The Strategic Use of Consumer Search Cost *

Transcription

1 The Strategic Use of Consumer Search Cost * Florian Zettelmeyer Haas School of Business University of California at Berkeley Berkeley, CA florian@haas.berkeley.edu ( ) (510) (Office) (510) (Fax) This version: October 1998 Keywords: Competitive Strategy, Search Costs, Internet Marketing, Game Theory. * This paper has benefited greatly from many discussions with Meghan Busse, Jeromin Zettelmeyer and especially Birger Wernerfelt. Very helpful suggestions from three anonymous reviewers, the area editor and the editor are gratefully acknowledged. I also thank Eric Anderson, John Hauser, Leslie Marx, and Nader Tavassoli for detailed comments. Further, I have benefited from comments and discussions by seminar participants at MIT, Columbia University, Carnegie-Mellon University, Harvard University, Washington University in St. Louis, University of Pennsylvania, Dartmouth College, UCLA, UC Berkeley, Stanford University, USC, New York University, and the University of Rochester.

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3 The Strategic Use of Consumer Search Cost Abstract Through their communications mix, firms make decisions that have implications for the ease with which consumers can search for product information. A common intuition is that firms would like to make information easily available to consumers, but choose not to because facilitating consumer search is costly to them. The main result of this paper counters this intuition firms may not want to make consumer search easy, even if it is costless for them to do so. I identify two reasons why firms will choose to make search hard for consumers. First, firms can soften price competition by differentiating themselves on the basis of consumer search cost, even if consumers don t differ in their disutility of search. Second, firms have an incentive to take advantage of consumer optimism. It is shown that the reduced cost of providing information in new electronic channels such as the Internet does not necessarily imply that firms will aid consumers in their search for information. Some of the marketing implications of this result are: The Internet may not develop into a smorgasbord of vendor provided information; firms can use the existence of multiple channels to ease price competition; the fact that stores have low service might not be related only to cost pressure.

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5 1 Introduction How a firm designs its communications mix will determine how easy or hard it is for consumers to search for product information. In a traditional retail environment, the ease with which consumers can acquire product information depends on the extent to which the product can be evaluated at a retailer (shrink-wrapped package vs. display model), or the amount of technical information provided on the shelf tag or packaging. In mail-order, the ease with which consumers can acquire product information may depend on the availability of an 800 number for product inquiry, the layout of the catalog, or the amount of information, including product comparisons, provided in the catalog. Over new electronic channels, firms can influence the ease of acquiring product information by the number of on-line services in which they offer information and the amount of information they allow consumers to retrieve while on-line (e.g. only technical data or also a picture). For the rest of this paper I use consumer search cost to mean the time and effort that consumers incur in acquiring product information that allows them to determine how much they like a product. It is a common intuition that firms want to make consumer search for their own product easy in order to provide value to the customer or to treat the customer as a partner. However, we frequently observe that firms don t make it as easy as possible for consumers to search. Many software companies, for example Microsoft, Acron, or Adobe, do not make demonstration versions of their software available for downloading from the Internet, thereby making it harder for consumers to evaluate how much they like the software before purchasing. Many drug companies, for example the manufacturers of Tylenol, make it very hard for consumers to determine their valuation for any particular drug. Consumers are offered multiple drugs with identical active ingredients with little or no information on the drug packages about the differences between them. A similar example, but of a retailer, is the OfficeMax catalog. A comparison of handheld tape recorders reveals that the three line descriptions provide very little quality information; different features are highlighted in each description and the reader is uncertain whether the absence of particular feature in a description implies that it is missing from the product. An obvious answer for why we observe that firms don t try to minimize consumer search cost is that it is costly for them to do so. This does not explain the above examples. Demo versions of software can be provided at a negligible marginal cost. A table listing features of handheld tape recorders by product does not take up more space in the catalogue than text descriptions and would be far more helpful for consumers

6 The main result of my paper is that the common intuition that firms want to make consumer search as easy as possible need not be true, even if firms costs of facilitating search are not a factor. I will show that there may be additional, strategic 1 incentives to keep consumer search costs high. These reasons are of particular interest in view of the emergence of electronic shopping. Electronic channels such as on-line services and especially the Internet make it very cheap for firms to allow interested consumers to find out more about their products. A typical quote from the business and trade press early in the development of electronic shopping stated: [On-line shopping] allows merchandisers to serve individual customers better by getting information on relevant products and services to them exactly when they need them. (American Demographics, September 1994) This paper sets out to answer two questions which are of both fundamental and applied interest. Even if it is costless for a firm to make consumer search cost very low, will it want to do so? How does competition affect a firm s decision to make search cheap for consumers? To this effect I model consumers that are considering the purchase of a product in a particular category. Consumers have already done some preliminary search or have been exposed to enough advertised information to know the product offerings, their associated prices, and some characteristics that are common to the offerings in the product category. From their basic knowledge of the product category they are aware of the distribution from which their valuations are drawn but do not have a precise idea of the benefits they might derive from each particular product. They can determine their valuation for a product by searching for information about this product and inspecting the product. For some products, increased knowledge about the product category generally increases consumers perceived differentiation between products. This is true of wines, for example. Where a wine novice might not know the difference between a $10 bottle of red wine with the Pinot Noir grape and the Cabernet Sauvignon grape, a wine expert, for any particular meal, will not consider them to be particularly good substitutes. For other products, increased knowledge about the product category generally 1 Strategic in the sense that a firm considers the reactions of other firms and of consumers when deciding what to do. As an example, consider a consumer that is interested in purchasing a personal computer and knows how much she values having a 00 Mhz Pentium. She is aware from magazine advertising that IBM and Compaq both sell personal computers. From the ads she has identified prices and basic features of 00 Mhz Pentiums, as well as where to look for more information. The features she could identify from the ads are very similar for both products, so the consumer can t establish which product she prefers. She knows that she can put some effort into finding out more about each computer by searching the manufacturer website for product information, or by visiting a store and inspecting the computer. - -

