Firms Incentives to Disclose Information about Product Quality: The Case of Multi-Attribute Products with Heterogeneous Consumers*

Transcription

1 Prelmnary Draft. Please do not quote wthout authors permsson. Frms Incentves to Dsclose Informaton about Product Qualty: The Case of Mult-ttrbute Products wth Heterogeneous Consumers* by V. Joseph Hotz UCL and NER and Mo Xao UCL September 2002 *We wsh to thank Dan ckerberg, Harold Demsetz, Gnger Zhe Jn, John Rley, Phllp Lesle, Robert Porter, Kenneth Sokoloff, partcpants of the IO Semnar at UCL, and partcpants of the 2002 North mercan Econometrc Socety Summer Meetng and 2002 nnual Conference of the European ssocaton for Research n Industry Economcs for comments on a prelmnary verson of ths paper. ll errors are ours. Ths research was funded by a grant from the Natonal Insttute for Chld Health and Human Development (R01 HD035382). The authors are solely responsble for the contents of the paper.

2 bstract In ths paper, we examne the ncentves for frms to voluntarly dsclose otherwse prvate nformaton about qualty attrbutes of dfferentated products when those products have multple attrbutes and consumers are heterogeneous n ther tastes over these attrbutes. In partcular, we focus on whether the so-called unravelng result n equlbrum, frms fully dsclose the qualty of ther products voluntarly when dsclosure costs are zero holds when dsclosure of qualty nformaton adds vertcal dfferentaton nto a product world wth exstng horzontal dfferentaton. We show that there exst certan confguratons of consumer multdmensonal preferences under whch frms, even wth hgh-qualty products, may not have ncentve to dsclose. Ths falure to dsclose voluntarly wll arse when dsclosure results n more elastc demand for products and hence trggers more ntense prce competton among frms, leadng to lower prces for all products. The escalaton of competton can make all frms worse off and lead frms to not dsclose the qualty of ther products, even wth zero dsclosure costs. s a result, the equlbrum n whch qualty dsclosure s voluntary may dverge from that n whch qualty dsclosure s mandatory. JEL classfcatons: L15 (Informaton and Product Qualty); L5 (Regulaton and Industral Polcy) Keywords: Qualty Dsclosure; Multple ttrbutes; Consumer Heterogenety V. Joseph Hotz Mo Xao Department of Economcs Department of Economcs UCL UCL Los ngeles, C Los ngeles, C hotz@ucla.edu xaomo@ucla.edu

3 1. Introducton In ndependent studes, Grossman (1981) and Mlgrom (1981) consder the decsons of frms to voluntarly supply nformaton about the (unobserved) qualty of ther products to less than perfectly nformed consumers. The prvately-nformed frms are assumed to have access to mechansms wth whch they can costlessly and credbly dsclose the qualty of ther products. These frms then decde whether to voluntarly dsclose the qualty of ther products to consumers. In what has become known as the unravelng result, Grossman and Mlgrom establsh that frms wll end up voluntarly dsclosng the qualty of ther products and those undsclosed are (correctly) nferred by consumers to have products wth the worst qualty. The logc of ther fndng s as follows. If no frm dscloses the qualty of ts product, then consumers beleve the hghest-qualty product to be no dfferent from the lowest-qualty one. s a result, frms producng products wth the hghest qualty have a clear ncentve to dsclose ther qualty, snce they wll then be able to charge hgher prces and acheve hgher profts. Frms wth the next hghest qualty products smlarly have the same ncentve to dfferentate themselves from the remanng frms (wth lower qualty products) and, as a result, wll fnd t n ther nterests to dsclose the qualty of ther products, charge hgher prces and realze hgher profts. Ths unravelng of the prvate nformaton held by frms contnues, so long as the benefts of dsclosure outwegh the costs. If the costs of dsclosng credble nformaton about product qualty are truly zero, then, n the lmt, full dsclosure by all frms prevals n a market,.e., the stuaton n whch frms hold prvate nformaton about product qualty unravels. s a result, t follows that there s lttle scope for frms to act strategcally wth respect to product qualty dsclosure decsons. Hgh-qualty frms, by dstngushng themselves from lower- 1

4 qualty ones, can always gan from revealng ther true qualty level by chargng a premum for the qualty dfference. Only those wth the lowest qualty wll choose no revelaton, because they wll certanly lose from not beng vewed as wth average qualty. s has been noted elsewhere, 1 the unravelng result of Grossman and Mlgrom has rather startlng mplcatons for regulatory polcy for products and servces wth (qualty) attrbutes that are dffcult for consumers to determne pror to ther purchase. In partcular, t would appear to mply that mandatory requrements that sellers dsclose the qualty of ther products are, at best, redundant, snce the presence of compettors would appear to provde suffcent ncentves for frms to voluntarly dsclose suffcent nformaton about product qualty to consumers so that the latter group s fully nformed about the products and servces avalable n a partcular market. More precsely, the unravelng result suggests that the only nterventon needed by consumers s ensurng the avalablty of low-cost and credble dsclosure mechansms for sellers to use. number of subsequent studes have examned seller ncentves for voluntary dsclosure of product qualty for refnements of the Grossman and Mlgrom models and ther unravelng result. 2 For example, studes have extended ther models to allow for certan types of dsclosure costs (Jovanovc, 1982; Verreccha, 1983; Dye, 1986), costs of nformaton acquston by sellers (Matthews and Postlewate, 1985; Farrell, 1986, Shavell, 1994), and alternatve market structures (Jn, 2000). For most of these extensons, the basc concluson that voluntary dsclosure by sellers about product qualty wll occur n equlbrum contnues to hold, so long as dsclosure costs are zero. To our knowledge, there are only two lnes of research that challenge 1 See Farrell (1986) and Fshman and Hagerty (1999) for surveys of ths lterature and dscussons of the mplcatons of the unravelng result of Grossman and Mlgrom. 2 For a revew of the nformaton dsclosure lterature, see Fshman and Hagerty (1997) 2

