − pA + p)] + rˆA (p) + rA (p), where

1 − F (a)m hA = m (1 − F (a)) is the number of consumers who come to this firm for the first time, Z a rˆA (p) = F (u)m−1 f(u + p − pA )du a−∆

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(1)

is the number of consumers who return to this firm after sampling all prominent products, and Z a

rA (p) =

pB

F (u − ∆)m−1 F (u)n−m f(u + p − pB )du

is the number of consumers who return after sampling all products. To understand (1), consider three possible sources of a prominent firm’s demand. Let i be this firm’s index. (i) A consumer may come to firm i after searching k ≤ m − 1 prominent products but without finding a satisfactory one (i.e., all of them have net surplus less than zA = a − pA ). This probability is m1 F (a)k .8 Summing up these probabilities over k = 0, · · · , m − 1 leads to hA . For such a consumer, she will buy at firm i immediately if ui − p ≥ zA , of which the probability is 1 − F (a − pA + p). This explains the first term in (1). We call this portion of firm i’s demand the “fresh demand”. (ii) If this consumer finds that all prominent products’ net surplus less than zA but product i is the best one and has net surplus greater than zB , then she will return to buy it without searching on among non-prominent firms. (If firm i happens to be the last firm in group A, she just buys at it immediately.) The probability of this event is µ ¶ Pr max {zB , uj − pA } < ui − p < zA j6=i,j∈A Z p+zA = F (u − p + pA )m−1 dF (u), p+zB

which is equal to rˆA (p) by changing the integral variable. We call this portion of demand the “midway returning demand”. (iii) The last possibility is, after sampling all products (which requires that each product has net surplus less than zB ), this consumer goes back to firm i if its product has the highest positive surplus. The probability of this event is µ ¶ Pr max {0, uj − pA , ul − pB } < ui − p < zB j6=i,j∈A,l∈B Z p+zB = F (u − p + pA )m−1 F (u − p + pB )n−m dF (u), p

which equals rA (p) by changing the integral variable. We call this portion of demand the “final returning demand”. Secondly, we claim that a non-prominent firm’s demand, if it deviates to a price p while other firms stick to their equilibrium prices, is qB (p) = hB · [1 − F (a − pB + p)] + rB (p), 8

(2)

Notice that 1/m is just the probability that this prominent product is on the (k + 1)th position in the consumer’s search process.

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where hB = F (a − ∆)m

1 − F (a)n−m (n − m) (1 − F (a))

is the number of consumers who come to this non-prominent firm for the first time, and Z a F (u − ∆)m F (u)n−m−1 f (u + p − pB )du rB (p) = pB

is the number of consumers who return to it after sampling all products. The explanation goes as follows. Let j be this non-prominent firm’s index. For a typical consumer, she will come to firm j fresh if she has left all prominent firms (which requires that each prominent product has net surplus less than zB ) and has sampled k ≤ n − m − 1 non-prominent products in B but has not found a satisfactory 1 one. This probability is F (a − ∆)m n−m F (a)k . Summing up these probabilities over k = 0, · · · , n − m − 1 yields hB . Then she will buy at firm j immediately if uj − p > zB , of which the probability is 1 − F (a − pB + p). This consumer will return to firm j if all products’ net surplus is less than zB but product j offers the highest positive surplus. The probability of this event is ¶ µ Pr max {0, ui − pA , ul − pB } < uj − p < zB l6=j,i∈A,l∈B Z p+zB = F (u − p + pA )m F (u − p + pB )n−m−1 dF (u), p

which is equal to rB (p) by changing the integral variable. A useful observation is that how a firm’s returning demand varies with its actual price crucially depends on the density function f . In particular, for the uniform distribution, a firm’s returning demand is independent of its actual price, and so the fresh demand is more price responsive than the returning demand. All else equal, a higher fraction of returning demand makes a firm more want to raise its price.

2.2

Equilibrium prices

We now derive equilibrium prices by assuming the uniform valuation distribution on [0, 1]. (In Appendix A.8, we will extend our main price result to the setting with more general distributions.) In this case, a is the solution to Z 1 (u − a)du = s, a

√ and so a = 1 − 2s. Throughout this paper, we keep the following condition which ensures that equilibrium prices pA and pB are less than a and so an active search market exists. 9

Assumption 1 The search cost is not too high: 0 < s < 18 , or

1 2

< a < 1.

For expositional convenience, we introduce a piece of notation: 1 − ai . Ki = i(1 − a) Then a prominent firm’s demand function is9 qA (p) = hA (1 − a + pA − p) + rˆA + rA , where hA = Km , rˆA =

Z

a m−1

u

du, rA =

a−∆

Z

a

pB

(u − ∆)m−1 un−m du.

Notice that, when ∆ tends to zero, the midway returning demand rˆA will vanish. The firm wishes to maximize pqA (p). Then the first-order condition in symmetric equilibrium is hA (1 − a − pA ) + rˆA + rA = 0. (3) Notice that, if m = n, this equation with pA = pB is the first-order condition in the random search case. A non-prominent firm’s demand function is qB (p) = hB (1 − a + pB − p) + rB , where m

hB = Kn−m (a − ∆) , rB = The first-order condition of this firm is then

Z

a

pB

(u − ∆)m un−m−1 du.

hB (1 − a − pB ) + rB = 0.

(4)

Notice that, if m = 0, this equation with pA = pB is also the first-order condition in the random search case. From (3)—(4), we can see that the equilibrium demands for a prominent product and a non-prominent product are qA = hA pA and qB = hB pB , respectively. Combining them with (??), we have the following useful equation: 1 − am 1 − an−m n−m . pA + (a − ∆)m pB = 1 − pm A pB 1−a 1−a

(5)

Proposition 1 Given Assumption 1, on the area [0, a]2 , (3)—(4) have a unique solution (pA , pB ) ∈ (1 − a, 12 )2 , and pA < pB . 9

If p is too high, then the fresh demand will be zero and the returning demand will depend on p. However, we can show that, at least when the search cost is relatively small or n is relatively large, the equilibrium derived below will not be overturned by the global deviation problem.

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Proof. We prove the existence and uniqueness in Appendix A.1. Here we show pA < pB . Notice that Z a Z a m−1 u du + 4(u − ∆)m−1 un−m−1 du rˆA + rA − rB = a−4

pB

has the sign of 4 when pB < a. Also notice that hA > hB is always true in equilibrium (a consumer who comes to a firm in pool B must have visited a firm in pool A), so we have rB rˆA + rA 1 4 = pB − pA = − > (rB − rˆA − rA ). hB hA hA (We have used (3)—(4) in deriving the second equality.) Since the last term has the sign of −4, then 4 > 0 follows. The reason for pA < pB is, due to the consumer search order, each prominent firm’s demand consists of more fresh demand proportionally, and as we have known, the fresh demand is more price sensitive than the returning demand in the uniform-distribution setting.10 Before proceeding, we discuss the issue of multiple equilibria. Remember that our demand functions are based on consumers’ expectation of pA < pB , and we have confirmed that pA < pB is indeed an equilibrium outcome. Nevertheless, we have not yet discussed other possible equilibria associated with different expectations. In particular, we are concerned about whether pA > pB could also be an equilibrium outcome. The following proposition, which is proved in Appendix A.2, excludes this possibility in our uniform-distribution setting. Proposition 2 In the uniform-distribution setting, there is no equilibrium with pA > pB . The following are three special cases in which the price difference 4 will vanish. (i) When n → ∞, both pA and pB converge to 1 − a. Notice that Z a ³ ´n−m−1 rB u < du. hB pB a The right-hand side tends to zero as n → ∞, so pB = 1 − a + hrBB tends to 1 − a. Since 1 − a < pA < pB , pA tends to 1 − a too. Note that 1 − a is also the equilibrium price in the random search case as n → ∞ (see below for the detail). So this limit result 10

In effect, the result that the fresh demand is more price sensitive will hold in a more general setting (see Appendix A.8). The intution is as follows. When a firm raises its price, its fresh demand will decrease for sure since more consumers will then search on. But these consumers become potential returning consumers, so part of the effect of raising a firm’s price on its own returning demand is positive.