7 decreases consumers perceived differentiation between products. Pain killers fall in this category. A consumer that is not particularly well informed about the active ingredients in pain killers might not consider Advil and a generic brand of ibuprofen as particularly good substitutes. A knowledgeable consumer on the other hand, will consider the products perfect substitutes since both carry identical active ingredients. Personal computers also fall into this category of products. A consumer with limited product specific information will not consider an IBM PC to be of equal value to a Packard Bell, even if they have identical core specifications. A consumer that is very well informed will know that their differentiation is not based on objective product attributes and is hence more likely to consider them of equal value. The paper considers products that fall into this second category, i.e. products for which increased knowledge about the product category generally decreases consumers perceived differentiation between products. I model these product types by assuming that, while a percentage of fully informed consumers have a higher valuation for one or the other product in the category, a sufficiently large portion of fully informed consumers consider the goods of competing firms to be of equal value. In summary, I model products (a) for which consumers valuations are initially uncertain, (b) for which consumers can determine their valuations through (potentially costly) search, (c) for which consumers can determine prices more easily than their exact valuation for the product, and (d) that are close substitutes in so far as a portion of fully informed consumers considers the goods of competing firms to be of equal value. Among the category of goods that fit this description are many infrequently purchased search goods, search goods that undergo rapid technological change, or products that are characterized by generics. For such products I show that there are situations in which firms will not want to facilitate consumer search. I highlight two reasons for this: (1) firms can soften price competition by differentiating themselves on the basis of consumer search cost, and () firms can take advantage of consumer optimism. The first reason results from the analysis of a vertically integrated duopoly, in which I show that firms can avoid ruinous price competition by using search costs to differentiate themselves. 3 There exists an equilibrium in which one firm offers a high price but makes search easy while the other firm 3 Since the firms modeled in this paper are vertically integrated the results apply only to firms with direct distribution. To determine whether the results generalize to channels with intermediaries requires further research and will depend on the way in which intermediaries are added to the model

8 makes search costly to consumers but offers a lower price. If firms did not differentiate themselves in this way, for example, if neither made it easy for consumers to obtain information, consumers would have to choose which product to buy on the basis of price alone. Similarly, if both firms informed consumers, then the portion of the consumers who valued the products equally would also choose on the basis of price alone. By differentiating themselves, both firms can sustain higher profits by softening price competition. For example, if consumers are only informed by firm 1 but not by firm, then after evaluating firm1 s product, consumers will decide either to buy from firm 1 at a higher price but knowing what they will get or to buy from firm at a lower price but with only an estimate of the value of firm s product to them. If consumers differ in their realized valuation for firm 1 s product, then a change in prices by either firm 1 or firm will induce only a few consumers on the margin to switch from store one to the other. This insensitive reaction of consumers demand softens price competition because none of the stores can capture the whole market by slightly lowering prices. The second reason can be shown in the simple case of a monopoly (but also holds in a duopoly). I show that higher search costs can yield higher profits if consumers are sufficiently 4 confident that they will like a product, even before they have precise knowledge of the product s value to them. Cheap search would allow those consumers whose true valuation is slightly below their expected valuation to avoid buying a product that they would have bought, had they not searched, but nevertheless don t return because of the cost associated with returning the product. These two reasons suggest that the mere fact that electronic channels allow cheap communication with consumers does not imply that firms will use this ability to lower consumer search cost. The role of marketing communications includes both informing and persuading consumers. Much of a firm s communications mix is geared towards persuasion and a large stream of marketing research analyzes various aspects of persuasion. In this paper, however, I want to concentrate on the information aspect of the communications mix since it is of increased importance on new electronic communication channels such as the Internet. While some literature portrays consumers as passive recipients of communication, I will look at consumers as active searchers for information, although they incur costs in this process. Like Wernerfelt (1994a, 1996) I deal with efficiency in marketing communication but focus on identifying situations where firms strategically communicate inefficiently. 4 In relation to the firm s marginal cost of production. See section for an explanation