5 the robustness of the unravelng result and ts polcy mplcatons. Fshman and Hagerty (1999) argue that voluntary dsclosure may not occur when a subset of consumers n the market are unsophstcated and do not understand the nformaton dsclosed by sellers about the qualty of ther products. 3 lternatvely, Farrell (1986) notes that voluntary dsclosure may not occur n markets where the sellers, themselves, do not have complete nformaton about the qualty of ther own products. In both of these cases, the falure to obtan voluntary dsclosure from sellers hnges on a form of costs assocated wth dsclosure. In ths paper, we develop a model wth consumers heterogenety over mult-attrbute products to suggest alternatve explanatons for the non-robustness of the unravelng result, even when there are no costs assocated wth dsclosure. In partcular, we examne the ncentves for voluntary dsclosure by sellers for products that have multple attrbutes whch dfferent consumers value dfferently. The work of ecker (1965), Lancaster (1966), Muth (1966), Rosen (1974), and Gorman (1980) emphasze that all goods and servces are best vewed as bundles of characterstcs, ncludng qualty, and that tastes are plausbly heterogeneous over these attrbutes and, thus, over the bundles. These two features products-as-bundles-of-characterstcs and consumer-heterogenety are at the core of the lterature on hedonc prcng and markets for dfferentated products. Followng the lterature on product dfferentaton, 4 we consder a model n whch products are both horzontally and vertcally dfferentated and where the vertcal attrbute s not observable by consumers. 5 In ths context, we show that sellers whose products are hgh n qualty 3 Stvers (2001) offers a smlar model n whch voluntary dsclosure may not occur. 4 See Chapter 7 of Trole (1994) for a summary of ths lterature. 5 s dscussed below, the results we derve do not requre ths partcular confguraton of product dfferentaton. Products may consst of attrbutes wth any mx of horzontally- and vertcally-dfferentated attrbutes, ncludng goods that consst of attrbutes that are exclusvely of one type or the other. What s crucal for our model s that consumers have heterogeneous preferences over product attrbutes and that some of them are not observable to 3

6 (the vertcal attrbute) actually may beneft from mantanng consumer gnorance about ther product s qualty. Whether ths happens depends on whether the elastcty of demand for a seller s product would become more, rather than less, elastc after dsclosure. Whether the demand for products become more or less elastc wth dsclosure depends on consumer preferences over both the vertcal and horzontal attrbutes of products. If the demand for the product becomes more elastc, dsclosure can result n ntense prce competton wth ther (lower-qualty) rvals, causng prces and profts to fall. s such, no frm n a market may fnd t n ts nterest to voluntarly dsclose the qualty of ther products, even though dsclosure costs are zero, sellers know ther products and consumers have no dffculty n nterpretng the nformaton about product qualty f t were dsclosed. Our paper s ndrectly related to the lterature on horzontal and vertcal dfferentaton n that these papers worry about the tenson between the benefts to a frm dfferentatng from ts compettors to mnmze competton versus the potental gans to mnmzng dfferences n order to maxmze one s attractveness to large numbers of consumers. Whle we assume that the attrbutes of products are exogenously gven to sellers, we note that the decsons of frms about whether to dsclose the qualty of ther products are smlar to frms decsons to dfferentate ther products along that dmenson. Our paper also s related to the lterature on nformatve advertsng. 6 In partcular, Grossman and Shapro (1984) consder a model of nformatve advertsng n whch they consder the strategc effect of frms use of provdng truthful nformaton about ther locaton. Grossman and Shapro fnd that n a market wth dfferentated products, frms profts may nconsumers pror to purchase. 6 More generally, nformatve advertsng refers to truthful nformaton supply about products prces, attrbutes, etc. Ths s n contrast to prestge advertsng, whch refers to the provson of nformaton that mght alter consumers valuaton of the advertsed products, e.g., Peps clams to be for new generaton n ads. 4

7 crease wth the cost of advertsng snce an ncrease n advertsng costs reduces advertsng and thus ncreases nformatonal product dfferentaton ths allows frms to rase prces. 7 Ths strategc effect, n essence, s smlar to the one that we argue can dscourage frms from voluntarly dsclosng the qualty of ther products. Ths remander of the paper s organzed as follows. In secton 2, we develop a duopoly model of two frms that each sell products havng a horzontal attrbute (locaton) and a vertcal attrbute (qualty), where we assume that the latter attrbute s not readly observable by consumers pror to purchase. We descrbe the structure of consumer preferences over these attrbutes, the nature of dsclosure optons for the frms and the structure of the game that characterzes consumer product choce and the qualty dsclosure and prcng decsons of frms. We characterze the equlbrum for ths two-stage game under alternatve assumptons about the dstrbuton of consumer preferences and dsclosure mechansms. We establsh that whether a frm chooses to voluntarly dsclosure ts qualty depends on the nature of the nteractons n preference orderngs over the two attrbutes of the products. In secton 3, we provde an analyss and an ntutve explanaton of how dsclosure of qualty can affect the elastcty of demand for a frm s product and, as a result, ts wllngness to voluntarly dsclose the qualty of ther product to consumers. In secton 4, we brefly descrbe the polcy and potentally testable mplcatons of our model dependng on whether qualty dsclosure s mandatory or at the dscreton of frms. Secton 5 offers some concludng observatons. 7 Note ths nformatonal product dfferentaton vew can be contrasted wth the search costs vew, whch argue that better nformaton flow (due to advertsng, nformaton supply from government or other authortes, etc) wll reduce consumers search costs, ncrease prce elastcty of demand, cause tenser prce competton from frms and reduce market prce levels. 5

8 2. The Model Set Up In ths secton, we descrbe the set up of the model we analyze. We consder a duopoly model n whch two frms sell products wth two dmensons or attrbutes. Each frm, Frm and Frm, s endowed wth a product Y j,(j =, ) whch has two attrbutes. Followng the lterature on product dfferentaton, we assume that these products dffer across frms n ther horzontal attrbute, 9 locaton (denoted by L),andnthervertcal attrbute, 10 the qualty of ther product (denoted by Q), so that Y j = Y(L j,q j ). We assume that the attrbutes of a frm s product are exogenously gven to them and cannot be altered. Wth respect to a frm s horzontal attrbute, frms are located vs-à-vs consumers at the end ponts of a lnear cty. (See the followng dagram.) Let L j denote (0 L j 1) denote the locaton of the j th frm (j =, ) nthe lnear cty, where we assume that Frm s locaton s fxed at L =0andFrm s at L =1. Wth respect to the vertcal attrbute, we assume that Frm sells a low qualty product (Q = q l ), whle Frm sells one a hgh qualty one (Q = q h ). We denote the dfference, or spread, n qualty between these two products by,.e., q h q l >0. Frm : Y (L =0,Q =q l ) Frm : Y (L =1,Q =q h ) TheLnearCty 8 See Corts (1998) for how prce dscrmnaton can lead to an all-worse-off for frms rankng consumer groups dfferently by ther elastctes. 9 In the ndustral organzaton lterature, locaton s used as a typcal example of horzontal attrbutes of a product, whch means, holdng prces constant, dfferent consumers have dfferent preferences over the attrbute. For example, gven the same prce, some consumers may buy a black Honda ccord, whle some may buy a slver one. 10 In the ndustral organzaton lterature, the qualty of a product s referred to as a vertcal attrbute of a product. Vertcal attrbutes of products are characterzed by the followng condton: holdng prces constant, all consumers have the same preference order over ths attrbute. For example, all consumers prefer a 6-cylnder Honda ccord to a 4-cylnder one, holdng the prces of the two dfferent automobles constant. 6

