Some Implications of Search Costs for the Price Dynamics of Electronic Markets

Transcription

1 Some Implications of Searc Costs for te Price Dynamics of Electronic Markets Pedro Pereira Autoridade da Concorrência, R. Laura Alves, nº4, 7º, Lisboa, Portugal pone: ; fax: May 004 Abstract: Tis paper develops a model based on switcing costs and tecnological uncertainty, wic explains some aspects of te price dynamics of e-commerce. Switcing costs and intertemporal cost correlation lock-in consumers. Firms initially carge low prices to build a customer base. If firms fail to reduce costs, and reservations prices are low, firms exit te industry. Over time, prices increase if no exit occurs, and decrease if exit occurs. Prices may also decrease over time, if te proportion of low searc cost consumers increases. Key Words: E-Commerce, Searc, Switcing Costs, Learning, Industry Evolution JEL Classification: D43, D83, L, L3, L8, O3, O33 I tank anonymous referees for useful comments.

2 Introduction. Te Recent Evolution of Electronic Commerce In tis sub-section, I review te recent evolution of electronic commerce. Te Internet allowed te creation of a new retailing tecnology: electronic commerce. Initially, te creation of new markets suggested a big growt potential. Between January 998 and July 000, venture capital invested $65 billion in Internet companies (Fortune, October 30, 000. In 999, Internet firms carried out 55% of te initial public offerings. And during 999 and 000, first-day returns on initial public offerings for Internet firms averaged 88%, wereas first-day returns on initial public offerings averaged 7% in 996, 69% in 999, and 56% in 000 (Ljungqvist & Wilelm (00. Between June 998 and July 999, firms tat canged teir names to Internet related dotcom names, ad cumulative abnormal returns of 74% on teir stock valuation (Cooper, Dimitrov & Rau (00. But in spite of all tis investment euporia, firms ad small revenues. One reason was tat firms deliberately carged very low prices. Tis beavior was justified as an investment in consumer acquisition (Hoffman & Novak (000 and Reiceld & Scefter (000. Watever consumer acquisition means, it suggests te existence of consumer inertia or switcing costs. 3 Most notable was te general assumption tat te deployment of te Internet would increase switcing costs and create strong network effects, wic would provide first-movers wit competitive advantages and robust profitability, Porter (00, p. 68. [Amazon] sells music CD s at an average price of $.99 wile incurring costs of $4 per unit. ( But tere was a rationale: build a customer base of loyal site users and profitability will follow, Rayport (999. Lieberman (00 using data from early 999 to September 00, for 06 publicly traded firms, in 46 Internet markets, found tat early entrants in te market maker and broker segments, or wit patented innovations, earned a premium on teir stock market valuation, relative to teir peers. He was unable to develop direct measures of switcing costs. But Cen & Hitt (00 report evidence of switcing costs for te broker segment, discussed in sub-section.. [Insert Figure ere] After te fall of te NASDAQ in April 000, capital markets closed for most Internet companies, wic ten faced one of tree options: survive on teir own revenues, often minimal, sell out, or go bankrupt. In eiter case, a wave of consolidation started, and it is expected tat of te large number of entrants, few will survive. In new Trading goods based on te processing and transmission of digitized data over te network of computers tat use te Transmission Control Protocol/Internet Protocol. 3 A switcing cost is a one-time product specific cost, a consumer must bear in order to consume a product, e.g., learning to use a word processor, or finding a new store.

3 3 industries, a build up in te number of firms followed by a sakeout is a well-documented penomenon (Gort & Klepper (98 and Klepper & Graddy (990. Geroski (995 conjectured tat te likeliood of firm survival is lower, in industries in wic te innovative opportunities available to small firms are large. Audretsc (995 provides evidence tat supports tis ypotesis. Internet tecnologies allow firms to operate on a small scale, due to teir modularity, and offer many innovation opportunities. Tis suggests a severe sakeout. 4 In fact, according to Webmergers.com, between January 000 and February 00, 804 Internet companies sut down or declared bankruptcy (Figure. And between January 00 and April 00, about $43 billion were spent to buy more tan,600 firms. Bugin (00 using data from mid 00, of worldwide Internet retailing firms, reports te following: (i about 0% of firms were profitable, (ii te average profitable firm ad a profit margin of 30%, (iii te average non-profitable firm ad a profit margin of 40%, and (iv te bottom alf of non-profitable firms reaced profit margins of 0%. Since tese firms also ad a low and declining conversion of online visitors to customers, it is unlikely tat tey will ever be profitable. It is premature to know te intertemporal profile of prices online, or to infer its causes. Price dynamics will certainly vary across industries. However, some evidence starts to emerge. Kwak (00 reports tat online book prices, decreased between te spring and fall of 999, were flat for several monts, and started to increase in 000, wen Amazon raised prices by 0-0%. Clay et al. (00 also report an upward trend for prices of online books. Brown & Goolsbee (00 found tat te spread in Internet use decreased te price of term life insurance by 8 5%, after price-comparison searc engines were introduced, and for insurance types covered by te searc engines.. Te Building Blocks: Switcing Costs and Tecnological Uncertainty In tis sub-section I discus te building blocks of te paper. I develop a model to explain some aspects of te price dynamics of electronic commerce. Te model as two pases. 5 First, a pase in wic te product is introduced, firms experiment wit te new tecnology, consumers try to locate a low cost firm taking into account future purcases, and tere is intense price competition. And second, a 4 An industry sakeout consists in a joint: (i decrease in te number of firms, (ii increase in total output, and (iii decrease in prices. Klepper & Miller (995 sowed tat during teir early evolution, new industries commonly experience a sakeout period, during wic te number of producers declines by 50%, and in extreme cases by 80%, in ten to fifteen years. Te automobile industry in te United States started in 894 wit 4 producers (Klepper & Simons (997. Te number of firms increased to 74 in 909, fell to by 98, and fell to 7 by 955. Entry was concentrated in te years preceding te peak, wit 490 entrants before 909, and 33 entrants after Klepper & Graddy (990 argue tat te istory of a product can be divided into tree stages. In te first stage te number of firms in te industry grows. In te second stage tere is a decline in te number of firms. In te tird stage te number of firms stabilizes.