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implies that prominence has little impact on the market prices if the market has many suppliers. (ii) When a → 1 (i.e., when the search cost tends to zero), both pA and pB converge to the full information price p¯ that satisfies n¯ p = 1 − p¯n . It is straightforward to verify that pA = pB = p¯ satisfy the first-order conditions when a approaches one. (iii) When a → 12 , both pA and pB converge to the monopoly price 12 . This is just because both pA and pB are between 1 − a and 12 . The intuition is that the high search cost makes consumers willing to stop searching whenever she finds a product with positive surplus, and so each firm is acting as a monopoly. AVZ have shown that, compared to the random search case, introducing one prominent firm will make all non-prominent firms raise their prices but make the prominent firm lower its price. Will this effect persist when there are more prominent firms? We first introduce the equilibrium price p0 in the random search case: 1 − an 1 − pn0 = . 1−a p0

(6)

This is from (5) by letting m = 0 or n. Now we give the result concerning the relationship between pA , pB and p0 when consumers adopt the optimal stopping rule. Proposition 3 Given Assumption 1, (i) p0 < pB for sure, and pA < p0 if µ ¶m ∆ ∆ 1− >1− . a pB

(7)

Particularly, if m = 1, pA < p0 must be true. (ii) For fixed n and 2 ≤ m ≤ n−1, there exists ε1 > 0 such that pA < p0 if a > 1−ε1 (i.e., if the search cost is sufficiently low), and there exists ε2 > 0 such that pA > p0 if a < 12 + ε2 (i.e., if the search cost is relatively high). Proof. (i) Since 4 > 0, the left-hand side of (5) is less than 1 − am 1 − an−m m 1 − an pB + a pB = pB , 1−a 1−a 1−a

while the right-hand side of (5) is greater than 1 − pnB . Thus, 1 − an 1 − pnB > . 1−a pB Comparing it to (6) yields p0 < pB . 12

Notice that (7) is equivalent to (a − ∆)m pB > am pA . If this inequality holds, then n the left-hand side of (5) is greater than 1−a p . Meanwhile, the right-hand side of (5) 1−a A n is less than 1 − pA since pA < pB . So 1 − pnA 1 − an < , 1−a pA which implies pA < p0 . If m = 1, (7) is always true since pB < a under Assumption 1. (ii) Since µ ¶m ∆ m∆ 1− >1− , a a

pA < p0 if pB < a/m. When a→1, pB tends to the full information equilibrium price p¯ = (1 − p¯n )/n < 1/m, and so pA < p0 . When a → 12 , we have ∆ → 0, so (a − ∆)m pB ≈ (am − mam−1 4)(pA + 4)

≈ am pA + am−1 (a − mpA )4.

Then the left-hand side of (5) can be approximated by 1 − an 1 − an−m m−1 (a − mpA )4. pA + a 1−a 1−a On the other hand, when ∆ → 0, we have n−m n−m pm = pm A pB A (pA + 4)

≈ pnA + pn−1 A (n − m)4.

Therefore, when ∆ → 0, (5) implies ¸ ∙ 1 − an 1 − an−m m−1 n n−1 . (mpA − a) − (n − m)pA pA − (1 − pA ) ≈ 4 a 1−a 1−a When a tends to

1 2

(so pA also tends to 12 ), the square-bracket term approaches to ¤ 1 £ (m − 1)(2n−m − 1) − (n − m) ,

2n−1

which must be nonnegative when m ≥ 2 and n − m ≥ 1. Therefore, when m ≥ 2 and a → 12 , we have 1 − an 1 − pnA , > 1−a pA so pA > p0 . Part (i) of the proposition says that introducing prominent products will always induce non-prominent firms to raise their prices. This is because their demand now includes more returning demand proportionally. But whether prominent firms will 13

lower their prices is uncertain (except when m = 1). There are two forces working here. On the one hand, now each prominent firm has more fresh demand proportionally than before. This tends to make them lower prices. On the other hand, price competition here involves strategic complements, so the higher price of non-prominent products induces them to raise prices. The final outcome depends on which force is stronger. Part (ii) reports two limit results: when the search cost is sufficiently small, the prominent firms will always lower their prices; while they will raise their prices if the search cost is sufficiently large. When m ≥ 2, an interesting result beyond the single-prominence case has emerged: introducing more than one prominent product could lead all firms to raise their prices. We have proved that it will take place when the search cost is relatively large or when the market is rather competitive and the number of prominent firms is not too small. Actually, numerical simulations show that this can even take place under mild conditions (see an numerical example below). The basic reason is that the existence of prominent products induces non-prominent firms to raise their prices, which further drives prominent firms to do so. Now we study how m affects the market prices. The first simple observation is, when m = n, pA will return to p0 , so pA should be non-monotonic with m. Since pB has no definition when m = n, this observation does not apply. A general comparative static analysis with respect to m is hard to proceed. In the following, we focus on the limit case in which the search cost is close to zero. Proposition 4 Given Assumption 1, for fixed n, there exists a ˆ < 1 such that, for a>a ˆ, pA , pB , and the price gap 4 all increase with 1 ≤ m ≤ n − 2, and pA increases with m even at m = n − 1. Proof. See Appendix A.3. The first result says that, when m is sufficiently small relative to n, the prices and the price gap always increase with m. The second result means that, when the search cost is sufficiently small, the prices and the price gap always increase with m even if m is close to n. Note that pA increasing at m = n − 1 does not conflict with pA = p0 at m = n, because pA < p0 for a sufficiently large a and 1 ≤ m ≤ n − 1. For intermediate n and a, it is hard to get analytical results, but numerical simulations suggest that pB always increases with m but pA may not. For example, as a → 12 , pA > p0 at any 2 ≤ m ≤ n − 1 (part (ii) in Proposition 3), but pA < p0 at m = 1 and pA = p0 at m = n, so pA must be non-monotonic with m as a → 12 . The following graph presents an example of the relationship between equilibrium prices and m when a = 0.7 and n = 8. The thick solid line is pA , the thick dashed 14

line is pB , and the thin dashed line is p0 . We can see that pB increases with m, but pA decreases first when just one prominent firm emerges and then increases with m and even exceeds p0 if m ≥ 3.11 However, from m = 5 to m = 8, pA falls again.

0.375

0.3625

0.35

0.3375

0.325

0

2

4

6

8 m

Figure 1: An example of equilibrium prices and m Now we give some intuition about how equilibrium prices vary with m. Consider the non-prominent firms first. When there are more prominent firms, fewer consumers will visit pool B, so each non-prominent firm’s fresh demand should decrease. On the other hand, larger m also means that, if consumers come to pool B, they must be less satisfied with products in pool A as a whole, which gives non-prominent firms more advantage in competing for the returning consumers. Therefore, we should expect that a nonprominent firm’s returning demand decreases less fast with m than its fresh demand, i.e., the relative proportion of returning demand should increase with m. That is why pB tends to rise with m. For a prominent firm, initially its price goes down because of the abrupt increase of fresh demand. Eventually, as m goes up to n, this effect will tend to vanish. In the middle of this process, higher pB will contribute to the increase of pA .

2.3

Welfare

This part examines the welfare implications of prominence in the competitive-pricing model. AVZ have shown that introducing one prominent firm will usually improve industry profit but harm consumer surplus and total welfare. Here we want to know whether this effect will persist as we introduce more prominent products. Due to the complication of the problem with m ≥ 2, again we focus on the limit cases with sufficiently low search cost. 11

Our asymptotic condition for pA > p0 in Proposition 3 works well in this example: am + aKm = 0.7m + 73 (1 − 0.7m )/m which is greater than one for m = 1 and 2 but less than one for m ≥ 3.

15

We first give the expressions for relevant welfare variables. Total output is n−m , Qm = 1 − pm A pB

and industry profit is Πm = pB Qm − 4 · mhA pA , where mhA pA is the output supplied by all prominent firms. We subtract the second term because prominent firms are charging a lower price than others. The expression for total welfare is Z a n (u − 4)m un−m du, (8) Wm = a(1 − a ) + w(4, m) + n pB

where w(4, m) = m

Z

a

a−4

um du − a(1 − an−m ) [am − (a − 4)m ] .