9 Consumers are assumed to be unformly dstrbuted along the lnear cty, where X (0 X 1) denotes the th consumer s locaton,.e., consumers dffer wth respect to ther proxmty to the two frms. Consumers care about both ther dstance from products, ther qualty, f known to consumers, and the prces of products, P j, j =,. Moreprecsely,the th consumer values any gven product accordng to the followng utlty functon: (,, ) U L X Q P V + θ Q λd P (1) j j j j j j j where V s the stand-alone value of consumng ether good (nstead of consumng the outsde good), the dsutlty of payng prce P j for product j s normalzed to 1 and D j L j - X denotes the dstance of the th consumer from the j th product. (We normalze the utlty from the outsde good s 0 and assume V s hgh enough that no consumer wll choose t.) s specfed n (1), the utlty a consumer derves from a product s decrease n her dstance from t, where λ >0. 11 Thus, as s the usual set up for horzontal attrbutes, consumers obtan the same dsutlty per unt of dstance they must travel to purchase a partcular product but they dffer wth respect to the dstances they have to travel. Wth respect to the qualty of a product, we allow dfferent consumers to value ths product attrbute dfferently. To capture ths source of consumer heterogenety n a parsmonous way, assume that there are two types of consumers: those qualtylovers who value qualty,.e., θ = θ, whereθ > 0, and qualty-neutrals, who do not value t,.e., θ = θ 0, where we set θ 0 = 0 as a normalzaton. Thus, t follows that θ measures the dfference, or spread, n ths wllngness to pay between the two types of consumers, snce θ - θ 0 = θ -0=θ. crucal dmenson of the heterogenety of consumers and ther preferences for prod- 11 The greater the value of λ, the harder t s for consumers to travel from one end of the cty to the other. Thus λ s a measure of consumer heterogenety over the horzontal attrbute of products. 7

10 ucts concerns the jont dstrbuton of ther locaton (and, thus, dstance from products) and ther tastes for product qualty. t one extreme, consumers locaton and ther tastes for qualty may be uncorrelated,.e., Pr(X, θ )=Pr(X )Pr( θ ). Ths s but one possble dstrbuton. The dstrbuton of consumer locaton and preferences for qualty, n fact, may be correlated. To allow for ths possblty n a tractable way, let consumer s locaton and qualty preferences be dstrbuted accordng to the followng condtonal probablty functons: 1 β Pr ( θ = θ X) = βx + (2) 2 1+ β Pr ( θ = θ0 X) = βx + (3) 2 where β [-1,1]. 12 The nature and degree of correlaton n consumer s tastes over a product s horzontal and vertcal attrbutes vares wth the parameter, β. In partcular, consder the followng three cases: Case I: 1 Pr( β θ θ ) 1 and Pr( θ θ0 ) = = X = X = X = X 1 1 = = = = = 2 2 Case II: β 0 Pr( θ θ X) and Pr( θ θ0 X) Case III: β ( θ θ ) ( θ θ0 ) = 1 Pr = X = X and Pr = X = 1 X In Case I, qualty-lovers are more lkely to lve close to Frm (L =0), whch s the low-qualty product (Q =q l ). In ths case, we say that X and θ are negatvely correlated. In Case III, qualty-neutrals are more lkely to lve close to Frm and we say that X and θ are postvely correlated. Fnally, n Case II, qualty-lovers and qualty-neutrals are equally lkely to lve close to ether product and we say that X and one another. s β varesfrom-1to1,therelatonshpbetweenx and θ are uncorrelated or are orthogonal to θ goes from beng nega- 8

11 tvely to postvely correlated. To complete the model, we need to take a stand on what consumers and frms know about product attrbutes. We assume consumers possess perfect nformaton about ther preferences over qualty have perfect nformaton, ther own locatons, and the locatons of frms. However, consumers are assumed not to know, a pror, the qualty of a partcular frm s product, at least not wthout a frm dsclosng t. Consumers do know the dstrbuton of qualty levels n the market. 13 That s, wthout addtonal nformaton, consumers beleve both products qh + ql are of the same qualty,.e., EQ ( ) =. Furthermore, we assume that consumers do not 2 know how other consumers are dstrbuted wth respect to ther tastes,.e., they do not know the condtonal probabltes n (2) and (3). In one sense, the latter assumpton whch restrcts the ablty of consumers to make nferences about product qualty from knowledge of where consumers are located and frms dsclosure decsons does not seem unreasonable. However, relatve to formal models of product dfferentaton and dsclosure, ths assumpton does severely restrct what s common knowledge and, as such, does severely lmt the ablty of consumers to make nferences about product qualtes. We leave to future work any relaxaton of ths assumpton. Fnally, wth respect to the sellers (frms), we assume that they know the qualty of ther rval s product and they each know the dstrbuton of consumer tastes,.e., they do know (2) and (3). 2.2 Dsclosure Technology and Game Structure Suppose there exsts a costless truthful, accurate and credble dsclosure mechansm for 12 It follows from the specfcatons of the condtonal probabltes n (2) and (3) that Pr(θ 0 X) +Pr(θ X) =1. 13 Ths means, consumers know that a gven frm s product s ether hgh or low qualty, and both levels of qualty are offered n the market. 9