4 4 pase in wic firms learn teir true cost, and tere is possibly a sakeout. Te two building blocks of tis process are: (i switcing costs, and (ii tecnological uncertainty. Since tere are switcing costs tat lock in consumers, firms are prepared to initially carge low prices to build a customer base for te future, were tey ope to ave low costs. 6 If owever firms fail to reduce costs, tey exit te industry. Over time, prices increase if no exit occurs, and decrease if exit occurs. Prices may also decrease over time, if te proportion of low searc cost consumers increases. Regarding switcing costs, electronic commerce reduces searc and switcing costs compared wit pysical sop retailing, but it does not eliminate tem. Browsing Web sites is not costless, and it is easier to learn te current price of a previous supplier, tan te price of anoter firm. Soppers can bookmark te site of teir previous supplier, or can be ed price updates by teir current vendor, wile tey ave to searc to learn te price of a new supplier. Opening an account wit a Web mercant, or learning ow to use its website, also creates switcing costs. It is revealing tat Amazon tried to patent te -Click-Sopping. 7 An emerging empirical literature supports tis perspective. Hong & Scum (00 using data collected from Pricescan.com for electronics and books, estimate for several model specifications, median searc costs tat range from 3% to 40% of te median observed price. Consider for example a Palm Pilot Vx. Te median observed price was $99, and te median estimated searc cost was $5.03, for one of te model specifications. Te average ourly wage for an engineer was $8.97 in Cen & Hitt (00 using data provided by MediaMetrix from July 999 to June 000, on te eleven largest retail brokers, report evidence on switcing costs for te online brokerage industry. 9 6 Clay et al. (00 report tat on April 999 some lowest priced firms may ave carged prices close to cost. Sopping.com and books.com offered discounts of 40% on bot ardcover and paperback bestsellers. 7 Te -Click-Sopping ordering system allowed clients to sop witout reentering teir sipping and billing information every time tey purcased from te firm. Amazon was awarded US patent 5,960,4 for te -Click-Sopping tecnology on September 9, 999. On October, 999, Amazon filled a patent-infringement suit against Barnes&Noble.com alleging tat it willfully infringed of te -Click-Sopping ordering system, wit its Express Lane ordering system. In December 999, a Federal District Court in Seattle granted an injunctive relief barring Barnes&Noble.com from using te Express Lane ordering system. In February 00 a Federal Appeals Court in Wasington overturned te preliminary injunction until a trial, sceduled for September 00, took place. In Marc 00, Amazon announced it ad settled te case wit Barnes&Noble. 8 According to te National Compensation Survey collected by te Bureau of Labor Statistics 9 Oter studies present evidence of consumer inertia or loyalty online. (i Hann & Terwiesc (000 use data from a German online reverse buying retailer, similar to Priceline.com, wic owever allows consumers to increase teir bid if teir earlier bid as failed. By increasing teir bid by cent in eac consecutive round, consumers can identify te minimum price for wic te seller is willing to sell, at te cost of incurring te utility loss of placing additional bids. Tey estimate tat consumers placing bids for PDAs prefer paying an average of 5.5, over keying in an extra bid. (ii Smit & Brynjolfsson (00 documented te importance of brand, for omogeneous products, and among users of pricecomparison searc engines, wo are presumably te most price sensitive consumers online. Using data for searces for books conducted at Dealtime.com in late 999, tey report tat wile price is te strongest predictor of customer coice, only 49% of customers coose te lowest priced vendor. Among consumers wo do not coose te lowest priced offer, te average selected offer was 0% iger tan te lowest priced offer. Consumers were willing to pay 5% more to purcase from Amazon, rater tan from te lowest priced vendor, and 3% more to purcase from Barnes & Noble or Borders. (iii In Brynjolfsson & Smit (000, te autors use a cookie number to track te loyalty of customers to retailers tey ad selected on previous visits. Tey find tat retailers wo were selected on a previous visit by a particular customer old a 7% price advantage over oter retailers on subsequent visits by tat customer. (iv Jonson et al. (00 using data from Media Metrix from July 997 troug June 998, report tat 70% of CD soppers, 70% of te book