9 I add to the literature on search and search costs by considering firms strategic decisions about the level of search cost that consumers have to incur if they decide to search. Daughety and Reinganum (1991), and DeGraba (1995) also consider firm decisions that impact consumer search cost but focus on product availability. An alternative explanation that also leads to the result that firms purposefully limit the information they make available to consumers is the potential for information overload. Since information overload suggests that amount of information could increase or decrease consumer s ease of search I model firms as influencing consumers search cost directly. I begin with the simplest case (monopoly) in section, and then model a duopoly in section 3. While this progression aids logical explication, it means that the results will be derived in an order slightly different from the presentation above. Section 4 discusses the results and section 5 concludes the paper. Monopoly.1 Model Assume consumers are interested in purchasing one unit of a product in a particular product category. Consumers know the price p of the product offered by the monopolist. Consumers do not know ex ante the gross utility u they will derive from the product. 5 They are, however, aware of the distribution from which their reservation prices are drawn. Consumers willingness to pay is distributed uniformly between 0 and 1 ( u U[ 01, ] ). A consumer can find out her reservation price u by evaluating the firm s product. In doing so she incurs search cost s. Consumers facing a purchase decision can either buy, search or decide not to buy at all. If they have searched and learned their reservation prices they then have the option to buy or to pass, i.e. searching allows consumers to ensure that they purchase only when their willingness to pay exceeds price. After the purchase consumers can choose to return the product. In doing so they incur a return cost r that can consist of a restocking fee, the hassle associated with returns, or the shipping and handling fee as- 5 I will use reservation price or willingness to pay synonymously with u

10 sociated with many products that are ordered on the Internet or through mail order (Hess, Chu, Gerstner 1996). Figure 1: Consumer decisions Stage 1 Buy Search Pass Stage Buy Pass In stage consumers know their reservation prices and only purchases if the reservation price u exceeds the price p. Hence consumers never return a product after buying at stage, and their payoffs are: Table 1: Consumer utilities in stage Action buy pass Utility s + u p s Since reservation prices u are distributed uniformly between 0 and 1, the density function of u is f() u = 1. In stage 1, i.e. before search, the expected utility for each of a consumer s choices are: Table : Expected consumer utilities in stage 1 Action buy 1 ( p r) Expected utility ( p r) ( u p) du rdu for p > r udu p for p r search pass: 1 s + ( u p) du p 0 With these utilities I can describe consumers best response functions to any price - search cost pair ( ps, ). Notice that every consumer has the same expected utility. Hence, given ( ps, ), if any consumer prefers a given action, all consumers will prefer that action

11 The monopolist has two choice variables, price p problem is given by: and search cost s. The monopolist maximization max ps, ( p c)dp (, s) (1) where c is marginal cost and D( p, s) is the fraction of consumers who buy and do not return the product. Given consumer behavior, this fraction is as follows: Dp (, s) = 1 ( p r) if consumers buy 1 p if consumers search 0 if consumers pass (). Solution From table we can derive the conditions on p and s for which buy, search, or pass is consumers best response. Consumers search rather than pass iff s ( 1 p). Notice that consumers never return products for p r. For p > r consumers buy rather than search 6 iff s ( r ) ( p r), and buy rather than pass iff p 1 r + r. For p r consumers buy rather than search iff s p, and buy rather than pass iff p 1. By graphing these thresholds in the firm s strategy space ( ps, ) for high and for low return costs r we obtain the best response regions shown in figure : Figure : Firm strategy space and consumer best response High return costs ( r = 1 ) Low return costs ( r = 1 10) buy pass 0.15 buy pass search 0.05 search The regions of consumers best responses for ( ps, ) are separated by dashed lines. To illustrate figure, consider for example a price of 0. and search cost of All consumers will want to buy 6 Note that in stage 1 search as a consumer strategy means: search and buy if u p, otherwise pass. Likewise in stage 1 buy means, buy and return if u< p d

12 immediately without searching. Although the value of information that could be obtained by searching is lower than the search cost, the price is so low that consumers priors regarding their reservation prices significantly exceed the price the monopolist charges. Maintaining the same level of search cost but increasing price to 0.6 makes it worthwhile for consumers to search before buying since the probability that the willingness to pay is lower than the price has risen. A substantial increase in search cost from ( ps, ) = ( 0.6, 0.03) makes consumers drop out of the market entirely if return costs are very high since consumers expected reservation price of 1/ is lower than p. If return costs are low and search costs high, buying dominates searching because potentially incurring return costs is lower in expectation than incurring search costs for sure. If both, prices and search costs are very high, consumers drop out of the market altogether, unless return costs are negligible. I can now specify the equilibria of this game: Proposition 1: Let F be the cumulative distribution of consumers on [ 01, ]. Then the following characterizes the game s pure-strategy equilibria: Assume r < 1. Then for c < 1 r + r such that Fc () c () r, p * ( 1 + c+ r) = s, * ( 1 + c)r, and for c 1 r + r such that Fc () c () r, p * = 1 r + r s * r, 1 r + --, r all consumers buy in stage 1 and some consumers return the product. For c such that Fc () > c, p * ( 1 + c) = s, all consumers search in stage 1, * ( 1 c), where c () r = 1 ( r 14 / r 34 / ) Assume r 1. Then for c such that Fc () c ( 1 ) = 1, p * = 1, s * 1 8, all consumers buy in stage 1 and no consumers return the product. For c such that Fc () > c ( 1 ) = 1, p * ( 1 + c) = s, all consumers * ( 1 c), search in stage 1. Proof of proposition 1: see appendix Suppose the firm has low marginal cost c. Then there are many consumers whose reservation prices are larger than marginal cost, i.e. 1 F() c is large (or Fc () is small). This allows the firm to set price well - 8 -