12 sellers to dsclose the qualty dmenson of ther products. For example, there may be a nonproft certfcaton agency offerng free servces to frms who want to dsclose ther product qualty. If both frms do not use ths mechansm, consumers have no way to fnd out true product qualty. However, f ether frm stands out and dscloses ts qualty, consumers know the qualty of ths frm as well as the other frm. 14 To characterze the qualty dsclosure problem, we use a two-stage dynamc game. In the frst stage, both frms make dsclosure decsons smultaneously. In the second stage, frms engage n ertrand competton to maxmze profts and consumers choose whch product to purchase so as to maxmze ther utlty, where ther valuatons of these products are condtonal on product prces and what they know about the qualty of these products. The essence of ths two-stage game s that each frm makes ts frst-stage, dsclosure decsons, consderng the possble second-stage prce decsons of all frms n the game. We solve for a subgame perfect Nash equlbrum usng backward nducton. That s, a frm evaluates ts payoff (profts) n the second stage under varous nformaton scenaros, whch are determned by frms dsclosure decsons n the frst stage, and then elmnates the frst-stage strategy that yelds ts worse fnal payoff, takng ts rval s frst-stage and second-stage responses nto consderaton. y constructon, there can only be two nformaton scenaros one n whch nether frm dscloses the qualty of ts product so that consumers have no nformaton about product qualty and the other n whch one or both frms dsclose ther qualty so that consumers have full nformaton about product qualty n the market. We refer to the payoffs under the frst scenaro as non-dsclosure outcomes and those n the second-scenaro as dsclosure outcomes. s llustrated n the followng table, f both frms choose not to dsclose, 14 For example, f a hgh-qualty frm dscloses tself to be of hgh qualty, consumers wll know the other frm n the market s of low-qualty, snce consumers know the qualty dstrbuton. The same logc apples n reverse,.e., 10

13 they are face the non-dsclosure outcomes. If ether frm dscloses, they both face dsclosure outcomes, regardless of whether the other frm chooses to dsclose or not. frm s dsclosure decson bols down to comparng the proft t would receve under the dsclosure and non-dsclosure outcomes. If each frm s payoff assocated wth the non-dsclosure outcomes s worse than those n the dsclosure case, both wll choose not to dsclose. 15 If the latter happens, the subgame-perfect Nash equlbrum wll be (non-dsclosure, non-dsclosure). Frm Non-Dsclosure Dsclosure Frm Non-Dsclosure Non-dsclosure outcomes Dsclosure outcomes Dsclosure Dsclosure outcomes Dsclosure outcomes In what follows, we wll show how the outcomes and, as a result, the equlbrum depend on the assumptons made about the nature of consumer heterogenety,.e., dfferent values of β n (2) and (3). 2.3 Frm Outcomes under Non-Dsclosure Consder frst the purchase choces of consumers when no frm opts to dsclose the qualty of ts product. Snce consumers can not tell the qualty dfference of two products, a consumer wll only care about prces and transportaton costs and wll purchase product Y [=Y(0,q l )] f and only f X P P + λ. Thus, consumers who lve close to Frm wll tend to buy Y, holdng prces of both products constant. Ths s the standard result n the Hotellng model of product dfferentaton. It follows that the best-response functons for the two frms a low-qualty frm dscloses tself to be low-qualty, allowng consumers to nfer that the other frm s hgh-qualty. 15 We assume f a frm s ndfferent between non-dsclosure and dsclosure, t always chooses non-dsclosure. useful way to thnk about ths s that dsclosure s assocated wth an arbtrarly small cost. 11

14 are P = 0.5( P + λ) (4) R, non dsclosure R, non dsclosure P = 0.5( P + λ) (5) and that, n equlbrum, the prces charged by the two frms are P = λ = P, non dsclosure, non dsclosure. (6) That s, the two frms charge the same prce, splt the market equally, and each earns a proft of 0.5λ Frm Outcomes under Dsclosure Now consder the case when ether frm chooses to use the dsclosure mechansm to dsclose the qualty of ts product, whch results n consumers havng perfect nformaton about the qualty of products offered n the market. We consder the dsclosure outcomes under alternatve assumptons about consumer preferences and compare them to the non-dsclosure out- comes derved above. ecause θ takes on one of two values, we have: If a consumer s qualty-neutral ( θ = θ 0 = 0), she wll buy the product wth lower qualty [Y = Y(0,q l )] f and only f X P P + λ and the hgh-qualty product [Y = Y(1,q h )] f X P P + λ >. If a consumer s qualty-lovng ( θ = θ > 0), wll buy the low-qualty product Y f and only f X P P + λ θ and the hgh-qualty product Y otherwse. 16 Thnk about restaurants: tastes can be vewed as the horzontal attrbute, whle hygene qualty as vertcal attrbute. In a crcumstance that restaurants have no credble method to reveal ther hygene qualty to consumers, or they choose not to reveal even f such a mechansm exsts, they may stll earn postve profts, competng over prces and tastes. 12

15 These cases are llustrated n Fgure 1. The horzontal axs represents the locaton of consumers relatve to consumers, whle the vertcal axs represents the probablty that a qualty-lovng consumer lves at locaton X. The (negatvely-sloped) dashed lne that cuts the fgure dvdes the (X, Pr(θ)) space nto qualty-lover (reas C 1 and C 4 ) and qualty-neutral (reas C 2 and C 3 ) consumers. The fgure depcts the stuaton n whch X and θ are negatvely correlated over consumers. The shaded area the sum of C 1 and C 2 equals s, the proporton of consumers who wll buy the lower-qualty product Y. The unshaded area the sum of C 3 and C 4 equals s, the proporton buyng the hgher-qualty product, Y. lgebracally, these market shares for the two frms are gven by: s = area( C ) + area( C ) β P P + λ θ 1 β P P + λ θ = + β β P P + λ 1 β P P + λ β βθ P P + λ βθ θ = ( 1 β ) 8λ 4λ s = area( C ) + area( C ) = 1 s βθ P P + λ βθ θ = ( 1 β ) + 1 8λ 4λ (7) (8) and, assumng there s no costs of producton, the proft functons for both frms are gven by: Π = Ps (9) Π = Ps (10) To ensure that there are maxmal values of proft functons, that prces are strategcally complementary, and that there s a unque, stable prce equlbrum, we assume that θ λ. That s, the assumpton θ λ ensures that the proft functons are well defned. The followng frst-order condtons characterze the frms optmzaton problems: 13