5 5 Regarding tecnological uncertainty, electronic commerce allows cost savings compared to pysical sop retailing. Tese cost savings vary across industries, and conceivably are more relevant for digital goods. 0 But since te tecnology is new, acieving tese cost reductions is uncertain, and firms only learn over time, by producing, if tey succeeded or not. Te creation of a new production process involves a process of experimentation, learning, and failure. To learn teir true cost function, firms ave to experiment wit different bundles of production factors, to identify wic are efficient. Tis process of trial and error requires time (Ericsson & Pakes (995, Hopenayn (99, Jovanovic (98, Klepper & Graddy (990, Lippman & Rumelt (98, and Zeira (987. In line wit tis perspective, Bugin (00 reports tat for is dataset, te number of customers and revenue per customer was not statistically significantly different between profitable and unprofitable firms. However, te cost per customer was statistically significantly different, and four times lower for profitable firms tan for unprofitable firms. Altoug te classical example of te electric dynamo refers to a general-purpose tecnology, rater tan to a consumer product, it illustrates te process of learning ow to use a new tecnology (David (990. Te deployment of electricity started by te 890s, but its impact on productivity was negligible until te 90s. Initially firms replaced te power source, but left te way production was organized uncanged. But by taking advantage of te new tecnology s caracteristics, production could be reorganized in more flexible and productive ways. It took several years and experiments to discover tis..3 Overview of te Paper In tis sub-section I give an overview of te model and te main results. I develop a model related to Benabou (993, Fisman & Rob (995, MacMinn (980, and Reinganum (979, were firms set prices, and consumers searc for prices. Te model was developed aving in mind te price dynamics of e-commerce, and more generally, te price dynamics of retailing industries. soppers, and 4% of te travel soppers, were observed as being loyal to just one site troug te duration of te is data. On average, ouseolds tat browsed a category, visited only. book sites,. CD sites, and.8 travel sites. 0 Digital goods are products tat can be stored and transmitted as zeros and ones. Initially, firms only replaced steam or water powered motors by electric motors. Tis allowed fuel savings and improved macine speed control. However, instead of a primary motor turning separate safting sections and driving related groups of macines, individual electric motors could be used to run macines of all sizes. Furtermore, electric wires could replace power transmission troug safts and belts. Te reduction of friction in transmission allowed furter fuel savings. Factories could also be redesigned, wit ligter single-story structures replacing costly multistory structures. Tis allowed savings in fixed capital. But more importantly, single-story, linear factory layouts, allowed a reconfiguration of materials andling, of macine placement, and of andling equipment. Tese canges in product and process design were te largest source of te productivity gains. See Goldfarb (00 for an alternative perspective.

6 6 Firms ave different marginal costs, wic may cange over time. Initial low costs elp predict future low costs, and ig costs may lead to exit. Tese assumptions about costs are intended to reflect te stocastic learning about te new tecnology. However, tey agree wit stylized facts on intra-industry microeconomic dynamics. Foster et al. (000 using U.S. data from te manufacturing sector from 977 to 99, and from some service sector industries from 987 to 99, report tat: (i tere are large and persistent differences in productivity levels across firms, and (ii low, firm specific productivity levels, elp predict exit. In te model, since searc is costly, consumers accept prices above te minimum carged in te market. Tis gives firms market power. 3 Switcing costs lock in consumers to teir period suppliers. And since production costs in period are positively correlated wit production costs in period, in period consumers conduct a more toroug searc tan tey would for a single purcase, i.e., in period tey old a lower reservation price tan in te period. Low cost firms carge te lowest price. Tus, tey are not constrained by consumer searc, and carge teir monopoly price. Hig cost firms may also benefit from te market power generated by costly searc. If te consumers reservation price is iger tan teir marginal cost, tey carge te reservation price. If te reservation price is lower tan teir marginal cost, in period tey exit te industry. But in period, due to te lock-in effect, tey remain active to secure a larger consumer sare in period. Over time, prices increase if no exit occurs, and decrease if exit occurs. Wen consumers are eterogeneous wit respect to te searc cost, prices may also decrease over time, if te proportion of low searc cost consumers increases. Exit is also associated wit: (i an increase of bot te output per firm, and te industry output, and (ii a decrease of te industry average price. Tese last predictions are in line wit evidence on te evolutionary trends of industry variables, reported by Agarwal (998. My results contrast wit te switcing costs literature (Farrell & Klemperer (00 for tree reasons. First, altoug consumers ave switcing costs, prices need not increase over time. Second, if prices do increase, it is not because firms exploit locked-in consumers, but because te consumers reservation prices increase over time. In te switcing costs literature consumers are perfectly informed of prices, and reservation prices are exogenous. Initial Te model is intended to apply to te retail industry. I use te manufacturing industry as an example due to data availability.

7 7 price lure consumers. And after consumers are locked-in, firms increase prices. In my model consumers are imperfectly informed about prices. Initial prices cuts occur, because initially consumers conduct a more toroug searc and old a low reservation price, wic forces prices down. As te consumers reservation prices increase over time, firms tat are constrained by consumer searc are able to raise teir prices. Price movements are driven by endogenous canges in te reservation price. And tird, intertemporal cost correlation alone locks-in consumers, and leads to price cuts followed by price ikes. If production costs are positively correlated, finding a low cost firm in period is valuable for bot periods, even if tere are no switcing costs. Tus, consumers old a lower reservation price in period tan in period, wic leads to prices increasing over time. Tis paper s results about some implications of searc and switcing costs for price dynamics of electronic markets, are derived in a context were firms may exit te industry, i.e., in a context were a sakeout may occur. But, to be sure, te paper is not intended to explain te process tat generates te sakeout. Rater, te paper explains te underlying price dynamics, and in a way oter papers fail to do so, namely tose associated wit te switcing costs literature. I also discuss four generalization of te model. I consider: (i consumer eterogeneity, (ii cost reducing investment, (iii entry, and (iv pases of unequal lengt. Section presents te model, and section 3 caracterizes its equilibria. Section 4 conducts te analysis. Section 5 discusses generalizations, and section 6 concludes. Proofs are in te appendix. Te Model In tis section I present te model, wic is simple to ligten te exposition. In section 5 I discuss 3 generalizations: (i consumer eterogeneity, (ii cost reducing investment, (iii entry, and (iv pases of unequal lengt.. Te Setting Consider a market for a perisable, omogeneous good, tat opens periods. Subscript t refers to time. Eac of te game s periods consists of stages. Eac period, in stage firms coose prices, and in stage consumers searc for prices. Ten agents receive teir period payoffs. 3 Market power is te ability to raise price above marginal cost.