13 above marginal cost and still price below consumers expected utility of purchasing and potentially having to return the product at a cost r. Setting high search costs to induce consumers to buy without searching results in purchases by some ( r ) consumers with reservation prices below p that do not return the product but would not have bought it they had known their reservation price before the purchase. With marginal cost below most consumers reservation prices, profits reaped from each customer can be large and it will not pay for the firm to charge a higher price but lose a portion r of demand by allowing consumers to search. The distinction of two cases for Fc () c reflects that for larger marginal costs c the firm cannot price at p * = ( 1 + c+ r) without exceeding consumers expected utility of purchasing and potentially having to return the product. That is why for marginal costs such that 1 r + r c c () r the firm prices at consumers expected utility of purchasing and potentially having to return the product. The higher the marginal costs c, the less profit that the firm can reap of each individual consumer. If fewer than Fc () = c consumers have reservation prices that are above marginal cost, the firm is better off selling to only those with reservation prices above the firm s price but at a higher price than previously possible. Hence the firm permits search. I can now state the main result of this section: Corollary 1: For any strictly positive return cost there exists a region of the parameter space for which a monopolist is strictly better off setting strictly positive search cost, even if the provision of information to consumers is costless to the monopolist. Corollary 1 makes use of the fact that in the profit function of the monopolist (equation 1) there are no costs associated with lowering consumer search cost s. 3 Competition 3.1 Model To illustrate the effects of competition I introduce a second firm. The two firms products are substitutes. There is one segment of consumers with reservation prices distributed uniformly between 0 and 1. Consumers willingness to pay for firm 1 s and firm s product are u 1 and u respectively. These are identically but not necessarily independently distributed. For simplicity I assume the following correlation structure between reservation prices u 1 and u : if a consumer searches at firm i and learns about her reservation price u i then with probability q her reservation price at firm j is identical to the res

14 ervation price she just learned, i.e. Pr( u j = u i ) = q. With probability 1 q the reservation price at firm j is different 7 in which case her best estimate about her reservation price at firm j is her prior. The consumers possible actions are illustrated in figure 3: Figure 3: Consumer decisions Stage 1 Stage Buy at 1 Search at 1 Pass Search at Buy at Stage 3 Buy at 1 Pass Search at Buy at Buy at 1 Search at 1 Pass Buy at Buy at 1 Pass Buy at Buy at 1 Pass Buy at A consumer has the option to buy from either firm without any search, to search either firm or to pass altogether. If she has decided to search at firm i she knows her reservation price at that firm as well as her reservation price u j at firm j with probability q. With this knowledge she can decide to buy at either firm, to pass or to search at firm j. If the consumer searches at firm j she has full information, i.e. she knows and and decides to buy from one of the firms or to pass. To simplify the u i u j analysis in the duopoly case I assume that consumers can t return products or that consumers return costs are sufficiently high to prevent returns. As we saw in the monopoly case, allowing for returns changes the degree to which firms need to facilitate search costs in order to induce consumers to search. The qualitative results, however, remain the same as long as return costs are strictly positive. u i 7 By continuity of the distribution of reservation prices different means the same as independent of the reservation price of firm i

15 To determine consumers optimal responses to both firms price - search cost offerings ( p 1, s 1 ) and ( p, s ) let us consider a consumer s expected utility at each stage. In stage 3 a consumer knows both reservation prices, hence her overall payoff for each action is given by: Table 3: Consumer utilities in stage 3 Action buy at firm 1: buy at firm : pass: Utility s 1 s + u 1 p 1 s 1 s + u p s 1 s In stage the consumer has only searched one firm, say firm 1. 8 Her expected utilities then are: Table 4: Expected consumer utilities in stage Action buy at firm 1: buy at firm : search at firm Expected utility s 1 + u 1 p 1 s 1 + qu 1 + ( 1 q) u du p s 1 s + q max{ 0, u 1 p 1, u 1 p } + ( 1 q) 1 0 ( u 1 p 1 + p ) 1 max { 0, u 1 p } du 1 + max{ 0, u p } du ( + ) 0 u 1 p 1 p pass: s 1 Since at stage the consumer has searched firm 1, she is certain about her payoff if she buys from firm 1. She also knows that Pr( u 1 = u ) = q and Pr( u 1 u ) = 1 q so that she forms her expected value from purchasing at firm as the weighted average from her known reservation price at firm 1 and her prior expected reservation price at firm. If the consumer decides to do a stage search for her reservation price at firm she has to pay s in addition to the search cost s 1 already incurred. 8 Throughout this paper and without loss of generality I will assume that if there is search at all, firm 1 will be the first firm to be searched