16 s s βθ 1 P = 0, (11) βθ 1 P = 0. (12) The condtons n (11) and (12) mply the followng best-response (R) functons: 2 2 R, dsclsoure 1 βθ 2 λ(1 β) θ 1 1 P = P + λ+ = P + λ θ (1 ω) 2 4λ 2βθ 2 2 (13) 2 2 R, dsclosure 1 βθ + 2 λ(1 + β) θ 1 1 P = P + λ+ = P + λ+ θ (1 + ω), (14) 2 4λ 2βθ 2 2 β where ω =, and the equlbrum prces for the two products are gven by: βθ P, dsclosure θ 6 λβ (2 λ βθ ) θ 1 = λ+ λ ω 6 βθ = (15) P It follows from (15) and (16) that:, dsclosure θ 6 λβ + (2 λ βθ ) θ 1 = λ+ λ ω 6 βθ = + +. (16) 2 3 P P + P = ω β. θ P = 3, dsclosure, dsclosure, dsclosure, dsclosure It also follows from (15) and (16) that that the profts of the two frms under dsclosure are:, dsclosure, dsclosure 1 θ 1 θ βθ 1 P s λ 1 ω 1 ( Π = = ) λ 3, dsclosure, dsclosure 1 θ 1 θ βθ 1 P s λ 1 ω 1 ( Π = = ) λ 3 (17) (18) 14

17 2.5 Frms Equlbrum Qualty Dsclosure Decsons Comparng the dsclosure outcomes wth non-dsclosure outcomes,,non dsclosure P =,non dsclosure P = λ and Π =Π = 2, non dsclosure, non dsclosure 1 λ, we are able to show: 1) When 1 ω θ <, equvalently, β < 6λ θ,17 dsclosure by ether frm wll cause both prces to be lower than those assocated wth the non-dsclosure outcome. 2) When 1 1 ω, equvalently, 3 3 < β < 6λ θ 6λ+ θ,18 dsclosure by ether frm wll cause P to rse and P to fall relatve to the non-dsclosure case. 3) When 1 2 λ < ω 3 θ, equvalently, β 1 6λ + θ <, dsclosure by ether frm wll cause both prces to ncrease relatve to the non-dsclosure case. Meanwhle, 1) When 5 ω θ <, 19 equvalently, λ 1 β <, dsclosure by ether frm 1 5θ 17 It can be shown that the expresson s bounded from above and below as follows: 6λ θ λ θ 3 18 It can be shown that: 1 0 <. 6λ + θ When ω <,wehave ω + < and 1 βθ < It follows that + θ λ 3 2 θ βθ 1 θ 1 0 < + < ω + 6λ 3 3 and one can show that:, dsclosure 1 θ 1 θ βθ 1 1 θ 1 θ 1 1 Π = λ 1+ ω 1 λ 1 ω 1 ω λ < < λ

18 wll cause both profts to be lower than those assocated wth the non-dsclosure outcome. 2) When 5 11 ω, equvalently, λ 2 β, dsclosure by ether frm 1 5θ 30λ+ 11θ wll cause Π to rse and Π to fall relatve to the non-dsclosure case. 3) When 11 2 λ < ω 15 θ,20 equvalently, 2 β 1 30λ+ 11θ <, dsclosure by ether frm wll cause both profts to ncrease relatve to the non-dsclosure case. s these results make clear, the equlbrum prces chosen by the frms under product qualty dsclosure depend on the dstrbuton of consumers locaton and ther preferences for qualty. s the correlaton of X and θ goes from beng negatve to postve, dsclosure by ether frm wll, n terms of profts, frst make both worse-off, then make the frm wth the lowqualty product worse-off whle makng the frm wth the hgh-qualty product better-off, and, fnally, make both frms better-off, relatve to the non-dsclosure case. More formally, we characterze the followng proposton concernng the dsclosure decsons of frms when products have multple attrbutes: tthesametmewhen 5 1 βθ 1 ω <,wehaveω < 0 and < 0,and + θ 6 3 6λ 3, dsclosure 1 θ 1 θ βθ 1 1 Π = λ 1+ ω 1 λ + < λ When 11 2 λ < ω 15 θ,wehave 1 2 βθ 1 1 ω > and. Thenwe canshow: 3 5 6λ 3 3, dsclosure 1 θ 1 θ βθ 1 1 θ 2 θ 1 Π = λ 1+ ω 1+ > λ λ tthesametmewhen < ω λ λ θ, we have 1 βθ 1 ω + > 0 and + > 0,and 3 6λ 3, dsclosure 1 θ 1 θ βθ 1 1 λ 1 ω 1 λ 2 3 6λ θ θ 1 θ θ 1 = λ 1+ 1 = λ 1+ 1 > λ 2 5λ 6λ 2 30λ λ 2 Π = >.. 16

19 PROPOSITION 1: For mult-attrbute products, wth at least one attrbute (qualty) that s not mmedately observed by consumers, the decson of one (or both) frms to dsclosure the qualty of ther product can lead to the prces of both frms products to declne and, thus, profts to declne. s a result, both frms wth prvate nformaton about the qualty of ther products may choose not to dsclose. 1 Proof: s long as ω <,.e., 3 β <, dsclosure from ether frm wll cause the result- 6λ θ ng prces of both frms to decrease relatve to ther non-dsclosure levels. Profts wll decrease for both frms when β s negatve enough, that s, when 10λ β <. Under ths crcum- 1 5θ stance, ether frm, n antcpaton of ts rval s response and the prce equlbrum, followng dsclosure, wll choose not to dsclose. The subgame-perfect Nash equlbrum s (non-dsclosure, non-dsclosure). Q.E.D. To better understand ths proposton, consder how the frms best-response functons under dsclosure are affected by the nature of the correlaton between consumer locaton and ther preferences for qualty and how they dffer from the response functons n the non-dsclosure case. When β = -1, the best-response functons are: P R, β = = P λ θ θ (19) P R whle f β = 1, the best-response functons are:, β = = P λ θ θ, (20) P R, β = = P λ θ θ (21) 17