(See Appendix A.8 for how to derive this expression and its intuition.) Consumer surplus is Vm = Wm − Πm . If m = 0 and pA = pB = p0 , we get the expressions for Q0 , Π0 , W0 , and V0 in the random-search case. We now investigate the relationship between welfare and m. The first simple observation is that making all firms prominent is the same as no prominence at all, so all welfare variables should vary with m non-monotonically. In the following, we try to specify this non-monotonic relationship in the limit cases. Let us discuss total output first. Remember p¯ is the full-information price and it satisfies n¯ p = 1 − p¯n . Proposition 5 Given Assumption 1, for fixed n, there exists a ˆ < 1 such that, for a > aˆ, total output Qm decreases with m if and only if p + (n − 2m)(2n − 1 − p¯n−1 ) > 0, m2 (n − 1)¯ and Qm < Q0 for any 1 ≤ m ≤ n − 1. In particular, if m ≤ n2 , Qm always decreases √ with m; if m > n2 , Qm could increase with m and this must take place if m > 1+√2 2 n ≈ 0.586n. Proof. See Appendix A.4. This result says that, when the search cost is small, Qm must decrease with m first and then increase, and the switch point is around n/2. The intuition is as follows. Let us decompose the impact of m on total output into two parts. First, as we have shown, when the search cost is small, both pA and pB increase with m. Hence, larger m tends to reduce total output. Second, larger m shifts more consumers to prominent firms. Since they are charging a lower price, the rise of m also has a positive effect on

16

total output. Our non-monotonic result is a reflection of the combination of these two opposite effects.12 We now turn to the impact of m on welfare. Proposition 6 Under Assumption 1, for fixed n, there exist aˆ < 1 such that, for a > a ˆ, industry profit increases with m and total welfare and consumer surplus decrease with m if and only if total output decreases with m, Πm > Π0 , Wm < W0 , and Vm < V0 . Proof. See Appendix A.5. This result is consistent with the welfare conclusion in AVZ. It also implies that, when the search cost is small, industrial profit will reach its maximum and total welfare and consumer surplus will reach their minimums when m is between n/2 and 0.586n. We know that total welfare is mainly determined by total output Qm and the price gap 4. On the one hand, since the production cost is zero, every consumer should be served. Hence, higher Qm means higher output efficiency. On the other hand, since consumers’ search behavior is socially efficient in the uniform-price case, pA < pB makes too few consumers search beyond, and too many consumers return to, the prominent pool. Thus, larger 4 tends to result in less efficient search behavior. When the search cost is sufficiently small, the output effect dominates and so the impact of m on Qm totally determines the welfare results. The following graphs report an example of the relationship between welfare and m when a = 0.7 and n = 8. In the first graph, the dashed line is consumer surplus and the solid line is industry profit. In effect, more numerical simulations suggest that the results we derived in the case with a small search cost hold in general.

0.375 0.6954 0.3625 0.6952 0.35 0.6951 0.3375 0.695 0.325 0

2

4

6

8

0

2

4

6

8 m

m

Industry profit and consumer surplus

Total welfare

Figure 2: The impact of the number of prominent firms From Proposition 3, we have known that, when m ≥ 2 and a → 12 , both pA and pB will be greater than p0 . Thus, Qm < Q0 also holds in that limit case. In effect, we have not found any numerical example for Qm > Q0 , so we conjecture that Qm < Q0 would hold in general. 12

17

3

Central Pricing

We now turn to the central-pricing model in which a multi-product firm chooses the prices of all products.13 For example, the restaurant offers a menu of dishes and sets the prices by itself. The local supermarket usually sells several brands of a product and it also has some discretion to influence their retail prices. Many other retailers have the similar situation. In these examples, we also often see some prominent options (e.g., the brands displayed on the gondola ends and the dishes recommended in a special menu). We use the same framework as in the competitive-pricing case except that now all prices are decided centrally. Notably, we keep the assumption that consumers will sample prominent products first (because of some form of bounded rationality or exogenously restricted search order). Our aim is to investigate whether the impact of prominence here is different from that in the competition case. Intuitively, given the specified search order, raising the price of prominent products will be more likely to drive consumers to buy non-prominent products, while raising the price of non-prominent products will be more likely to drive consumers to leave the market. Thus, we should expect that the monopoly has more incentive to raise the price of prominent products, and so prominent products will be more expensive than others in equilibrium. In the following, we verify this prediction first and then examine the welfare implications. Compared to the competition case, there are two subtle issues deserving discussion. First, as we have discussed in Section 2, if consumers expect prominent products to be more expensive but their search order is still restricted, their optimal stopping rule among the prominent pool will be non-stationary. However, a non-stationary stopping rule will make the analysis rather intricate. In the following, we mainly deal with the case with m = 1 (in which case the stopping rule is stationary), and we will discuss the results for m ≥ 2 in due places. Second, when we use the optimal stopping rule, we should be more careful in specifying consumers’ off-equilibrium expectations. In the competition case, it is reasonable to assume that consumers will hold the equilibrium expectation even after they encounter unexpected prices, since firms make pricing decisions independently and simultaneously. However, in the central-pricing case, consumers might be cautious to a deviation price and then contemplate that the monopoly may be also adjusting other prices accordingly. This kind of wary belief will greatly complicate the analysis and may be also too demanding for ordinary consumers. In the following, we will focus on passive beliefs, i.e., consumers always hold their equilibrium beliefs about prices.14 We may also won13

Our monopoly setup abstracts from the potential competition between multiproduct sellers, so it is more suitable for the situation where there is substantial differentiation (e.g., physical distance) between sellers. 14 The distinction of these two kinds of belief has an analogy in the literature on secret contracts (see, e.g., McAfee and Schwartz (1994) and Rey and Verge (2004)). A potential justification for

18

der whether the monopoly can announce and commit all prices up front. (Note that the monopoly always owns more if it is able to do so.) In the following, to be consistent with the competition case, we will mainly focus on the case with imperfect price information. We will discuss in the end of this section how our results might change if the monopoly can announce prices in advance.

3.1

Equilibrium prices

The case with m = 1. In this case, we have similar price results no matter which stopping rule is used since both of them are stationary. We focus on the optimal one for the purpose of welfare analysis. Let product 1 be the prominent product, and consider the equilibrium where the monopoly firm charges product 1 at pA and other products at pB .15 Keep the notation ∆ = pB − pA , and a still solves Z umax (u − a)dF (u) = s. a

If a consumer has decided to enter the market, she will stop searching if and only if the highest net surplus so far is greater than a − pB . As before, to have an active search market, we keep assuming that pi ≤ a in equilibrium. Basically, this requires that the search cost is not too high and n is not too large.16 (We will specify the condition when it becomes possible.) With the prices pA and pB , the monopoly firm earns £ ¤ Π1 = pA qA + pB 1 − F (pA )F (pB )n−1 − qA (9) £ ¤ = pB 1 − F (pA )F (pB )n−1 − ∆ · qA , where

qA = 1 − F (a −

peB

+ pA ) +

Z

pB +a−peB

pB

F (u)n−1 f (u − ∆)du

is the demand for product 1 (this is from (1) by letting m = 1), and 1 − F (pA )F (pB )n−1 is total demand. Note that peB is consumer’s fixed expectation of pB , which reflects passive beliefs is that consumers may regard a deviation price as a tremble of the monopoly instead of intentional behavior. 15 In the central-pricing model, we are implicitly assuming the existence of an equilibrium in which symmetric products are charged at the same price. In a general setup, we do not know the primitive conditions for this. But in the uniform setup, it can be verified under some conditions we will specify below. 16 A larger n will induce the monopoly firm to raise its prices if it believes that consumers will enter and search. However, expecting this, for a fixed search cost, consumers are less likely to enter the market in the beginning. That is why a larger n needs to be associated with a lower search cost to have an active search market. An alternative way to get around this problem is to introduce heterogenous reservation utilities among consumers and assume they are realized independently from the product match utility. The price of using such a setting is the complication in welfare analysis.