8 . Consumers Tere is a unit measure continuum of risk neutral, identical consumers. A consumer wo buys at price p on + R 0 demands D(p, were D(. is a twice differentiable, bounded function, wit a bounded inverse, and decreasing for p on [ 0,D ( 0 ]. Denote by S(p: = + D(xdx, te surplus of a consumer wo pays p. p 8 Consumers do not know te prices carged by individual firms. However, tey old common beliefs about te price distribution. Cumulative distribution function, F t (., gives te consumers' beliefs about te period t price distribution; te lowest and igest prices on its support are p and t Consumers searc sequentially wit recall, and ave a constant marginal searc cost, σ > 0. 4 Witin eac period, searc is instantaneous, and consumers may observe any number of prices. Consumers pick randomly wic firm to sample, from te set of firms wose price tey do not know. In period, consumers learn for free only te period price of teir period supplier. Tis creates a switcing cost, equal to te expected searc expenditure. In sub-section 3.3 I weaken tis assumption. Tis way of modeling switcing costs as attractive features. First searc and switcing costs are related in a natural way. And p t. second, switcing costs, rater tan assumed, are explained by te model. A consumer's information set just after is k-t searc step, consists of all previously observed prices. A consumer s strategy for stage of period t is a stopping rule, s t, tat says if searc sould stop or continue, for every searc cost, beliefs about te price distribution, and sequence of observations. A consumer's payoff is te sum of expected period surpluses, net of te searc expenditure..3 Firms Tere is a unit measure continuum of risk neutral firms. 5 I could add a stage 0, in wic firms decide if tey enter te market for a fixed set-up cost, and normalize te measure of firms tat enter to. In sub-section 5.3 I discuss additional entry in period. My focus is not on entry, but rater on price dynamics and exit. 6 4 Arguably te Internet realizes its full potential to reduce searc costs troug price-comparison searc engines. Searc engines provide a sample of between 0 to 40 prices at a fixed cost, wic is te opportunity cost of te time required to download software, learn to use te searc engine s interface, configure te interface, wait for te data to be downloaded, etc (Pereira (003. Searcing troug searc engines is seemingly inconsistent wit my assumption tat consumers searc sequentially. My point in tis paper is tat low searc costs online lead consumers to only accept low prices, wic in turn forces firms to carge low prices. And tis does not depend on te assumptions about te searc tecnology. Besides, te available evidence does not suggest a widespread use of price-comparison searc engines, at least yet. A Media Metrix study found tat during July 000 less tan 4% of Internet users used a price-comparison searc engine, wile over 67% visited an online retailer (Montgomery et al. (00. And a Jupiter Communications survey found tat 8% of te respondents were unaware of te existence of price-comparison searc engine (Iyer & Pazgal (00.

9 9 [Insert Figure ere] Marginal costs are constant wit respect to te production level, and can be low, c l, or ig, c, were - 0 c < c < D (. In period a firm as a low marginal cost wit probability µ on ( 0,. In period, a firm tat l 0 ad cost c i in period, as cost c s wit probability υ is (i,s=l, (Figure. A period low cost firm is more likely to ave a low cost in period, tan a period ig cost firm, υ l < υ, i.e., costs are positively correlated across periods. Te unconditional probability of a firm aving a low cost in period is: ( l ll + µ cost distribution is te same in bot periods, ( l ll µ υ + υ. I assume tat te ll µ µ = µ υ υ. Every period, eac firm observes only its cost level before coosing its price. To simplify notation, I assume tat te realized value of a random variable equals its expectation. In sub-section 5. I discuss cost reducing investment, and argue tat period low cost firms ave a no smaller incentive to invest in cost reduction, tan period ig cost firms. Tis provides an explanation for positive cost correlation, complementary to te stylized facts on intra-industry microeconomic dynamics, reported by Foster et al. (000. For expository reasons, I assume tat: (i tere are only costs levels, and (ii a simple intertemporal cost correlation structure. Te results of section 4 generalize to a continuum of marginal costs, and to ricer correlation structures, as in Tommasi (994, wit no added economic insigts. Denote by p ti on + R 0, te period t price of a cost i period t per consumer profit of a cost c i firm. Let p := argmax π(p c π c firm, and denote by c := ( p c D(p i p ; i ; (pti i ti i ti, te ; I will refer to p i as firm i s monopoly price. I assume tat π (. is strictly quasi-concave in p. Denote by ϕ, te period t expected consumer sare of a cost c i firm; denote by Π t ( pti; ci : = π ( pti; ci ϕt ( pti, te period t expected profit of a cost c i firm; and denote by V i [ υ Π (p ;c + (p ;c ] : = Π (p ;c + υ Π i i il l l i t (p ti, te sum of te expected period profits of a period cost c i firm. Instead of modeling explicitly te firms entry and exit decisions, I follow an equivalent, but more parsimonious approac, in line wit te literature, e.g., Benabou (993 and MacMinn (980. I assume tat all firms 5 Assuming tat tere are many firms may seem awkward in te context of Industrial Organization. Tis assumption is not essential. Te model can be reinterpreted as a duopoly, at te risk of straining a bit te restrictions on te consumers beliefs required to construct te equilibrium. But te assumption does ave te virtue of making it clear, tat in tis context, costly searc is te source of te firms market power. 6 Audretsc (995 found tat te variance of te survival rates across industries is considerably larger tan te variance of te entry rates across industries. Geroski (995, p. 3 commented tat: Entry appears to be relatively easy, but survival is not. And Klepper & Simons (997 sowed tat in product industries entry nearly stops wit sakeouts.