20 P R, β = = P λ θ θ. (22) These two cases, along wth the response functons n the non-dsclosure case, are llustrated n Fgure 2. In the general case, the best-response functons are a weghted average of those gven n (19)-(20) and (21)-(22), respectvely. That s: and P = αp + (1 α) P (23) R R, β= 1 R, β= 1 P = αp + (1 α) P. (24) R R, β= 1 R, β= 1 where 1 β + θ α = 2 βθ and α [0,1].21 Notce that the pont of ntersecton of R P and R P s the prce equlbrum. The above decomposton shows that any pont along the bold lne LH can be supported as an equlbrum, gven that α [0,1]. 22 Whch equlbrum wll be realzed depends solely on the correlaton between X and θ. If, for example, X and θ are postvely correlated (β =1),thenα = 1, and the equlbrum s at pont H (the north-east corner of lne LH). There, the prces charged by both frms are hgher under dsclosure than those charged under non-dsclosure. If X and θ are negatvely correlated (β = -1), then α = 0andthe equlbrum would be at pont L, where the prces of both products are lower under dsclosure than wth non-dsclosure. s can be seen n Fgure 2, the best-response curve for Y can shft downward wth α 4λ θ 21 Note that = < 0 2 β 2(2 λ βθ ) bounded by 0 and 1. ether when β =-1andα =1orwhenβ =1andα = 0. Therefore α s 22, dsclosure, dsclosure θ Snce P P =, t follows that no matter how β changes, the resultng equlbra form a straght 3 lne and any pont on ths lne s a weghted average of two end ponts. 18

21 dsclosure by more than the correspondng functon for Y shfts upward. Ths can happen when β s suffcently negatve. In ths case, both frms are worse off,.e., each frm s prces and profts are lower than f nether frm dsclosed to consumers the qualty of ts product. s a result, nether frm has an ncentve to voluntarly dsclose the qualty of ts product. 2.6 n Illustraton To help clarfy the mplcatons of Proposton 1, we consder the followng hypothetcal stuaton to llustrate the results from our model for frms decson-makng wth respect to qualty dsclosure. Suppose there are two restaurants n a market. 23 One restaurant s a fast food outlet that specalzes n hamburgers. The other s a French restaurant that features escargot, among other dshes. Two types of consumers populate ths market: students and professors. t the same prces for a meal, we suppose that, on average, students prefer hamburgers, and thus fast food restaurants, to French cusne, whle, on average, professors, who have more sophstcated palettes, prefer escargot, and, thus the French restaurant, relatve to fast food. The restaurants also dffer wth respect to the hygene practced n ther preparaton of food. Suppose, n fact, that the fast food restaurant mantans a very santary ktchen, whle the French restaurant s hygenc practces are more lax. Nether type of consumers, on ther own, can readly determne the hygenc practces of ether restaurant. Whle consumers do not know the hygene practces of ether frm, restaurants are nspected by the local Publc Health department. We assume that the fndngs of these nspectons are accurate and credble, but that they are not dsclosed to the general publc. 24 Rather, the department ssues warnngs when they fnd poor hygene practces and provde ths nformaton only to the restaurants. t the same 23 Ths example s nspred by a recent paper by Jn and Lesle (2002), who consder restaurants n the Los ngeles market and ther hygene practces, as measured by Los ngeles County s Department of Publc Health. 24 For sake of ths example, assume that restaurants cannot be closed down by the Publc Health department for 19

22 tme, restaurants could choose to dsclose the hygene ratngs they receve, by postng them at the entrance of ther restaurants. 25 When wll one or more of the restaurants choose to post ther ratngs? The above analyss ndcates that ths depends on the dstrbuton of consumer tastes for the two types of cusne and for the hygene practces of restaurants. Recall that professors, on average, are more lkely to prefer French cusne to fast food and, on average, students have just the opposte preferences. Consder the case where, on average, students have stronger preferences for better hygene practces n the preparaton of ther food than do professors. 26 In essence, preferences for hygene and tastes for food are postvely correlated, as those who have stronger preferences for hygene also prefer the taste of the more santary food and those who have weaker preferences for hygene tend to prefer the taste of the less santary food. Under ths dstrbuton of preferences, we should expect the fast food restaurant to post ts better hygene ratng for consumers to see. Ths wll happen because these two restaurants, upon dsclosure, become less substtutable for both students and professors than when consumers know nothng about hygene. For students, the fast food restaurant offers the taste they prefer and better hygene, whch they also prefer under the assumed dstrbuton of preferences. Professors, on the other hand, prefer the taste of French food and are less wllng (than students) to pay for better hygene; they are content to stay wth the French restaurant. Thus, under the dsclosure of restaurants hygene practces, the degree of prce competton between the two restaurants actually may be reduced, due to the declne n substtutablty between the two restaurants for bad hygene practces. 25 For example, the Los ngeles County Department of Publc Health ssued hygene grade cards to restaurants and, n some areas of the county, allowed restaurants the choce of whether or not to dsplay them. See Jn and Lesle (2002) for further detals. 26 Recall that we assumed n our model that both frms know about the dstrbuton of preferences over both cusne-type and hygene. 20

23 the two types of consumers. oth frms potentally gan from ths relaxaton of competton. s a result, the fast food restaurant wll fnd t n ts self-nterest to dsclose ts better hygene practces, whch wll result n t achevng hgher profts. Under the above dstrbuton of preferences, one fnds that voluntary dsclosure about product qualty holds, as n the unravelng result of Grossman (1981) and Mlgrom (1981). ut now suppose that, on average, professors care more about the hygene practces of restaurants than do students. 27 That s, whle professors prefer French cusne relatve to fast foods, they also tend to prefer better hygene somethng that the French restaurant does not practce and students, who prefer hamburgers, do not place hgh value on better hygenc practces, at whch the fast food restaurant excels. Under ths dstrbuton of preferences n the populaton of potental patrons, wll the fast food restaurant stll want to post ts better hygene ratng? Consder what we would expect to happen f the fast food restaurant dd dsclose. Naturally, some professors, who value French food not as strongly as other professors (and/or who value hygene qualty more strongly than others) have ncentve to swtch to the fast food restaurant upon learnng that t mantaned better santary condtons than dd the French restaurant. In response, the French restaurant may want to decrease ts prce to keep ts consumer base. ut ths competton for dnng customers wll affect the fast food restaurant s market share, as some students, who do not care much about hygene qualty and who value hamburgers not as strongly as other students, would be wllng to swtch to the French restaurant for lowered prces. In turn, the fast food chan may also want to lower ts prce to keep ts consumer base, whch may nduce further prce-cuttng by the French restaurant. In the end, both restaurants would end up wth lower prces and profts f the fast food restaurant were to ds- 27 Ths mght arse because professors cannot afford to mss the classes they teach due to food posonng whle students do not mnd mssng a few of those classes, even f they have to spend the tme n the student nfrmary! 21