19

our assumption of passive beliefs. In equilibrium, of course peB = pB . The following proposition confirms our initial conjecture that the prominent product will be more expensive. As a result, the impact of prominence on the market price is opposite to that in the competition case. Proposition 7 If there is only one prominent product, in the equilibrium with an active search market, we have pA > pB . Proof. If pA < pB would hold in equilibria, then charging product 1 at pB and charging some non-prominent product at pA is a profitable deviation. To see that, notice that such a deviation will not change total demand, so it leads to a new profit level £ ¤ pA q 0 + pB 1 − F (pA )F (pB )n−1 − q0 ,

where q 0 is the new demand for that non-prominent product with price pA . Given consumers’ passive beliefs (so their stopping rule remains), we have q0 < qA due to the restricted search order. Thus, this new profit level is higher than the original one in (9). This is a contradiction, so pA ≥ pB . Suppose pA = pB = p, then they should satisfy two necessary conditions: ¯ ∂Π1 ¯¯ = qA − pf(p)F (p)n−1 = 0, ¯ ∂pA pA =pB =p ¯ ∂Π1 ¯¯ = (n − 1)qB − (n − 1)pf (p)F (p)n−1 = 0, ∂pB ¯pA =pB =p

where qB is the equilibrium demand for any non-prominent product. Clearly, they require qA = qB , but that is impossible given pA = pB . Thus, pA > pB .

An intuitive explanation goes as follows. When the monopoly raises the price of a product, it earns more from consumers who still buy this product, it may gain or lose from those who switch to buy other products depending on the relative prices, and it loses from those who thereby leave the market. Suppose pA = pB and the search market is active, and let us compare slightly raising the price of a prominent product with slightly raising the price of a non-prominent product. The first positive effect is larger for the prominent product since it has a larger demand, the second effect is negligible for both since pA = pB , and the third negative effect is smaller for the prominent product since consumers visit it first and so have more opportunities to find other satisfactory products after leaving it. Therefore, adjusting up the price of the prominent product is more profitable. We proceed to compare the prominence case with the random search case. For tractability, we focus on the case with the uniform valuation distribution on [0, 1]. As we have pointed out in footnote 16, to have an active search market, when the number of products increases, we must have a lower search cost. The following is the specific condition in the uniform setting: 20

Assumption 2 a ≥ aˆn , where a ˆn increases with n ≥ 2 from about 0.614 to 1.17 From (9), it is ready to derive two necessary equilibrium conditions:18 ∂Π1 = qA − pnB + ∆ = 0, ∂pA ∂Π1 = 1 − (n + 1)pA pn−1 − qA + pnB − an−1 4 = 0, B ∂pB

(10)

where qA = 1 − a + ∆ + (an − pnB ) /n. Adding them together yields 1 − (n + 1)pA pn−1 + (1 − an−1 )∆ = 0. B

(11)

So (10) and (11) define the equilibrium prices. If there is no prominent product, the equilibrium price p0 should maximize p (1 − pn ) given consumers’ expectation of symmetric prices. Thus, p0 solves 1 − (n + 1)pn0 = 0.

(12)

Notice that p0 (so the corresponding profit Π0 ) is independent of the search cost (as long as the search market is active). It is ready to check that p0 increases with n from √ 3 ≈ 0.58 to 1. It is also clear that, when a tends to one, both pA and pB defined in 3 (10) and (11) will converge to p0 . Proposition 8 If there is only one prominent product, in the uniform-distribution setting with Assumption 2, (i) on [0, 1]2 , the solution to (10) and (11) exists uniquely and pi < a; (ii) pB < p0 < pA , and the firm serves more consumers in the prominence case than in the random search case. Proof. See Appendix A.6. Thus, relative to the random search case, the firm will raise the prominent product’s price but lower other non-prominent products’ price, and the prominence case leads to higher total output. These results also contrast with the competition case. The following graph is a numerical example when n = 2, where the thin dashed line is p0 . 17

Explicitly, a ˆn solves the equation 3a − 1 1 − an + = 2 2n

r n

1 . n+1

q √ 1 increases with n ≥ 2 from 33 to 1. Note that n n+1 18 Though a little lengthy, one can verify that these necessary conditions are also sufficient when n = 2 or when a is close to one. Beyond that, it is hard to verify the sufficiency due to the complication of the objective function.

21

0.6

0.5875

0.575

0.5625

0.55

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1 a

Figure 3: Prices and a in the central-pricing case (n = 2) The case with m ≥ 2. Due to the complication of the stopping rule in this case, we are unable to derive similar price results though we conjecture they would be true. However, if we adopt a modified stopping rule in which consumers stop searching if and only if the available surplus is greater than some appropriate threshold, then the same results can be established.19 Unlike the competition case in which following the guidance of prominence is actually optimal for consumers, now prominence is misguiding them since the firm is charging a higher price for the prominent product. If consumers are rational and can choose their search orders freely, they will avoid sampling the prominent product first. Expecting this, the firm actually has no incentive to charge more for the prominent product. Then, in equilibrium the firm should charge the same price for all products and consumers sample at random. Therefore, the assumption that consumers will somehow sample the prominent product first is crucial in our central-pricing model. A more flexible setting should permit both rational consumers and consumers who will be biased by prominence. In that richer model, our price result still holds as long as the fraction of rational consumers is not too large.

3.2

Welfare

This part again focuses on the case with m = 1. First of all, the monopoly must earn more in the prominence case, because it can at least charge pA = pB = p0 to obtain Π0 (see (9)). Therefore, the multi-product monopoly does have incentive to make some product prominent if it is costless to do so. As far as total welfare is concerned, following the discussion in the competition case, the non-uniform prices in the prominence case always tends to lower efficiency because of consumers’ suboptimal search behavior; while prominence also gives rise to higher 19

Though not optimal, such kind of stopping rule is in the spirit of satificing behavior. All details are available from the author.

22

output in our central-pricing model, which improves efficiency. Therefore, the final outcome depends on which effect is stronger. We will show that, at least for relatively small search cost, making one product prominent can boost total welfare and consumer surplus. This is opposite to the welfare results in the competition case. We first derive the expression for consumer surplus difference V1 − V0 . Let V (p, p) be consumer surplus when all products are charged at p. When p is increased by ε, all buyers have to pay more, which leads to a consumer surplus loss ε(1 − pn ). On the n) other hand, −ε d(1−p more consumers will be excluded, but these marginal consumers’ dp surplus is of order , so the surplus loss from them is of order ε2 and can be ignored for (p,p) small ε. Thus, dV dp = pn − 1 and V (pB , pB ) − V (p0 , p0 ) =

Z

p0

pB

(1 − pn )dp.

Let V (δ) ≡ V (pB + δ, pB ) be the consumer surplus when all products are charged at pB except that product 1 is charged at pB + δ. Consider an increase ε of δ. First, more consumers are excluded, but as before, this effect is of order ε2 . Second, buyers of product 1 pay more, so their surplus is reduced by εqA (pB + δ, pB ). Third, a fraction (with order of ε) of consumers are shifted from product 1 to other products, but the surplus change of each shifted consumer is of order ε, and so the last effect is also of order ε2 . Therefore, V 0 (δ) = −qA (pB + δ, pB ), which is an analogy of Roy’s identity in our search model. Then one can show20 Z −∆ 3∆ ). V (−∆) − V (0) = V 0 (δ)dδ = ∆(pnB − 2 0 Therefore, V1 − V0 = V (−∆) − V (0) + V (pB , pB ) − V (p0 , p0 ) Z p0 3∆ (1 − pn )dp + ∆(pnB − ). = 2 pB Since Π0 = p0 (1 − pn0 ), and n 2 Π1 = pB (1 − pA pn−1 B ) − 4 · qA = pB (1 − pB ) + 4 20

Note that qA (pB + δ, pB ) = 1 − a − δ + rA , where rA = for product 1 according to (9). So Z

−4

V 0 (δ)dδ =

0

R pB +a−peB pB

un−1 du is the returning demand

42 + 4(1 − a + rA ). 2

Then using (11) yields our expression.

23

where we have used pnB − qA = 4 from (10), we get Z p0 ∆ W1 − W0 = V1 − V0 + Π1 − Π0 = n pn dp + ∆(pnB − ). 2 pB Proposition 9 In the uniform-distribution setting with Assumption 2, there exists a∗ < 1 such that, for a > a∗ , we have W1 > W0 and V1 > V0 . Proof. Let ε = 1 − a. When ε → 0, we have known that both pA and pB converge to p0 . Since p0 is independent of a, we can approximate these prices as pi = p0 +ki ε, where ki needs to be determined. By extending (10) and (11) around a = 1 and discarding all higher-order terms, we can show k1 = k2 = 0.21 We further claim that a sufficient condition for both W1 > W0 and V1 > V0 is 3∆ 1 − an−1 pB + > 0, n+1 2 which is proved in Appendix 9. Then, when ε is around zero but positive, we have 1 − an−1 n−1 3∆ pB + ≈ p0 ε > 0, n+1 2 n+1 which means that W1 > W0 and V1 > V0 for a → 1. This result is mainly because, when the search cost is small, the search inefficiency caused by the non-uniform prices is of second order, while the output effect is of first order. In effect, numerical simulations suggest that our welfare results would hold for any a permitted by Assumption 2. The following graph is an example when n = 2, where the solid line is W1 − W0 and the dashed line is V1 − V0 .