10 0 are in te industry. However, firms may price temselves in or out of te market. More specifically, a firm may carge a price iger tan te maximum consumers are willing to pay, teir reservation price, in wic case I say tat te firm is inactive; oterwise te firm is active. Wen indifferent between being active and inactive, a firm cooses te latter. Consumers know if a firm is active witout searc, wic seems appropriate for electronic markets. 7 [Insert Figure 3 ere] I assume tat ig cost firms lose money if tey carge p l, i.e., p < c l (Figure 3. One can interpret tis assumption as meaning tat cost eterogeneity among firms is large. In sub-section 3.. I comment tis last assumption. A firm s period t information set, consists of its previous prices, costs, and consumer sare realizations. A firm s stage strategy for period t is a pricing rule, p ti, tat says wic price a firm sould carge, for every possible istory. A firm's payoff is te sum of te expected period profits..4 Equilibrium An equilibrium is: a stopping rule for eac period, consumer beliefs, and a pricing rule for eac period and cost type, { s,f,p t =, ;i l,} t t ti =, suc tat: 8 (E Given σ and F t, consumers coose s t to maximize te net sum of te expected surpluses; (E Given t s and (,υ, µ, firms coose is c i p ti to maximize te sum of te expected period profits; (E3 Beliefs F t agree wit te price distributions induced by ti µ.,υ is p and ( 7 Tus, F gives te consumers beliefs about te prices of active firms. In my approac, assuming tat consumers know wic firms are active, is equivalent to assuming tat consumers know wic firms are in te market, wen te firms entry or exit decisions are modeled explicitly. Te searc literature usually assumes tat consumers: (i know wic firms are active, i.e., wic firms are in te industry, (ii know te price distribution, but (iii don t know te prices of individual firms. Tere is a branc of te searc literature going back to Rotscild (974, were consumers learn troug searc, bot individual prices, and te price distribution. Tis literature addresses different issues from tose addressed in my paper. 8 Te equilibrium concept is related to a sequential equilibrium (Kreps & Wilson's (98, and requires tat te consumers beliefs about te price distribution satisfy (i sequential rationality, and (ii te independent prices conjecture, wic generalize subgame perfection to incomplete information games. Te first restriction implies tat consumers beave optimally, at every information set, given teir beliefs about te firms' strategies. Te second restriction implies tat consumers do not cange teir beliefs upon observing te price of any finite set of firms, and tat on te equilibrium pat, consumers' beliefs agree wit te price distribution induced by te firms pricing strategies. See Bagwell & Ramey (994 and Pereira (00.

11 3 Caracterization of Equilibrium In tis section I construct te equilibrium by working backwards. Te consumers' equilibrium searc beavior consists of olding reservation prices. Low cost firms are always active and carge teir monopoly price. Hig cost firms in te first period are always active; in te second period, sometimes tey are active, and oter times tey are inactive. Wen active, ig cost firms carge te consumers reservation price. 3. Second Period 3.. Second Stage: Te Searc Game In tis sub-section I caracterize te searc equilibrium for period. In period, consumers can eiter accept te offer received for free from teir period supplier, i.e., recall te current offer of teir previous period supplier, or alternatively, incur in te searc cost and visit anoter firm cosen at random. Te consumers optimal strategy consists of visiting first teir period supplier, and olding a reservation price, ρ, wic equates te expected marginal benefit of searc to te searc cost (Benabou (993 or Reinganum (979: 9 ρ p [ p S( ρ ] df ( p = σ S ( ( Tat is, te consumers optimal strategy is to visit first teir period supplier and buy, if and only if, offered a price is no iger tan ρ ; and oterwise, continue to searc. Consumers tat patronized in period a low cost firm, old te same reservation price as consumers tat patronized in period a ig cost firm. Tis occurs because te optimal strategy for sequential searc wit recall is stationary, i.e., it does not depend on te sequence of observed prices (DeGroot (970, Kon & Savell (974, or Yaav (966. Te next Lemma groups results tat will be useful later. 9 Searc occurs if eiter consumers get te first price quote for free, or te searc cost is small enoug. Given sequential rationality (see footnote 8, consumers optimize wit respect to beliefs, wic given te independent prices conjecture, do not depend on observed prices. Tus, te consumers' searc problem can be solved troug dynamic programming. Under my assumptions sequential searc is optimal (Morgan & Manning (985, Prop. 3.

12 Lemma : (i For all strictly positive searc costs, te period reservation price is iger tan te lowest price carged in te market. (ii Te period reservation price is increasing in first-order stocastic dominating sifts of te price distribution. Costly searc, σ > 0, gives firms market power, since it leads consumers to accept prices above te minimum carged in te market, p < ρ. Higer prices decrease te marginal benefit of searc, wic leads consumers to old a iger reservation price. 3.. First Stage: Te Pricing Game In tis sub-section I caracterize te equilibrium prices for period. Denote by n t, te measure of active firms in period t, and denote by C, te measure of consumers searcing in period, i.e., consumers tat in period patronized a firm inactive in period. If a firm carges a price iger tan te period reservation price, it makes no sales; if it carges a price no iger tan te period reservation price, it keeps its period consumers ϕ, and gets an expected consumer sare of C/n. Tus: 0 ϕ( p = ϕ + C / n ρ < p p ρ on Te next Lemma caracterizes te equilibrium prices for period. As mentioned in sub-section.3, I focus ρ < p. 0 Lemma : In period : (i Low cost firms carge teir monopoly price. If te period reservation price is no smaller tan te ig cost level, ig cost firms carge te period reservation price; oterwise, ig cost firms are inactive. (ii If te period reservation price is no smaller tan te ig cost level, ten eac firm s price is p l wit probability µ, and ρ wit probability µ ; if te period reservation price is lower tan te ig cost level, ten eac firm s price is p l : 0 p Or equivalently, I focus on σ on ( 0,σ, were σ is defined by [ S(p S(p ] df σ 0 p (p Te firms consumer sares depend on istory. However, prices are independent of consumer sares, and ence of istory, because marginal costs are constant..