24 close. s a result, dsclosng ts better hygene ratng s not n the fast food restaurant s self-nterest under ths latter dstrbuton of consumer preferences. Furthermore, nether wll the French restaurant, snce t also has nothng to gan from dsclosng to consumers ts poor hygene practces. s a result, voluntary dsclosure wll not occur n ths market, even though both professors and students would be better off by havng ths nformaton pror to decdng where to dne. What s central to ths second scenaro for our restaurant example s that consumers value both the horzontal attrbute (taste, or tme-savng, n the above example) and a vertcal attrbute (hygene qualty n the above example) of the product (a meal outsde the home). If consumers know both attrbutes of the meals the two restaurants are servng, they wll choose to trade off ther preferred cusne for santary condtons and ether wll need to be compensated for lower hygene or unwllng to pay a hgher prce for somethng (better hygene) that they do not value. In essence, ths confguraton of the preferences of consumers n the market can make dsclosure undesrable for frms even wth hgh qualty, precsely because dsclosure ncreases the substtutablty between the two products. 2.7 Comparatve Statcs: The Role of Consumer Heterogenety To ths pont, we have focused on how the ncentves of frms to voluntarly dsclose ther unobserved qualty to consumers vares wth β, whch characterzes the relatonshp between consumers preferences for the observable and qualty attrbutes of products. ut, as we have noted at varous ponts, our results wth respect to when voluntary dsclosure wll occur also depend on λ, the costs to consumers of havng to travel to purchase a product, and θ, whch s a measure of the heterogenety of consumers preferences for qualty. 28 In ths secton, 28 Recall that θ = θ - θ 0, gven that we normalze θ 0 to zero. 22

25 we brefly consder how frms prces, market shares and profts wth and wthout dsclosure of product qualty vares as we vary these two aspects of consumer preferences. Consder frst, how frm prcng decsons under dsclosure would change as we ncrease the dfferences, or spread, across consumers n ther tastes for qualty:, dsclosure 2 P ω 1+ θ = θ 2 β 3 (25), dsclosure 2 P ω 1+ θ = + θ 2 β 3 (26) It can be shown that the above two dervatves wll be negatve when β s suffcently negatve. Ths mples that under the condtons n whch we have found that ether frm s less lkely to dsclose ts qualty.e., when θ and X are suffcently negatvely correlated the more consumers are dfferentated n ther tastes for qualty, the lower are the overall market prce levels. The contrary case also holds. That s, when β s suffcently postve, ncreasng the spread n consumer tastes for qualty tends to lead to not only dsclosure but also hgher overall market prce levels. Now consder how ncreasng the cost to consumers for the locaton attrbute of a product,.e., when consumers face hgher travel costs. It can be shown that: P = 1 1 > 0 λ βθ 2 (27) P = 1 1 > 0 λ βθ 2 (28) That s, the prces of products under dsclosure ncrease wth λ. Note, however, that ths predcton also holds under the nondsclosure equlbrum, as prces ncrease wth λ n that case too. Thus, consumer heterogenety wth respect to the observed attrbutes of products tend to n- 23

26 crease product prces, whether or not consumers know about the (unobserved) qualty attrbutes of these products. We have shown that when product qualty s dsclosed to consumers, whether both frms may be made worse off and, thus, do not have an ncentve to dsclose depends on the nature of the heterogenety n consumer preferences, both wth respect to the jont dstrbuton of θ and X, as well as the (unvarate) dstrbuton of tastes for qualty (as measured by θ 1 ). In the model, consumer heterogenety wth respect to tastes for qualty were characterzed n a very smple way, allowng for only two types of consumers. In the ppendx, we examne whether our fndngs wth respect to frm prces, profts and ncentves to dsclose product qualty are robust by consderng a varant of our model n whch we allow for a contnuum of types of consumers wth respect to ther preferences over the qualty attrbute of products. We show that the overall thrust of our fndngs s not senstve to ths feature of the model. 3. Qualty Dsclosure, Product Substtuton Patterns and Demand Elastctes In the absence of dsclosure of product qualty, consumers are forced to choose products wth less than full nformaton about all attrbutes of a product. In general, ths wll lead to a msmatch of consumers and products. In contrast, full dsclosure allows consumers to assess the entre bundle of attrbutes contaned n each product and, as a result, more accurately assess ther wllngness to pay for each product. ut, as the results n the prevous secton make clear, allowng consumers to make ths assessment wth complete nformaton may not always be n the nterests of frms. Such dsclosure may make consumers more senstve to the prces charged by frms, to the extent that knowledge of product qualty, as well as ts locaton, may cause consumers to trade-off the two as the frms vary the prces of ther products. In ths secton, we characterze our fndngs concernng the ncentves of frms to dsclose product qualty 24

27 n terms of what effect dsclosure can have on the elastctes of demand for mult-attrbute products. s s well known from the lterature on product dfferentaton, a frm has a strategc ncentve to dfferentate ther product when such dfferentaton reduces the elastcty of demand for ts product. Dsclosure of the qualty of ts product can dfferentate one frm s product from that of ts compettor. ut, the results derved n the prevous secton ndcate that whether dsclosure wll reduce the prce responsveness of consumers for a frm s product (relatve to no dsclosure of product qualty) depends on how consumers tastes for qualty and ther locaton vs-à-vs frms are dstrbuted n markets. To see ths, we need to characterze the elastctes of demand for products Y and Y wth and wthout qualty dsclosure. Consder frst the demand elastctes of demand for the two products under the nondsclosure equlbrum. In the general case where P = P = P, these elastctes are gven by: e non dsclosure s P P non dsclosure s P = = e. (29) P s λ P non dsclsoure s non dsclosure non dsclosure non dsclosure t the non-dsclosure equlbrum, P = P = λ, t follows that e = e = 1. Note further that when the prce of a product s below the equlbrum level (λ), both frms have non dsclosure an ncentve to ncrease ther prces snce < 1, both frms wll want to decrease ther non dsclosure prces f ther prces are greater than λ, snce n that case > 1. e j Under the dsclosure equlbrum, the elastctes of demand for the two products are gven by: e j 25