0.0025

0.002

0.0015

0.001

0.0005

0 0.65

0.7

0.75

0.8

0.85

0.9

0.95

1 a

Figure 4: Welfare impact and a in the central-pricing case (n = 2) 21

Although the first-order coefficients are zero, the second-order coefficients are not. Denote them (n−1)p0 by l1 and l2 . One can show that l2 = 2(1−2np < 0 and l1 = (1 − n)l2 > 0. 0)

24

3.3

A discussion on announced prices

Now suppose the firm can announce all prices in advance, but consumer search order is still restricted in the prominence case. Let us focus on m = 1. We then need to replace qBe in (9) by qB since now all prices are observable. This change will only affect the ∂Π1 first-order condition ∂p = 0. Proposition 7 remains without any modification, so we B 1 still have pA > pB under general conditions. In the uniform-distribution setup, ∂Π =0 ∂pA ∂Π1 still leads to (10), but ∂pB = 0 now leads to 1 − (n + 1)pA pn−1 − qA + pnB − ∆ = 0. B Adding them together yields = 0. 1 − (n + 1)pA pn−1 B

(13)

From (13) and (10), one can check the existence result along the same logic in the proof of Proposition 8. (In footnote 26 of Appendix A.6, we further show that price announcement will raise all prices.) Comparing (13) with (12), we can see that the prominence case and the random search case have exactly the same total output. Then pB < p0 < pA follows since pB < pA . Based on the output result, the welfare analysis is also simple. The firm still earns more than in the case without prominent product since it can at least announce prices pA = pB = p0 . Total welfare (and so consumer surplus) must go down since prominence causes non-uniform prices (so less efficient search behavior) but does not improve output. That is, in the central-pricing model, the monopoly’s commitment power can reverse our welfare results. Proposition 10 If the firm can announce and commit all product prices in advance, we still have pB < p0 < pA under general conditions. However, in the uniform-distribution setting, introducing one prominent product does not affect total output but lowers consumer surplus and total welfare. The result in the second part is because price announcement raises all prices in equilibrium such that the output increase caused by prominence does not exist any more. In the imperfect-information case, lowering the actual price of non-prominent products will not reduce the prominent product’s fresh demand since consumers’ search decision is based on their expectations; while in the announcement case, it does decrease the prominent product’s fresh demand, which dampens the firm’s incentive to lower the price of non-prominent products. Thus, in equilibrium all prices will be higher.

25

4

Conclusion

This paper has studied the implications of prominence in a search market. The main contribution of this paper is that we find the impact of prominence on price and welfare is contrasting between the competitive-pricing case and the central-pricing case. Specifically, prominent products are cheaper than non-prominent products in the competitivepricing model but more expensive in the central-pricing case. As far as welfare implications are concerned, in the competitive-pricing case making some products prominent tends to increase industry profit but lower consumer surplus and total welfare; while in the central-pricing case it can boost all players’ surplus. A desirable extension is to consider the impact of prominence on firms’ quality choices. Will a more prominent firm produce a higher or lower quality product than others? Will a monopoly supplying products with heterogeneous qualities make the highest-quality one most prominent? We leave these questions to future work. Prominence is an important economic force that could lead to asymmetry among economic agents. Beyond the product market, prominence may also play an important role in the labor market. For example, some companies are more prominent than others and job seekers could be attracted to apply for their jobs first; and some job candidates could also be more prominent than others and so they are more likely to be considered by companies. Hence, two-sided prominence could exist in a search market.

A A.1

Appendix: Existence of equilibrium in the competition case

Existence: For expositional convenience, define Ki ≡

1 − ai . i (1 − a)

Rewrite the first-order condition (4) as pB = 1 − a + tB , where ¶m Z aµ u−∆ rB 1 = un−m−1 du. tB ≡ hB Kn−m pB a − ∆ tB is a decreasing function of pB on [0, a] since u−∆ decreases with pB when u < a. If a−∆ pB = 1−a, then condition (??) implies tB > 0 and so pB < 1−a+tB . If pB = 1/2, then pB > 1 − a + tB . This is because tB < a − pB by realizing Kn−m > an−m−1 . Therefore, for any fixed pA , on the range of [0, a] the first-order condition (4) has a unique solution pB = bB (pA ) ∈ (1 − a, 1/2). A Rewrite the first-order condition (3) as pA = 1 − a + tA , where tA ≡ rˆAh+r . We first A 26

show that, given pB ∈ [0, a], tA is a decreasing function of pA . Notice that Z a ∂rA = (m − 1) (u − ∆)m−2 un−m du ∂pA £ pB m−1 ¤ n−m m−1 < a − pA (a − ∆) ,

and so

£ ¤ ∂(ˆ rA + rA ) < an−m (a − ∆)m−1 − pm−1 − (a − ∆)m−1 A ∂pA = (an−m − 1)(a − ∆)m−1 − an−m pm−1 < 0. A Since the best response bB (pA ) ∈ (1 − a, 1/2), we can focus on pB ∈ (1 − a, 1/2). Then, if pA = 1 − a, we have pA < 1 − a + tA . This is because rA > 0 and 1 − pB < a also Ra implies rˆA = 1−pB um−1 du > 0. On the other hand, if pA = 1/2, then pA > 1 − a + tA if tA < a − 1/2. We now show it is actually true. When pA = 1/2, Z a rA = (u − pB + 1/2)m−1 un−m du pB n−m

<

a

m

and rˆA =

[(a − pB + 1/2)m − 1/2m ] ,

1 m [a − (a − pB + 1/2)m ] . m

They imply tA <

1 1−a m (am − 1/2m ) = (a − 1/2m ) < a − 1/2. mhA 1 − am

Therefore, for any pB ∈ (1−a, 1/2), (3) has a unique solution pA = bA (pB ) ∈ (1−a, 1/2). The continuity of bA (pB ) and bB (pA ) is no problem. Hence, the Brower fixed point theorem implies that, on the area (0, a)2 , the system of the first-order conditions has at least one solution (pA , pB ) ∈ (1 − a, 1/2)2 . Uniqueness: We first show b0A (pB ) ∈ (0, 1). Note that b0A (pB ) = where

∂tA /∂pB , 1 − ∂tA /∂pA

∙ ¸ Z a 1 ∂tA m−2 n−m m−1 (m − 1) = (u − ∆) u du − (a − ∆) ∂pA Km pB

and ∙ ¸ Z a 1 ∂tA m−1 m−2 n−m m−1 n−m (a − ∆) . = − (m − 1) (u − ∆) u du − pA pB ∂pB Km pB

27

It is clear that 1 − greater than

∂tA ∂pA

>

∂tA . ∂pB

Moreover,

∂tA ∂pB

> 0 since the square-bracket term is

£ ¤ m−1 n−m (a − ∆)m−1 − an−m (a − ∆)m−1 − pm−1 pB > 0 − pA A

given pB < a. Hence, we have b0A (pB ) ∈ (0, 1). Substituting bA (pB ) into the first-order condition (4), we obtain ¶m Z aµ u − pB + bA (pB ) 1 un−m−1 du. pB = 1 − a + Kn−m pB a − pB + bA (pB )

b0A (pB ) ∈ (0, 1) implies that bA (pB ) − pB decreases with pB , and so the term in the bracket is decreasing in pB . Therefore, the whole right-hand side of the above equation is a decreasing function of pB and our solution is unique.