13 3 0 p < p l µ p l p < ρ F p = ( ; ρ ρ p 0 p < p l p l p c ρ ρ < c Low cost firms carge te lowest price. Costly searc, σ > 0, leads consumers to accept prices above te minimum carged in te market, p < ρ. Tus, low cost firms are never constrained by consumer searc and carge teir monopoly price, p l. Due to costly searc, low cost firms gain no additional consumer sare by carging a price lower tan teir monopoly price. And by definition of monopoly price, low cost firms ave no incentive to carge a iger price eiter. Hig cost firms may also benefit from te market power generated by costly searc, by carging a iger price tan low cost firms. Tey are, neverteless, disciplined by consumer searc. If te period reservation price is ig, c ρ, ig cost firms carge te reservation price, ρ. If te period reservation price is low, cost firms are inactive, i.e., carge a price on ( ρ,+ (Figure 4. Since tis is a period model, a firm being inactive in period is equivalent to exiting te industry. ρ < c, ig To ave positive sales, firms ave to carge a price no iger te consumers reservation price. By definition, only firms tat are inactive, i.e., tat exit te industry, fail to do so. Tus, on te equilibrium pat, only consumers tat patronized in period a firm tat exits in period, searc actively. For consumers tat patronized in period a firm active in period, te option to searc serves only as a credible, out of equilibrium treat, constraining ig cost firms pricing beavior. I assumed tat p l < c. Under te alternative assumption tat c pl, ig cost firms are always active in period. Wereas if p l < c, ig cost firms may or may not be active in period, depending on ρ. Tus, case p l < c, considered by Benabou (993 and MacMinn (980, is more encompassing tan te alternative case c p l, considered by Reinganum (979. For some searc cost values, te equilibria for wic ig cost firms are active, overlaps wit te equilibria for wic ig cost firms are inactive, i.e., tere is multiplicity of equilibria. See Pereira (004b.

14 4 From Lemma : n = µυll + ( µ υ l c ρ ρ < c I focus on equilibria in symmetric pure strategies. However, te equilibria described in Lemma are unique for ρ c First Period 3.. Second Stage: Te Searc Game In tis sub-section I caracterize te searc equilibrium for period. Denote by G(p, te period maximum expected surplus, net of searc expenditure, of a consumer wose best available offer in period is p, and beaves optimally. Te next Lemma caracterizes te searc equilibrium for period. Lemma 3: In period, if consumers searc, teir optimal period strategy consists of olding a reservation price, ρ, wic equates te sum of te expected marginal benefit of searc for periods and, to te searc cost: ρ p ρ [ S(p S(ρ ] df (p + [ G(p G(ρ ] df (p =σ ( p Consumers learn for free te period price of teir period supplier. Tus, tey tend to buy at te same firm in bot periods. Wit te prospect of buying twice from te same firm, te consumers period incentives to searc depend on current savings, [ S(ρ ], and also on future savings, [ G( ρ ] S(p G(p. 3.. First Stage: Te Pricing Game In tis sub-section I caracterize equilibrium prices for period. Te period expected consumer sare of a firm tat carges p is: 3 Case ρ <c is obvious. For case ρ <c ρ c, uniqueness follows from te strict quasi-concavity of te profit function, and te independent prices conjecture (see footnote 8. For, tere are two oter types of equilibria. In bot of tese equilibria low cost firms play te same strategy as in Lemma. In one of tese additional equilibria, ig cost firms play asymmetric pure strategies; some firms carge p = c, and oters are inactive. In te oter equilibrium, ig cost firms mix between carging p = c, and being inactive. Since, ˆ ρ, as in Lemma, neiter of te conclusions of section 4 are affected. Te same reasoning applies to te equilibrium of sub-section 3... p = p < l p

15 5 0 ϕ( p = / n ρ < p p ρ To ensure tat ig cost firms are active in period, let: 0 π p,c + v π(p,c / µ. 4 ( l l l l Te next Lemma caracterizes te equilibrium prices for period. Again I focus on ρ < p. Lemma 4: In period : (i Low cost firms carge teir monopoly price. Hig cost firms carge te period reservation price. (ii Eac firm s price is 0 p<pl F (p;ρ = µ pl p<ρ ρ p p l wit probability µ, and ρ wit probability µ : Due to te lock-in effect, even if in period a firm carges a price acceptable to consumers, on te equilibrium pat, it will only sell eiter to its period customers, or to consumers tat are searcing. Tus, wen te period reservation price falls below te ig cost level, ρ <c, a ig cost firm sells below marginal cost in period, but secures a larger consumer sare for period. 5 From Lemma 4 n = and 0 C = µυll ( µ υ l c ρ ρ < c 3.3 Te Equilibrium Reservation Prices In tis sub-section I establis te equilibrium reservation prices. I also relax te assumption tat in period consumers learn for free te current price of teir period supplier. Let: ϖ : = [ ( υll υl ] σ [ ( υll υl µ ] σ c ρ ρ < c 4 If π( p l, c + [ υlπ (p l, c l + ( υl π (p, c ] < 0 a ig cost firm is inactive in period if ρ is low enoug, and tere is a level of ρ, s p, for wic a ig cost firm is indifferent s s between being active and inactive in period. Te analysis of tis paper corresponds to case p ρ. Case ρ < p allows more intertemporal profiles, but adds no economic insigts. 5 Hig cost firms can price below marginal cost in period, and by doing so, earn iger profits in period. Tis is not predatory pricing (Areeda & Turner (975. Te purpose of period ig cost firms is not to expel rivals, but to build a customer base for period, wic is necessary, since consumers do not move freely between firms.