16 With probability q (when u 1 = u ) the benefit of her stage 3 decision is the maximum of passing, buying at firm 1, and buying at firm, where the payoffs of each decision are already known. With probability ( 1 q) (when u 1 u ) her expected utility is the expected value of each choice for those values of u for which the respective choice is optimal. In stage 1 the consumer only knows the distribution of her reservation prices but not their realizations. Her expected payoffs at this stage are: Table 5: Expected consumer utilities in stage 1 Action buy at firm i: search at firm i s i + E ui max 0 u i p i Expected utility 1 0 u i du i,, qu i + ( 1 q) u j du j p j, p i 1 0 s j + q max 0 u i p i ( ) u i p i + p j {,, u i p j } + ( 1 q) 1 max { 0, u i p } du i + max{ 0, u j j p j } du j 0 ( u i p i + p j ) pass: 0 If a consumer decides to buy without any search, her expected utility from the purchase is just her expected reservation price (i.e. utility will be 0. ) minus the purchase price. If she decides not to purchase at all her The interesting case occurs if the consumer decides to search at one of the firms. She then incurs search cost and gains the option in stage to choose between passing, buying at firm i under full knowledge of her reservation price, buying at firm j under partial knowledge of her reservation price u j s i 1, or continuing to search at firm j. The firms have two choice variables, price and search cost. I will look at two versions of the game. In one game I assume that firms set search cost and prices sequentially and know each other s search cost at the time they compete in prices. The game is called with commitment since I assume that in the (second step 9 ) price game firms remain committed to the level of search cost that they chose in the 9 In this paper stage refers to consumers decision tree and step to the overall game

17 first step. In the game without commitment I assume that firms set search cost and prices simultaneously (or if they set them sequentially are not able to commit to first step search cost). In the game with commitment, firms equilibrium choices must satisfy: nd step: p i = argmax( p i c)d i ( p i, s i, p j, s j ) i (3) p i 1st step: s i = argmax( p * i ( s i, s j ) c)d i ( p * i ( s i, s j ), p * j ( s i, s j ) ) i (4) s i In the game without commitment firms equilibrium choices must satisfy: p i = max( p i c)d i ( p i, s i, p j, s j ) p i s i = max( p i c)d i ( p i, s i, p j, s j ) s i i (5) As in the monopoly case c stands for marginal cost and D i ( ) is demand for firm i s product. For different prices and search costs there are many different forms that firms demands can take; I will therefore refrain from specifying fully contingent demands at this point but refer the reader to the appendix. 3. Solution In this section I first comment on a crucial aspect of consumer demand and then present the results of competition with and without commitment Characteristics of consumer demand From the expected utilities in table 3 on page 11 through table 5 on page 1 we can derive a best response of consumers at each stage of the game and hence derive consumer demand for each pair of price and search cost. A familiar result from the industrial organization literature is that if firms compete on the basis of price alone, demand will be discrete; i.e., all consumers will buy from the firm with the lowest price. This is undesirable for firms because it leads to a result of marginal cost pricing and zero profits (Bertrand equilibrium). In much of the literature, this result is avoided by distributing consumers along a Hotelling line and positioning firms away from each other geographically or in product space. This dif

18 ferentiation makes the goods no longer perfect substitutes if their locations are different, and demand becomes continuous in price. The model in this paper has a similar outcome, but it is a result of the information structure. If there were no search, demand would be discrete in the first stage of the game, in which consumers willingness to pay at both firms are unknown and the only information available is price. However, as consumers realize the outcomes of search, they formulate their utilities as conditional expected values which are continuous in price, which implies that demand is continuous in price. Suppose for a moment that consumers had to decide between purchasing at firms 1and in stage 1. Their expected utilities from purchases at firm 1 and firm are 1 p 1 and 1 p respectively. Irrespective of their true reservation price (because it is unknown to them at this stage) consumers will choose to purchase from the firm with the lower price, meaning that the firm with the lower price will get the entire demand. This is the classic Bertrand result. Now suppose that consumers have searched for firm 1 s product and are consequently at stage. Consumers now know their reservation price at firm 1 and know that their reservation price at firm corresponds to that at firm 1 with probability q. A consumer s utility from buying at firm 1 thus is u 1 p 1 and the expected utility from buying at firm is qu 1 + ( 1 q)1 p. This means that buying at firm 1 is preferred to buying at firm for u 1 p 1 > qu 1 + ( 1 q)1 p, or after solving for u 1, u 1 > 1 ( p 1 p ) ( 1 q). Since the proportion of realizations of u 1 that fall above 1 ( p 1 p ) ( 1 q) will change continuously with p 1 and p, demand is now a continuous function of prices. Suppose finally that consumers decide to continue searching. At stage 3 they know both reservation prices, u 1 and u. A portion q of consumers find that u 1 = u, the rest will find that u 1 u. Those consumers with identical reservation prices across firms will buy from the firm with the lower price. Consumers with different reservation prices will buy at firm 1 as long as u 1 p 1 u p u 1 u p + p 1. Overall, the firms demand will be continuous where p i > p j (because the demand for 1 q of the consumers is continuous in price), with a discrete jump at p 1 = p (because the q consumers with equal reservation prices switch firms at this price). 3.. Competition with commitment In the two-step game in which firms face the demands I sketched out above, firms first set search cost and then compete in prices. I solve for a subgame perfect equilibrium in the standard way: I first cal