A.2

Proof of Proposition 2

The rough idea of this proof is simple: we will show that, if consumers hold expectation of pA > pB , then a prominent firm will have more fresh demand but less returning demand than a non-prominent firm. Since returning demand is less price sensitive, prominent firms tend to charge a lower price, which contradicts consumers’ expectation. The proof consists of several steps: Step 1: The stopping rule with pA > pB . If consumers expect pA > pB but their search order is still restricted, then what is their optimal stopping rule? We keep the notation ∆ = pB − pA . First of all, once a consumer enters B, her stopping rule is the same as in the case with pA < pB . Now consider the situation before she enters B. Denote by zk (k ≤ m) the reservation surplus level when she visits the kth firm in her search process. That is, she will buy at the kth firm immediately if and only if this firm provides surplus greater than zk . According to Kohn and Shavel (1974), these zk are well defined and unique in our setup. We further claim that a−pA ≤ z1 ≤ · · · ≤ zm = a−pB . Here zm = a − pB is easy to understand. Now consider a consumer who has visited the (m − 1)th firm and been ensured a surplus vm−1 . If vm−1 < a − pA , then searching the last prominent firm is always worthwhile. If vm−1 ≥ zm = a − pB , then she should stop searching now since a − pB > a − pA and she would never enter B. Therefore, a − pA ≤ zm−1 ≤ zm .22 Similarly, we can prove a − pA ≤ zm−2 ≤ zm−1 and others. The intuition is, when a consumer more approaches the end of pool A, she has more incentive to search on in pursuit of the lower price in B. Let us summarize the consumer’s stopping rule with expectation of pA > pB : 22

More precisely, zm−1 can be defined as follows: let μ ≡ max(um − pA , zm−1 ) and G(μ) be its R∞ R zm distribution function. Then zm−1 = zm μdG(μ) + −∞ VB (μ)dG(μ) − s, where VB (x) is the expected surplus from entering B when the consumer has been ensured a surplus x. We can recursively define other zi .

28

Among prominent firms, stop at the kth firm if and only if the highest available surplus so far is no less than zk , where a − pA ≤ z1 ≤ · · · ≤ zm = a − pB ;23 among non-prominent firms, stop searching if and only if the highest available surplus is no less than zB = a − pB ; after searching all firms, return to the firm providing the highest non-negative surplus (if any). Step 2: The demand system. Since now there is no midway returning demand, each firm’s demand consists of two parts: fresh demand and (final) returning demand. We consider the returning demands rA and rB first. One can show that a firm’s returning demand is independent of its actual price (for local deviation) and rA ≤ rB .24 The intuition for rA ≤ rB is simple: when a consumer leaves a prominent firm and a nonprominent firm, the former’s product on average has a lower net surplus since zi ≤ zm for i ≤ m, and so it can win this consumer back less likely. Now we are ready to write down demand functions. For a prominent firm, if it charges p while other firms stick to their equilibrium prices, its demand is ¸ m ∙ k−1 Q 1 X qA (p) = (1 − zk − p) (zi + pA ) + rA . m k=1 i=1

Q Here k−1 i=1 (zi + pA ) /m is the probability that a consumer will visit this prominent firm as the kth firm in her search process, and 1 − zk − p is the conditional probability that this consumer will buy immediately.25 For a non-prominent firm, if it charges p while others keep charging their equilibrium prices, its demand is qB (p) = (1 − zB − p)Kn−m

m Q

(zk + pA ) + rB .

k=1

Q Here Kn−m m k=1 (zk + pA ) is the likelihood that a consumer will come to this nonprominent firm as a fresh consumer. Qk−1 Step 3: pA > pB is incompatible with equilibrium conditions. Define αk ≡ i=1 (zi + pA ) and notice αk ≥ αk+1 . Then the first-order conditions are 1 X αk (1 − zk − 2pA ) + rA = 0, m k=1 m

(14)

23

The case with strictly increasing zi and z1 > a − pA can actually take place. For example, when n = 3, m = 2, a = 0.6, pA = 0.45, and pB = 0.4, one can show that z1 ≈ 0.17 and z2 = 0.2. 24 One can check that m Z k−1 Q 1 X pA +zk rA = (u + ∆)n−m um−k min(zi + pA , u)du, m i=1 k=1 pA Z a m Q un−m−1 min(zi + pA , u − ∆)du. rB = pB

i=1

The details for rA ≤ rB are available on request. 25 More precisely, all zi + pA terms should be replaced by min(1, zi + pA ) because of the boundary problem. But this does not change our following analysis.

29

and Kn−m αm+1 (1 − a − pB ) + rB = 0,

(15)

where we have used zB = a − pB . Suppose pA > pB is the solution. Then we must have pA > pB > 1 − a, where the later inequality is from (15). Since zk ≥ a − pA , we have 1 − zk − 2pA ≤ 1 − a − pA < 0. Then (14) implies

m 1 P αk (1 − a − pA ) + rA ≥ 0. m k=1

So

Kn−m αm+1 (1 − a − pA ) + rB > 0

Pm

since Kn−m < 1, k=1 αk /m > αm+1 , and rB ≥ rA . This, however, contradicts with (15) when pA > pB . Therefore, consumers’ initial expectation of pA > pB cannot be sustained in equilibrium.

A.3

Proof of Proposition 4

We first establish the following result: Claim 1 Let θ =

1−¯ pn−1 n−1

and

ϕA =

(θ − p¯) m + 1 + p¯n−1 (θ − p¯) m , ϕB = , 2 − m¯ p+θ 2 − m¯ p+θ

(16)

where p¯ is the full-information equilibrium price. Then, when a → 1, equilibrium prices can be approximated by pi = p¯ + ki ε, i = A, B where ε = 1 − a, and ki =

p¯ [n(1 − ϕi ) + m − 1] . 2(1 + p¯n−1 )

Proof. Since the procedure is standard, we only give a sketch of the proof. When a → 1, we can approximate pi as p¯+ki ε, where ε = 1−a and ki needs to be determined. Extend the first-order conditions (3) and (4) around a = 1 by using these approximated prices and discard all higher-order terms, and then we get two equations of kA and kB . Solving them yields £ ¤ n+m−1 p¯ − (θ − p¯) m + 1 + p¯n−1 k4 , 2 n+m−1 p¯ − (θ − p¯) mk4 , = 2

(1 + p¯n−1 )kA = (1 + p¯n−1 )kB

30

where k4 = kB − kA = Using the notation in (16), we have

n¯ p . 2(2 − m¯ p + θ)

2(1 + p¯n−1 )ki /¯ p = n − 1 + m − nϕi (m). It is then ready to see k4 is positive and increasing with m, so 4 always increases with m. For having pi increasing with m, it suffices to show that ϕ0i (m) is less than n1 . First, we have (θ − p¯)(θ + 2) (θ − p¯)(θ + 2) 2 < (2 − m¯ p + θ) (2 − n¯ p + θ)2 (θ − p¯)(θ + 2) (θ − p¯)(θ + 2) = . 2 < n (1 + p¯ + θ) (θ + 1)2

ϕ0B (m) =

We have used n¯ p = 1 − p¯n in the second equality. Second, ϕ0B (m) < ϕ0A (m) = ϕ0B (m) +

p¯(1 + p¯n−1 ) (θ − p¯)(θ + 2) + p¯ + p¯n < . (2 − m¯ p + θ)2 (θ + 1)2

Using the definition of θ, one can show that (17) is less than

1 n

if and only if

1 (n + 1)¯ p + p¯n−1 < 2. n This must be true since n¯ p = 1 − p¯n < 1 and p¯ + n1 p¯n−1 < 1.

A.4

Proof of Proposition 5

When a → 1, Qm is approximated by pn−1 ε. 1 − p¯n − (nkB − mk4 )¯ We need to investigate the property of nkB − mk4 . The results in Claim 1 imply ¶ µ n(n + m − 1) n(θ − p¯) nkB − mk4 = + 1 mk4 . p¯ − 2(1 + p¯n−1 ) 1 + p¯n−1 We also have ∂mk4 ∂k4 = k4 + m = k4 ∂m ∂m So

µ

¶ 2m (θ + 2)n¯ p k4 + 1 = . n 2(θ + 2 − m¯ p)2

∂ (nkB − mk4 ) n¯ p = − ∂m 2(1 + p¯n−1 )

µ

31

¶ (θ + 2)n¯ p n(θ − p¯) + 1 , 1 + p¯n−1 2(θ + 2 − m¯ p)2

(17)

which has the sign of L=

θ+2 1 − . n(θ − p¯) + 1 + p¯n−1 (θ + 2 − m¯ p)2

Using the definition of θ, one can further show that L has the sign of p + (n − 2m)(2n − 1 − p¯n−1 ). m2 (n − 1)¯ When 2m ≤ n, this is clearly positive, so Qm decreases with m. However, if 2m > n, the opposite result could happen. Since 2n − 1 − p¯n−1 > 2n(n − 1) p¯ (where we have used p¯ < 1/n and p¯n−1 < 1), a sufficient condition for L be negative is √ 2 √ n. 2(n − m)2 < m2 ⇐⇒ m > 1+ 2 √

Therefore, if m > 1+√2 2 n, Qm must increase with m. In the case without prominence, p0 is approximated by p¯ + k0 ε when a → 1. One can show 2(1 + p¯n−1 )k0 /¯ p = n − 1, and pn−1 k0 ε. Q0 ≈ 1 − p¯n − n¯ Qm < Q0 in this limit case is easy to be verified.