16 Te next Lemma uses Lemmas and 4 to restate te equilibrium conditions for te reservation prices in a more useful way. 6 Lemma 5: Te period and period equilibrium reservation prices are determined by, respectively: µ [ S(pl S(ρ ] [ S(p S(ρ ] l µ l ϖ σ= 0 σ= 0 [ S(p S(ρ ] 0 = c ρ ρ < c (4 (5 σ r Denote by σ r, te cost of a consumer learning te period price of its period supplier. I assumed tat = 0. Next I relax tis assumption. Let: υil /µ α i : = µ + υil c ρ ρ < c Te next Lemma identifies te searc cost values for wic te lock in effect olds. Lemma 6: If σ belongs to [, αiσ] r 0, ten clients of a period cost c i firm are better off visiting first in period teir period supplier, tan visiting first anoter firm cosen at random. Te lock-in effect is transparent wen it is costless to observe te period price of a period supplier. However, te lock-in effect olds under weaker conditions. Besides, it depends also on te intertemporal cost correlation. Consider, for example, te case of a consumer tat patronized a low cost firm in period, and let υ =. Ten σ >, and in period te consumer will be prepared to pay more tan σ, to return to its period supplier, l before visiting anoter firm cosen at random. Also, since υ period low cost firm, tan for clients of a period ig cost firm, α < α. l < υ, te lock-in effect is stronger for clients of a ll l ll 4 Price Dynamics In tis section I discuss price dynamics. Te next Lemma establises a useful result about reservation prices. Lemma 7: If tere is no exit, te period reservation price is lower tan te period reservation price.

17 7 Since period s costs are positively correlated wit period s costs, υ l < υ, period s costs are ll informative of period s costs. And, since ig cost firms carge iger prices tan low cost firms, period s prices are also informative of period s prices. Consumers tend to buy at te same firm in bot periods. In addition, period s prices are informative of period s prices. Finding a low cost firm in period is valuable only for period, wereas finding a low cost firm in period is valuable for period and also for period. Tus, if tere is no exit, and ence te measure of active firms is te same in bot periods, in period consumers conduct a more toroug searc tan tey would for a single purcase. Tat is, in period consumers old a lower reservation price tan in period, ρ < ρ. 6 Te next Proposition establises te results about price dynamics. Proposition : (i If ig cost firms are active in period, ten te period price distribution first-order stocastically dominates te period price distribution. (ii If ig cost firms are inactive in period, ten te period price distribution first-order stocastically dominates te period price distribution. [Insert Figure 4 ere] Wen active, ig cost firms carge te reservation price. Since in period te reservation price is lower tan in period, if ig cost firms are active in period, c < ρ, prices increase from period to period, F F (Figure 5 (a. If ig cost firms are inactive in period, ρ < c, prices decrease from period to period F F (Figure 5 (b. Te measure of inactive firms in period, n, is non-increasing in te searc cost, and decreasing in te probability of a firm aving a low cost in period. To sum up, switcing costs and te intertemporal correlation of production costs, wic emerges as firms learn about te new tecnology, lock-in consumers. Hence, firms are prepared to initially carge low prices to build a customer base for te future, were tey ope to ave low costs. If owever firms fail to reduce costs, and reservation price is low, peraps because te searc cost is small, firms exit te industry. Over time, prices increase if no exit occurs, and decrease if exit occurs. 6 If υ = υ, period s costs and prices are not Informative of period s costs and prices, ence ρ = ρ. If υ < υ and exit occurs, te period price distribution suffers a l ll l ll first-order stocastic dominated sift, wic puses ρ down. However, if µ > / ( υ + υ, ρ < ρ still olds. ll

18 8 I can now state, witout proof, te next Corollary about industry variables. Corollary : If tere is exit, ten from period to period : (i bot te output per firm and te industry output increase, and (ii te industry average price decreases. Te case in wic searc costs are low, and terefore te period reservation price is low, ρ < c, corresponds to a sakeout scenario, in wic output expands and prices decrease. A sakeout like te one wic occurred in electronic markets after April 000, emerges in my model wen searc costs are low. Tis is in line wit te common wisdom tat electronic markets reduce searc costs. According to an estimate, finding a ig interest rate certificate of deposit requires 5 minutes using te telepone, 0 minutes using te Internet, and less tan a minute using a price-comparison searc engine (Butler et al. (997. Wen searc and switcing costs are ig, emerges an intertemporal pattern of increasing prices. Initial low prices correspond to te case of penetration pricing, identified, e.g., by te switcing costs literature (Farrell & Klemperer (00. Te evidence reported in sub-section. is inconclusive about wic of te intertemporal price patterns will caracterize te evolution of e-commerce. Most likely, price dynamics will vary across industries. Te price decrease identified by Brown & Goolsbee (00, occurred due to te spread in searc engines use, and terefore is not accounted for by Proposition. In sub-section 6. I discuss consumer eterogeneity, wic explains te price decrease identified by Brown & Goolsbee (00. Exit leading to lower, rater tan to iger prices, in a context in wic firms ave market power, is seemingly counter-intuitive. In te model, market power is not determined by te number of rivals, but rater by ow costly it is for consumers to observe prices, and te consumers beliefs about te prices carged in te industry. Exit reduces prices for two reasons. First, because it as a selection effect. Hig cost firms exit te industry. And second, because it gives consumers information about te remaining firms. If exit occurs, only low cost firms remain in te industry, wic leads consumers to old lower reservation prices.