19 culate the second step price equilibrium ( p * 1 ( s 1, s ), p * ( s 1, s )) calculate equilibrium search cost ( s * 1, s* ). Define the following prices: as a function of search cost and then p* 1 = ( 8+ 16c( 1 q) + q( 47 ( q)q 31) +[ 4+ 16c ( 1 q) 4 + 8c( 1 q) ( q( 11 + ( 5 + q)q) 1) + q( 8 + q( 5+ 4q( 4 + q( 5+ ( 4+ q)q) )))] 1 / ( 4( 1 q) ) p* = ( + 4c( 1 q) + q( 13 ( 5+ q)q) +[ 4+ 16c ( 1 q) 4 + 8c( 1 q) ( q( 11 + ( 5 + q)q) 1) + q( 8 + q( 5+ 4q( 4 + q( 5+ ( 4+ q)q) )))] 1 / ( 1( 1 q) ) (6) (7) I can now state the main result of this section: Proposition : There exist parameters perfect equilibrium. cq, for which the following characterize a subgame Firms: firm 1 charges a higher price than firm, p* 1 > p*, but sets lower search cost, s* ( 1 q) 1 = 0 < ( 1 p*. Both firms make positive profits. ) = s* Π 1, Π > 0 Consumers: Stage 1: all consumers search firm 1. 1 p* Stage : consumers with u 1 such that 1 u p* buy at firm 1, q 1 p* consumers with u 1 such that -- 1 p* 1 1 p* > u buy at firm, 1 q q 1 1 p* consumers with u 1 such that > u search at firm, q 1 0 no consumers pass. Hence there is positive demand for firm 1 and firm. No consumers pass at stage, but all who did not buy from firm 1 or firm continue searching at firm. Stage 3: consumers with u such that 1 u p* buy at firm, consumers with u such that p* > u 0 pass, no consumers buy at firm 1. Hence there is positive demand for firm and no demand for firm 1 at this stage. Proof of proposition : see appendix

20 The significance of this proposition is that firms can use search cost strategically in order to soften price competition; this result depends fundamentally on firms ability to commit to different levels of search cost before they compete in prices. In equilibrium one firm will make search easy but charge a higher price and the other firm will make search costly but offer a lower price. The intuition behind this proposition is as follows. In equilibrium, firm 1 makes search costless. As a consequence all consumers will choose to begin by searching firm Consumers with high will choose to buy at firm 1 and those with lower reservation prices will consider buying at firm. For consumers with the lowest reservation prices, it is better to pass altogether than to buy at either firm; however, the search cost that firm sets is chosen so that those consumers who prefer passing to buying at either firm are indifferent between passing and searching at firm. For these consumers the expected value of search is 0, and thus they are just willing to continue to search at firm instead of passing. This way all consumers who might have left the market in stage now search for their reservation prices at firm ; for some of them it will then be beneficial to purchase at firm. Since the expected value of searching at firm is weakly lower than that of buying at firm 1 for u 1 p 1, any consumer for whom u 1 p 1 will have purchased already at stage ; firm 1 sells to no additional consumers in stage 3. Why don t firms 1 and have an incentive to deviate? Fix firm 1 s search cost at s 1 = 0 and consider first firm. If firm sets higher search cost, those consumers that now buy from either firm at stage are unaffected. Only those consumers that so far continued searching (and of whom some then bought at firm ) will now cease searching and pass at stage. Clearly, firm cannot gain from such a deviation. Suppose now that firm lowers search cost. Initially consumers who bought in stage from firm 1 are unaffected (i.e. they prefer buying from firm 1 to searching at firm ). However, some of the consumers that so far bought at firm in stage are added to the searchers. Allowing these consumers to get informed about their reservation prices can only hurt firm because some will detect that they should not buy (although they would have bought if they had not been given the information). As firm lowers search cost further some consumers that so far bought at firm 1 will also begin to search. In stage 3 some of these consumers will buy from firm 1 but also some from firm. Although firm gets some consumers that had been buying at firm 1, this does not make up for the loss in demand from those consumers that formerly bought at firm and now search instead. u 1 10 Actually there is a whole interval of search cost s 1 that would sustain the equilibrium. I only require that s 1 is low enough that all consumers search firm 1 in stage