A.5

Proof of Proposition 6

Since the approximation procedure is regular, the details are omitted. When a → 1, industry profit is Πm ≈ n¯ p2 + (nkB − mk4 ) (¯ p − p¯n )ε, and total welfare is Wm ≈

n (1 − p¯n+1 ) + (mk4 − nkB ) p¯n ε. n+1

We have known that, when a → 1, ∂Qm /∂m has the sign of ∂ (mk4 − nkB ) /∂m, so our results on welfare and m follow. The proofs for Πm > Π0 and Wm < W0 in this limit case is straightforward and so omitted.

A.6

Proof of Proposition 8

(i) Rewrite (10)—(11) as ∙ ¸ 1 an − pnB n 4 = − 1 − a − pB + , 2 n £ ¤ 0 = 1 − (n + 1)pnB + 1 − an−1 + (n + 1)pn−1 4. B 32

(18)

They imply

¤ 1 − (n + 1)pnB 1 £ 1 − an−1 + (n + 1)pn−1 = , (19) B n A − (n + 1)pB 2n where A = n(1 − a) + an . Since A > 1, the left-hand side is a decreasing function of pB , while the right-hand side is an increasing function of pB . Moreover, when (1 + n)pnB = 1 (i.e., pB = p0 ), the left-hand side is zero and so less than the right-hand side. When n−1 pB = 0, the left-hand side (1/A) is greater than the right-hand side ( 1−a2n ) since A < n. Therefore, (19) has a unique solution pB ∈ (0, p0 ). (This, together with (18), confirms 4 < 0.) Then pA = pB − 4 is also unique. Explicitly, ∙ ¸ 1 an − pnB n pA = pB + 1 − a − pB + . 2 n √ ∂pA n−1 1+n n−1 1 One can check ∂p = 1 − p > 0 since (1 + n)p < < 3, and so pA is B B 2 p0 B increasing with pB and we have ∙ ¸ 1 − an 1 pA < p0 + 1−a− . 2 n Notice that the bracket term decreases with a, so a sufficient condition for all equilibrium ¡ n¢ prices to be less than a is a > aˆn , where aˆn solves p0 + 12 1 − a − 1−a = a.26 n (ii) From (11)—(12) and ∆ < 0, it is ready to see pA pn−1 < pn0 , and so the prominence B case serves more consumers. Since pA > pB , we get pB < p0 . In the following, we show pA > p0 . (11)—(12) imply pn0 Suppose pA ≤ p0 . Then pA − pA pn−1 ≤ −∆ B So



pA pn−1 B

(20)

1 − an−1 pnA − pnB 1 − an−1 n−1 < ≤ p + ⇒ npn−1 . B B n+1 pA − pB n+1 (n +

Then the left-hand side of (11) were

26

1 − an−1 . = −∆ n+1

1)pn−1 B

1 − an−1 < . n−1

(21)

£ ¤ 1 − (n + 1)pnB + 1 − an−1 + (n + 1)pn−1 4 B £ ¤ n−1 n−1 + 1 − a + (n + 1)p 4 > 1 − (n + 1)pn−1 B B n−1 1−a > 1− (1 − n4) > 0. n−1 In the case with announced prices, it is ready to check that (19) will become 1 − (n + 1)pnB n + 1 n−1 = . p n A − (n + 1)pB 2n B

So we still have pB ∈ (0, p0 ). But now pB is larger than that in the case with imperfect price information. Since the expression for 4 does not change, that for pA also remains. Thus, pA in this case is also higher than in the case with imperfect price information.

33

This is a contradiction. The first inequality is because pB < 1, the second uses (21), an −(n+1)pn 1 1 B and the last one uses 1−n4 < which is because −4 = (1 − a + ) < 12 n−1 n−1 1−a 2 n from (10) and a > 12 from Assumption 2.27

A.7

Proof of Proposition 9

We continue the proof of Proposition 9 by showing that a sufficient condition for both W1 > W0 and V1 > V0 is 3∆ 1 − an−1 pB + > 0. (22) n+1 2 µ ¶ 1 − an−1 ∆ ∆ n n n pB + , W1 − W0 > pB (p0 − pB ) + ∆(pB − ) = −∆ 2 n+1 2 Rp Rp where the inequality uses pB0 pn dp > pB pB0 pn−1 dp and the equality uses pn0



pnB

µ

1 − an−1 + pn−1 = −∆ B n+1



(23)

which is further from (20). Since 4 < 0, (22) implies W1 − W0 > 0. V1 − V0 > (1 − pn0 )(p0 − pB ) + ∆(pnB −

3∆ 3∆ n )= (p0 − pB ) + ∆(pnB − ), 2 n+1 2

which is positive under (22) because pn0 − pnB −4 = p0 − pB p0 − pB

µ

1 − an−1 + pn−1 B n+1

¶−1

<

n (1 −

an−1 ) pB

+ (n +

The first equality is because (23), the first inequality uses 1)pn−1 = 1/p0 , and the last one uses (22). 0

A.8

1)pnB

n pn 0 −pB p0 −pB

<

n . (n + 1)(pnB − 3∆/2)

< npn−1 and (n + 0

Competitive pricing with a general valuation distribution

We aim to show that the price result pA < pB in Section 3 holds in a general setting. 1−F n Let F = F (a) and Kn = n(1−F . For expositional convenience, we further introduce a ) piece of notation: φ(p, x) = 1 − F (p + x) − pf (p + x). Note that φ1 (p, x) − φ2 (p, x) = −f (p + x) < 0. We also need the following two assumptions: Assumption 3 f (u) is logconcave and a >

1−F (a) f (a)

= p∞ .

1+n/2 1−n4 When n ≥ 4, 1−n4 n−1 < n−1 ≤ 1. When n = 2, n−1 = 1 − 24 < 2 ≤ 1−n4 1−34 When n = 3, n−1 = 2 < 54 < 43 ≤ 1−a1n−1 whenever a ≥ 12 . 27

34

1 1−an−1

whenever a ≥ 12 .

Assumption 4 f (p + x) + pf 0 (p + x) = −φ2 (p, x) ≥ 0 for p, x ≥ 0. The logconcavity assumption is satisfied by many distributions. (See, e.g., Bagnoli and Bergstrom (2005) for a detailed discussion.) Two well-known results are: (i) logconcave f (u) implies logconcave F (u) and 1 − F (u), and (ii) logconcave 1 − F (u) is equivalent to increasing hazard rate. The second part of Assumption 3 requires that the search cost is not too high, which corresponds to Assumption 1 in the main text. As we will see below, p∞ is the equilibrium price when there are an infinite number of firms. The interpretation of Assumption 4 goes as follows. If there is a monopoly firm which produces a product with valuation distribution F (u) and consumers’ outside option utility is x, then φ(p, x) is the firm’s marginal profit at price p. Thus, Assumption 4 is a sufficient condition for the optimal monopoly price to be decreasing with x. Let πA (p) = pqA (p) be a prominent firm’s profit function when other firms keep charging their equilibrium prices, and πB (p) = pqB (p) be a non-prominent firm’s profit function. One can check that the first-order conditions can be written as ˆ A + RA = 0, hA φ(pA , a − pA ) + R

(24)

hB φ(pB , a − pB ) + RB = 0,

(25)

where the R-terms are the equilibrium marginal profits from returning consumers.28 Explicitly, Z a ˆA = − R F (u)m−1 φ2 (pA , u − pA )du, Za−∆ a F (u − ∆)m−1 F (u)n−m φ2 (pA , u − pB )du, RA = − ZpBa F (u − ∆)m F (u)n−m−1 φ2 (pB , u − pB )du. RB = − pB

Now we can see that Assumption 4 guarantees that the returning demand has positive marginal profit in equilibrium (i.e., the returning demand is less price “sensitive” than the fresh demand). We can rewrite the first-order conditions as pA = p∞ +

ˆ A + RA 1 R , f(a) hA

(26)

1 RB . (27) f(a) hB Then it is not hard to verify that both pA and pB tend to p∞ as n → ∞. Our demand functions are based on consumers’ expectation of pA < pB , and now we confirm that this is indeed an equilibrium outcome. pB = p∞ +

28

One can show that our profit functions are actually concave under Assumption 3 if there is no boundary problem. Hence, the first-order conditions do define the equilibrium prices if they have solutions on the area (0, a)2 .