19 5 Generalizations Te model laid out in section captures some of te aspects I wanted to discuss in tis paper in a simple way. However, expository simplicity was obtained at te expense of imposing some limitations on te model. In tis section I consider four generalizations, wic address tese limitations Consumer Heterogeneity In tis sub-section I discuss consumer eterogeneity. Pereira (004a and Pereira (00 explore some consequences of consumer eterogeneity. Next, I explain briefly ow consumer eterogeneity can be introduced. Tis extension will allow prices to decrease over time, as a result of an increase in low searc cost consumers, and tereby explain te price decrease identified by Brown & Goolsbee (00. Consider section s model, except for te following. Tere are types of consumers, wic differ only wit respect to teir searc cost. Some consumers ave a low searc cost, and oter consumers ave a ig searc cost. For simplicity I will focus on te case were tere is no exit. In eiter period, low searc cost consumers old a lower reservation price tan ig searc cost consumers. Tere are types of equilibria. In bot, low cost firms carge teir monopoly price, and sell to bot types of consumers. At a competing equilibrium, ig cost firms carge te reservation price of low searc cost consumers, and compete wit low cost firms for bot types of consumers. At a segmentation equilibrium, ig cost firms carge te reservation price of ig searc cost consumers, and sell only to tese consumers; low searc cost consumers buy from low cost firms. Te iger is te proportion of low searc cost consumers, te more willing are ig cost firms to lower teir price to sell to low searc cost consumers. Suppose tat in period te proportion of low searc cost consumers is small, and as a consequence, te model is at a segmentation equilibrium. Ten, an increase in te proportion of low searc cost consumers from period to period, can cause te model to switc from a segmentation to a competing equilibrium. In oter words, an increase in te proportion of low searc cost consumers can cause prices to decrease over time. Price-comparison searc engines allow consumers to easily observe and compare te prices of several firms, effectively reducing searc costs for consumers tat use tem. If one interprets te spread in searc engines use, as an increase in te proportion of low searc cost consumers, ten te price decrease identified by Brown & Goolsbee (00 emerges.

20 0 Consumer omogeneity imposes an additional limitation. Consumers only switc of firms if exit occurs. Pereira (00 sows tat consumer eterogeneity wit respect to te searc cost, also allows consumer turnover even witout exit. 5. Cost Reducing Investment In tis sub-section I discuss cost reducing investment. Even if te creation of a new production process involves uncertainty, tat can only be resolved over time, firms can influence, possibly at a cost, teir tecnological type, as in Bagwell et al. (997. However, except in te implausible case were cost-reducing investment completely eliminates uncertainty about future costs, te question of weter te cost distribution is exogenous or endogenous, is marginal to te issues I raise in tis paper. Te insigts of section 4 apply, as long as firms face some uncertainty about teir future cost, inerent to te process of learning te new tecnology. Next, I explain briefly ow cost-reducing investment could be introduced, and wic additional insigts could be gleaned from tis exercise. Consider section s model except for te following. In period, first firms simultaneously make an investment tat increases teir likeliood of aving a low cost, c l.i assume tat te probability tat a firm wo ad cost c i in period as a low cost in period, υ il (a i, is twice differentiable, strictly increasing, and concave, in te firm s cost reducing expenditure, 0 a i. Let m = µυ ll + ( µ υ l At an interior solution, optimal investment, υ [ π(p ;c ϕ (p π(p ;c ϕ (p ] il(ai l l l = :. I drop te assumption tat µ = m. a i, equates te marginal benefit to te marginal cost: Te equation above defines implicitly a =A( ρ. And since m=m(a,a, µ, te period reservation price and investment levels, ( ρ,a, l a i i, are determined jointly. 7 Multiple equilibria cannot be ruled out in general. It is possible to sow tat at equilibria locally stable wit respect to te Cournot tâtonnement process (Pereira (00, lower searc costs lead to lower period prices, bot because: (i te measure of period low cost l firms increases, and (ii te period ig cost firms price decreases: a i / σ < 0 < ρ / σ. 7 Te period reservation price best response function is continuous and strictly decreasing in a, and A ( i i ρ are non-increasing and continuous in ρ, except for ρ =c, were tey ave downward discontinuities: lim + A ( ρ < A ( c. Existence of equilibrium follows from Tarski s fixed point teorem. ρ c i i

21 A decrease in te searc cost, given te investment level, i.e., given te measure of period low cost firms, m, reduces te period reservation price. Te fall in te period reservation price increases investment, troug effects. First, if ig cost firms are active in period, a fall in te period reservation price forces tem to lower teir price, and earn a smaller per consumer profit. Tis increases te marginal benefit of investment. Second, if te fall in te period reservation price forces ig cost to exit, ten te consumer sare of period low cost firms rises. Tis also increases te marginal benefit of investment. Te rise in investment, in turn, increases te measure of low cost firms in period, m, wic leads consumers to old a lower reservation price in period. An increase in te probability of a firm aving a low cost in period, µ, as a similar effects. If in period all firms ave te same investment capabilities, υ = υ, ten period low cost firms ave a l ll no smaller marginal benefit of investment tan period ig cost firms, a a l. Tis occurs because period low cost firms ave a no smaller consumer sare tan period ig cost firms. Tis last effect reinforces, or justifies, te positive intertemporal cost correlation. 5.3 Entry in Period In tis sub-section I discuss entry in period. Consider section s model except for te following. In period, first firms tat were in te industry in period observe teir period cost. Second, a large number of firms decide if tey enter te industry, for a fixed setup cost, F > 0. Ten firms coose prices and consumers searc for prices. I will consider extreme cases, regarding ow te knowledge about te new tecnology acquired in period, spills-over in te industry in period. Eiter tere is a complete knowledge spill-over, or tere is no knowledge spill-over at all. In te first case, firms tat consider entering te industry in period ave a low cost level, c l. Some firms tat were in te industry in period migt, neverteless, ave a ig cost level, due to irreversible decisions, regarding te design of teir organizations. In te second case, firms tat consider entering te industry in period ave a low marginal cost wit probability µ. Consider first te case were tere is no exit, c ρ. Tere will be no additional entry, independently of ow te knowledge about te new tecnology spills-over. Te reason is tat on te equilibrium pat, in period consumers patronize teir period suppliers. Tis is an extreme case were switcing costs constitute a proibitive entry barrier. Consumer renewal, or demand expansion, would cange tis, and give some scope for additional entry.