21 At very low search cost and under the assumption that firm charges the lower price, there is a large portion of consumers from both segments who have searched both firms and have found that they have the same reservation prices at both firms. These consumers will buy at whichever firm offers the lower price. This creates an incentive for firm 1 to undercut by ε and capture these consumers. no consumers will search and a change in s Analogous to the familiar result from the sales promotion literature, this case has no equilibrium in pure strategies (see for example Varian 1980 and Narasimhan 1988). It becomes clear from this discussion that the existence of a portion of fully informed consumers that considers the goods of competing firms to be of equal value is crucial to the results of this paper. 11 Now fix s = ( 1 q) ( 1 p ) and consider firm 1 s incentives to deviate. Demand is discrete in s 1 (in contrast to s ) since s 1 influences consumers first stage decision, which is a decision made before any individuals know their reservation prices. Thus in response to a given s1, either all or all consumers. Recall that in equilibrium all consumers search. If s 1 will either have no effect, or will change the behavior of is high enough to impede consumers search, but is still below firm s search cost, consumers don t know their reservation prices at either firm because firm s search cost also discourages first stage search. As discussed at the beginning of section 3..1 consumers will all choose to purchase from the firm with the lower price. This will result in Bertrand competition and zero profits. Firm 1 thus also has no incentive to deviate. If firm 1 impedes search, but consumers are willing to search at firm in stage 1, it is similar to firms 1 and swapping equilibrium roles. Since firm s profits in equilibrium are lower than firm 1 s profits, firm 1 has no incentive to reverse roles with firm. It is important to note that prices as well as search costs in this model do not convey any information about product quality. Consumers uncertainty about their willingness to pay for firms products comes from uncertainty about what product characteristics mean to them, not from uncertainty about the quality of the product. Since a consumer s willingness to pay in this model is uncorrelated with the willingness to pay of other consumers, a price or a level of search costs can t signal to a consumer whether she will have a high or low willingness to pay for a firm s product. p s1 11 If q = 0 the strategies proposed in proposition are not an equilibrium. Instead, both firms set very low search costs. This corresponds to modeling products for which more information does not decrease the perceived differentiation between products. As I mention in the introduction the results of this paper only apply to those product classes for which this assumption is satisfied

22 3..3 Competition without commitment In contrast to competition with commitment, now suppose firms simultaneously choose search cost and prices. This enhances firm j s ability to deviate from any price equilibrium derived under the assumption of a particular ( s i, s j ) : Proposition 3: The equilibrium proposed in proposition cannot be sustained if firms choose search cost and prices simultaneously or if they are not able to commit to first step search cost. Instead, for the parameters of proposition there will not exist an equilibrium in pure strategies. Proof of proposition 3: see appendix Recall that the price equilibrium in proposition with could be sustained because consumers partial information in stage led demand to be continuous in ( p 1, p ). Firm 1 was not interested in undercutting firm s price by ε because the potential gain in demand was minimal and firm s choice in price was optimal given that its search cost was. If however, firm were able to change the information structure of consumers and inform them of their reservation prices, there would suddenly be a large proportion of consumers that knew that their reservation prices at both firms were identical and who then would choose the firm with the lower price, namely firm. We would then be at a situation where s 1 = s = 0 p* 1 > p* s * and firms mix over prices. 4 Discussion I can summarize the main results of the paper as follows. First, firms in competition as long as they can commit to maintain search cost unchanged in response to a competitor s price can make use of search cost in order to differentiate themselves and thus ease price competition. This can lead to a situation where one firm offers a high price but makes search easy while the other firm prevents most consumers from searching but offers a lower price. Second, this result does not hold if firms cannot commit to maintain search costs constant while they compete in prices. In such a case, firms simply use consumer search cost as one more variable with which they can compete. Third, in certain situations a firm does not choose to facilitate consumer search, even if providing information to consumers is completely costless. The firm thereby induces consumers to buy based on expected value rather than to search

23 From these results it becomes clear that the principal use of consumer search cost as a strategic variable varies by market structure as summarized in table 6. Table 6: The role of search cost Market Structure Monopoly Competition with commitment Competition, without commitment Role of search cost Prevent low types from identifying themselves Ease price competition Compete on a second dimension In a monopoly consumer search cost enhances the monopoly power of the firm by fine tuning the information of each consumer segment. If consumer search costs are stickier than prices, i.e. if firms can change prices more frequently than they can change consumer search costs, they can make use of search costs to differentiate themselves so that price competition becomes less severe. If firms can change search costs as frequently as prices, we have simply introduced another variable with which they can compete in Bertrand competition. Note that we obtain positive profits in the equilibrium with commitment without resorting to a Hotelling-type structure to avoid Bertrand competition through product or geographic differentiation (see for example Hotelling 199, D Aspremont et al. 1979, Moorthy 1988). Other than the fact that for some consumers reservation prices are independently distributed, in my model both firms distinguish themselves only by their strategic variables. We can find a similar structure in Kreps and Scheinkman (1983), which shows that a Cournot outcome results from price competition if firms have quantity constraints. In their model, firms commit to a maximum level of production quantity and thereby prevent one firm from serving the entire market. This leads to prices above marginal cost and positive profits. The search model in this paper differs from traditional search models in which consumers search for price (see for example Diamond 1971 and Rothschild 1974) by more than the strategic nature of firms decisions on search cost. In most traditional search models consumers basic problem consists of trading off the search cost associated with visiting an additional firm against a potentially better price they might find at that firm. The models assume that consumers have no uncertainty about their valuation for products but face price uncertainty. My model, in contrast, assumes that consumers have knowledge about prices but are uncertain about their valuations for products. While these might seem dual problems at first sight, there is a fundamental difference. I assume that consumers have the option