35

Claim 2 Given Assumptions 3—4, if the system of the first-order conditions have solutions, then one solution must specify pA < pB .29 Proof. Let ˆ A + RA . ζ(pA , pB ) ≡ hA φ(pA , a − pA ) + R As we will show shortly, if all solutions to (26) and (27) would specify pA ≥ pB , then ζ(pB , pB ) < 0. But it is easy to see ζ(0, pB ) > 0, and then we would conclude that ζ(p, pB ) = 0 must have a solution p < pB . This is a contradiction. Now we confirm ζ(pB , pB ) < 0 if pA ≥ pB . It is ready to see that Z a F (u)n−1 φ2 (pB , u − pB )du. ζ(pB , pB ) = hA φ(pB , a − pB ) − pB

Using (25), we can rewrite it into hA ζ(pB , pB ) = − RB − hB

Z

a

pB

F (u)n−1 φ2 (pB , u − pB )du.

If φ2 (pB , u − pB ) ≤ 0 for u ∈ [pB , a], ζ(pB , pB ) is negative if F (u)n−1 <

hA F (u − ∆)m F (u)n−m−1 hB

for u ∈ [pB , a], which is further equivalent to Fm F (u)m Km < . F (u − ∆)m Kn−m F m F (a − ∆)m Notice that Km > Kn−m F m , so it suffices to show F (a) F (u) ≤ F (u − ∆) F (a − ∆) for u ∈ [pB , a]. This is true if

F (u) F (u−∆)

increases with u or equivalently if

f (u) F (u)



f (u−∆) . F (u−∆)

Assumption 3 implies logconcave F (u), and so Ff (u) is a decreasing function. Thus, if (u) pA ≥ pB (i.e., ∆ ≤ 0), the sufficient condition we need actually holds, and so ζ(pB , pB ) < 0. We have seen that this main result only requires φ2 (pB , u − pB ) ≤ 0 for u ∈ [pB , a], which is weaker than Assumption 4. In fact, if n is sufficiently large, this condition tends to hold for any valuation distribution satisfying Assumption 3. Therefore, at least for large n, pA < pB is a quite general result. We now show this point: Proposition 11 Under Assumption 3, there exists N such that, for n > N, we have −φ2 (pB , u − pB ) = f (u) + pB f 0 (u) ≥ 0 for u ∈ [pB , a].

ˆ A + RA − RB having the sign of 4 and does The technique used in the uniform case relies on R not apply in this general setup. 29

36

Proof. Since pB tends to p∞ as n → ∞, it suffices to show that f (u) + p∞ f 0 (u) > 0 (u) 0 for u ∈ [p∞ , a]. If f 0 (u) ≥ 0, we are done. If f 0 (u) < 0, then f (u) + 1−F f (u) > 0 f (u) 0 (which is implied by logconcave 1 − F (u)) implies f(u) + p∞ f (u) > 0 for u < a since (a) (u) p∞ = 1−F < 1−F . f (a) f (u)

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Kohn, M., and S. Shavell (1974): “The Theory of Search,” Journal of Economic Theory, 9(2), 93—123. Lohse, G. L. (1997): “Consumer Eye Movement Patterns on Yellow Pages Advertising,” Journal of Advertising, 26(1), 61—73. Madrian, B. C., and D. F. Shea (2001): “The Power of Suggestion: Inertia in 401(K) Participation and Savings Behavior,” Quarterly Journal of Economics, 116(4), 1149— 1187. McAfee, R. P., and M. Schwartz (1994): “Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity,” American Economic Review, 84(1), 210—230. Meredith, M., and Y. Salant (2007): “The Causes and Consequences of Ballot Order-Effects,” mimeo. Perry, M., and A. Wigderson (1986): “Search in a Known Pattern,” Journal of Political Economy, 94(1), 225—230. Rey, P., and T. Verge (2004): “Bilateral Control with Vertical Contracts,” Rand Journal of Economics, 35(4), 728—746. Robert, J., and D. Stahl (1993): “Informative Price Advertising in a Sequential Search Model,” Econometrica, 61(3), 657—686. Salop, S. (1977): “The Noisy Monopolist: Imperfect Information, Price Dispersion and Price Discrimination,” Review of Economic Studies, 44(3), 393—406. Varian, H. R. (2007): “Position Auctions,” International Journal of Industrial Organization, 25(6), 1163—1187. Weitzman, M. L. (1979): “Optimal Search for the Best Alternative,” Econometrica, 47(3), 641—654. Wolinsky, A. (1986): “True Monopolistic Competition as a Result of Imperfect Information,” Quarterly Journal of Economics, 101(3), 493—511.

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Dec 2, 1999 - an unlimited demand for networking service” (JISC Circular 3/98, ... Odlyzko (1997) has proposed to apply the same scheme to the Internet.

Simple Competitive Internet Pricing - Semantic Scholar
Dec 2, 1999 - the number of users, and the amount of traffic have been doubling approximately every ... minute Internet telephone call uses 500 times the capacity of a comparable paragraph of e-mail; one ..... Business, 72(2), 215–28. Odlyzko, A.,

Competitive Pricing: Capacity View - Clary Business Machines
Competitor A. Competitor B. Competitor C. Ports at 1080p30. 16. 7. 12. 7. Ports at 720p60. 16. 7. 0. 0. Ports at 720p30. 16. 15. 12. 15. MSRP. $64,999. $108,000. $159,000. $85,000. *Based on estimated MSRP and documented port configuration; cost in U

Mechanism Design and Competitive Markets in a ...
is enough to make money essential even if agents trade in a centralized market. ... equivalence theorem holds in the monetary economy with fixed money supply ...

Are Payday Lending Markets Competitive? - Cato Institute
payday loans at a lower price, or offer a different product with a price/characteristic mix .... a good metric of the loan markup when financing costs are the .... right now that test suggests a negative answer. ... phone survey mentioned in the pre-

Adverse Selection in Competitive Search Equilibrium
May 11, 2010 - With competitive search, principals post terms of trade (contracts), ... that a worker gets a job in the first place (the extensive margin), and for this ...

Are Payday Lending Markets Competitive? - Cato Institute
unions covered in the data, roughly 6 percent (479) offered pay- day loans; by June, ... credit unions via phone calls, starting from a list of 250 credit unions randomly .... It is well known that in credit markets, firms that set lower prices (typi

Monopolistically Competitive Search Equilibrium
Jul 18, 2017 - job search engines and services, among others—play an important role in helping ..... which is a constraint on recruiter j's optimization problem.

Monopolistically Competitive Search Equilibrium
Sep 25, 2017 - sult arises from the differential degree of (in)efficiencies between non-intermediated markets and. (monopolistically-competitive) intermediated ...

Firm pricing with consumer search
Dec 21, 2016 - products, and cost differences across firms, but search costs are not one of them ...... Unfortunately, accounting for such learning complicates.

Intermediation and Competition in Search Markets: An ...
Dec 14, 2015 - specific.1 This is especially true for retail service markets and those for investment goods. One common ..... of the waste was going to the Fresh Kills landfill, one of the largest on earth in that time frame (Royte (2007)). 9 ... fol

Two-Sided Platforms in Search Markets
France. Phone: +33(0)1.69.33.34.17. ...... See Appendix A.3. To grasp the intuition, consider the impact of a small increase in t on the total surplus and on agents' ...

Two-sided Search in International Markets
us to decompose trade and welfare changes into two basic driving forces: market entry by ...... Business and social networks in international trade. Journal of ...

Estimating demand in online search markets, with ...
Nov 6, 2012 - is engaged in "discovery", where she is learning about existing product varieties and their prices. ..... Second, the search horizon is finite.