28 e dsclosure P βθ 1 = 2 2 βθ P P + λ βθ θ ( 1 β ) 8λ 4λ β P = ω β βθ 1 ( P P λ ) ω 4λ ω P = θ ( P P + λ ) + ( ω 1) 2 (30) and e dsclosure βθ 1 1 = P 2 2 βθ P P + λ βθ θ ( 1 β ) + 1 8λ 4λ β P = ω β βθ 1 ( P P λ ) ω 4λ ω, (31) P = θ ω ( P P + λ) ( ω 1) + 2 β respectvely. Furthermore, at P =P =λ, dsclosure e 1 θ = 1 + ( ω 1), and dsclosure e = θ 2ω 1 ( ω 1) + β 1. Consder what happens to the elastctes of demand for the two products when X and θ are more negatvely correlated. When β < + θ, dsclosure e > 1,.e., the elastcty of demand for the low-qualty product s more than untary elastc, so that when the qualtes of products have been dsclosed, Frm wll want to lower ts prce n order to avod losng the consumers 26

29 t attracted when there s no dsclosure. t the same tme, dsclosure e = θ 2ω 1 ( ω 1) + β 1 < 1, 29 whch s why the best-response curve of the hgh-qualty frm always shft up after dsclosure. ut, when β s suffcently negatve, the elastcty of demand for the hgh-qualty product, dsclosure e, wll become greater than 1, as the low-qualty frm lower ts prce relatve to ts nondsclosure level. 30 Tradtonal wsdom tells us greater demand elastcty s assocated wth more substtutablty among products, and thus wth more ntense prce competton among frms. Therefore revelaton of a qualty attrbute, generatng greater product substtutablty and ntensfyng prce competton n the market, mght result n prce decreases for all frms, and possbly, proft decreases for all frms. It follows that frms of hgh qualty, out of strategc consderatons, may try to avod revelaton of ther true qualty level. Why do the elastctes of demand for the two products become greater (n absolute value) when X and θ are negatvely correlated? s noted before, consumers n ths case are systematcally msmatched wth respect to locaton and tastes for qualty n that qualty-lovers, on average, are located closer to the low-qualty product (sold by Frm ) and qualty-neutrals are located closer to the hgh-qualty product (sold by Frm ). Upon dsclosure, consumers are realze ths msmatch and, as a result, are less wllng to pay hgher prces for products near to them than they were when locaton was the only attrbute of the product upon whch 29 Ths nequalty s equvalent to [-1,1]. β > 1 θ 1 andthssalwaystrue,as 1 θ 1 s less than -1 and β 30 When P = λ, dsclosure e = 1 P θ 2ω 2 ( ω 1) + λ β. If P 1 2 θ β < θ λ 1, t follows that dsclosure e > 1. Hence we can see that when the low-qualty frm lowers ts prce P relatve to ts non-dsclosure level λ, a suffcently negatve β wll make the elastcty for the hgh qualty product greater than unty. 27

30 they based ther product choce. They prefer to compensate for the msmatch n locaton and qualty that they now face wth lower prces and, as a result, are more prce senstve n ther demand for products than when they were unaware of t. The above dscusson characterzes what happens to the elastctes of demand for each product when X and are suffcently negatvely correlated. One can show that when β s suffcently postve, the elastctes of demand for the two products wll be lower n absolute value ther demand curves wll be steeper 31 the dsclosure equlbrum relatve to those that preval under non-dsclosure. That s, when β s suffcently postve, frms are able to rase ther prces gven that the locaton of consumers vs-à-vs the two products s favorably matched wth ther tastes for qualty. To understand results derved above s to understand how demand elastctes would change wth the dsclosure of the qualty attrbutes of these products under alternatve assumptons about the structure of consumers preferences. s noted n the ntroducton, the prmary motvaton for frms to dfferentate ther products s to reduce the degree of prce competton wth rvals sellng otherwse smlar products. To the extent that ths s true, dfferentatng one s product should reduce the product s elastcty of demand, thereby allowng the frm to ncrease the product s prce and stll ncrease ts proft. Ths logc s borne out n the no-dsclosure-mechansm case consdered above. Theren, from the consumers perspectve, both prod- 31 Note that s h / P h and s l / P l, whch are the nverses of the slopes of the demand curves, are equal to: Therefore, f β <0,then steep; f β >0,then s h P h s h P h and and s l P l s s 1 βθ h l = = 1 P P s l P l h l, become bgger, and then the slopes of both demand curve become less become smaller, and the slopes of both demand curve become steeper. 28

31 ucts are fully characterzed by ther locatons and, by assumpton, are fully dfferentated, snce the two frms are located at opposte ends of the lnear cty. Wth no dsclosure about product qualty, each frm faces a downward slopng demand curve for ts product. Consumers closest to a partcular frm havng hgher wllngness to pay for ts product than for the product of ts rval and do not vew the two products as perfect substtutes. 32 s a result, frms sellng such a dfferentated product may earn postve profts. 33 Wth ths exstng horzontal dfferentaton, a frm s ncentve to dfferentate along another dmenson n our case va dsclosng the qualty of ts product depends on what would happen to the elastcty of demand for ts product f t (or the other frm) revealed the qualty of ts product and ths, n turn, depends on the nature of the relatonshp, or correlaton, of consumers preferences over these product attrbutes. In summary, the key message we try to convey can be phased as follows: n a world wth exstng product dfferentaton, revelaton of another dmenson of product dfferentaton mght change the substtuton patterns among products, whch could ntensfy or allevate competton, dependng on how consumers multdmensonal preferences are dstrbuted. Frms, even wth hgh qualty, out of strategc consderatons, may want to avod dsclosure f consumers better knowledge leads to more ntense competton among frms. 4. Polcy and Testable Implcatons s has been noted by others, there are two mmedate mplcatons that follow f the 32 t the ndvdual level, for consumer, who values ths product more, ths product s less substtutable than for consumer, who value t less. Consumer s more loyal than to ths product. 33 The same logc holds for the case of a sngle vertcal attrbute. Note n a standard ertrand model of vertcal dfferentaton frms wll earn zero proft f there s no qualty dfference; qualty dfference brngs postve proft to both the low-qualty frm and the hgh-qualty frm. It follows that there are always ncentves for frms of any qualty to dsclose. 29