24 of purchasing a product for which they have uncertain valuation. In traditional search models consumers cannot purchase a product whose price they don t know. This distinction reflects that consumers frequently make purchase decisions with product uncertainty, but almost never without price information at the time of a purchase transaction. Since most of my results rely on consumers trade-off between purchasing a product with uncertain value versus searching, my formulation of consumer uncertainty as uncertainty of valuation for a product and not the product s price is crucial. The results of this paper bear resemblance to those from models of vertical differentiation. In these models firms mitigate price competition by differentiating on a product or service dimension along which consumers willingness to pay differs. For example, in traditional models of dual distribution, firms differentiate by creating high and low service stores. Since consumers with a higher willingness to pay typically have a higher valuation for service they self-select into stores with high service and higher prices. Consumers with low willingness to pay choose stores with low service and lower prices. Based on an analogous argument, Gerstner, Hess, and Chu (1993) present a result that shows that sellers may profit from differentiation by introducing product features that are meaningless and even detrimental to consumer welfare, and Chu, Gerstner, and Hess (1995) demonstrate that firms can soften price competition by differentiating selling styles. In all of these models the existing heterogeneity of consumers is exploited to soften price competition. This paper, in contrast, shows how firms can use search costs to manipulate consumers valuations in order to create consumer heterogeneity from consumers with ex-ante homogeneous valuations. Different search costs do not segment consumers because their disutility of search differs, but because asymmetric information regarding their valuation for the products of competing firms leads to maximally heterogeneous consumer valuations and hence to less price competition between firms. A model of vertical differentiation along search costs predicts that consumers that search at low search cost firms have a disutility of search that is systematically higher than consumers that search at high search cost firms. My model predicts that firms have an incentive to differentiate, even if consumers disutility of search does not vary across consumers that search at one or the other firm. Limitations A number of assumptions in this paper clearly ignore factors that can affect a firm s decision to provide information in the real world. First, firms are commonly differentiated along some dimension such as product quality, service, or location, second, consumers often have the wrong expectations about the - 0 -

25 utility they will derive from a firm s product, and third, it can be very costly for firms to make it easy for consumers to determine their reservation prices. If firms are differentiated along product quality, service, or location, there are cases in which firms no longer have an incentive to differentiate themselves through search costs. However, the results of this paper will continue to hold as long as, at some particular set of prices, a discrete portion of consumers that have either no or full information are indifferent between competing firms products and those prices are near the firms equilibrium prices. If consumers have the wrong expectations regarding their reservation prices, firms have incentives to withhold or reveal information. A firm for whom consumers have average posteriors that surpass their priors will have an incentive to facilitate consumer search, a firm with lower average posterior reservation prices than priors will have an incentive to withhold information from consumers. Firms ultimate choice depends on the relative magnitude of incentives stemming from incorrect priors and the competitive effect that comes from having informed or uninformed consumers. By assuming that priors are consistent with posteriors this paper has shown that firms might have incentives to withhold information from consumers, even if they have nothing to hide. Finally, if reducing search cost is costly to a firm, this will reduce its incentives to facilitate consumer search. The model in this paper assumes that the reduction of consumer search cost is costless to the firm. The purpose of this assumption is to isolate reasons other than costs for why firms might not want to facilitate consumer search. The assumption is biased against my results, i.e. if my results hold under the assumption of no cost to the firm, they will also hold if it is costly for firms to lower consumer search cost. This paper show that there exist regions of the parameter space for which firms have incentives to withhold information. The results do not, however, indicate how relevant these regions are in practice. The importance of these regions are an empirical question. It is a standard argument that a firm s ability to capitalize on selling to consumers that don t find it worthwhile to return products (as happens to some consumers in my models) is limited by repeat purchasing or competitive pressure (see Wernerfelt, 1994b). However, there are circumstances under which firms can sustain strategies in which they sell to consumers that would not have bought if they had searched. For example, turnover of consumers in the market will lead to some consumers that are uninformed. Long purchase intervals and consequently forgetful consumers might also lead to uninformed consumers. Consumers might have gone through changes in taste or new models of a product - 1 -