When Gray is Good: Gray Markets and Market-Creating Investments*

Transcription

1 Vol. 0, No. 0, xxxx xxxx 2014, pp ISSN EISSN DOI /poms Producton and Operatons Management Socety When Gray s Good: Gray Markets and Market-Creatng Investments* Romana L. Autrey Unversty of Illnos at Urbana-Champagn, 515 E. Gregory Drve, MC 520, Champagn, Illnoss 61820, USA, romana@llnos.edu Francesco Bova, Davd A. Soberman Joseph L. Rotman School of Management, Unversty of Toronto, 105 St. George St., Toronto, Ontaro Canada M5S 3E6, francesco.bova@rotman.utoronto.ca, davd.soberman@rotman.utoronto.ca G ray markets arse when an ntermedary buys a product n a lower-prced, often emergng market and resells t to compete wth the product s orgnal manufacturer n a hgher prced, more developed market. Evdence suggests that gray markets make the orgnal manufacturer worse off globally by erodng proft margns n developed markets. Thus, t s nterestng that many frms do not mplement control systems to curb gray market actvty. Our analyss suggests that one possble explanaton les at the ntersecton of two economc phenomena: frms nvestng to buld emergng market demand, and nvestments conferrng postve externaltes (spllovers) on a rval s demand. We fnd that gray markets amplfy the ncentves to nvest n emergng markets, because nvestments ncrease both emergng market consumpton and the gray market s cost base. Moreover, when market-creatng nvestments confer postve spllovers, each frm bulds ts own market more effcently. Thus, frms can be better off wth gray markets when nvestments confer spllovers, provded the spllover effect s suffcently large. These results provde a perspectve on why frms mght not mplement control systems to prevent gray market dstrbuton n sectors where nvestment spllovers are common (e.g., the technology sector) and, more broadly, why gray markets persst n the economy. Key words: gray markets; unauthorzed dstrbuton; emergng markets; nvestment spllovers; management control systems Hstory: Receved: Aprl 2013; Accepted: Aprl 2014 by Anl Arya, after 2 revsons. 1. Introducton *The authors are lsted alphabetcally. An earler verson of ths study was ttled When Gray s Good: Complementary Goods and Emergng Markets. Gray market goods are branded products ntally sold n a market desgnated by the manufacturer, but then resold through channels not authorzed by that manufacturer nto a dfferent market. When the prce dfferental across markets s large relatve to transacton costs, entrepreneural gray marketers buy goods n the low-prced market and resell them n the hghprced market to compete wth the manufacturer s authorzed sellers. Emergng markets are often a key source of gray market goods (Leteler et al. 2003, Sakarya et al. 2007). In these markets, manufacturers often charge lower prces because of consumers lower wllngness to pay for a product or n order to establsh an early foothold n the market. Gray markets affect a wde varety of sectors (Anta et al. 2006). One sector where gray markets are partcularly promnent s the technology sector. A recent survey of large hgh tech frms by KPMG (2008) estmates that gray markets account for $58 bllon per year of lost sales n ths sector. Furthermore, a wde varety of technology products have actve gray markets. For example, 210 mllon gray market cell phones were expected to shp globally n 2012, comprsng 13% of the global handset busness (Yang 2012); 49% of the 1.07 mllon Pads sold n Chna n the frst half of fscal 2011 were gray market sourced (Kan 2011); n Inda, gray market flash cards captured 25% of the market (Guha 2010); n some geographc regons, gray market sales of PCs have outnumbered authorzed sales by two to one (Anta et al. 2006); and n the late 1990s, the gray marketng of software undercut the proftablty of Amercan retalers (Copeland and Campbell 1999). Gven the large mpact of gray markets on the technology sector, t s surprsng to note that technology companes do not always mplement systems to control or montor gray market dstrbuton. For example, KPMG (2008) reports that 42% of ts survey respondents dd not have a process to dentfy or montor gray market actvty. Addtonally, n a frm survey conducted by Delotte (2011), respondents felt that gray markets perssted prmarly because of poor chan- Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

2 Autrey, Bova, and Soberman: When Gray s Good 2 Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety nel nternal controls (33% of respondents number one response) and a lack of montorng/detecton processes (25% of respondents number two response). The combned evdence leads to two questons: Why are some technology frms not mplementng management control systems to curb gray market actvty? Gven ths wdespread nacton, mght there be an upsde to gray market actvty for technology frms? We argue that ths nacton may relate to the nature of the technology sector tself, and n partcular the exstence of postve nvestment externaltes that are conferred on a compettor s demand when a frm nvests to buld ts own market. Postve nvestment externaltes can arse from varous sources. For example, Lews and Nguyen (2012) llustrate that frm nvestments n onlne advertsng ncrease searches for not only the advertsed brand but also for other brands n the advertser s category. Our results suggest that a possble explanaton for the pervasveness of gray markets n certan ndustres les at the ntersecton of these nvestment externaltes and a growth strategy that s common amongst frms enterng emergng markets: nvestng n market creaton to buld demand n the new market. These market-creatng nvestments nclude buldng dstrbuton networks, creatng marketng partners, and promotng advertsng that nforms or educates potental consumers about benefts assocated wth the category. To provde a real world example of the nteractons we seek to document, we consder a technology product wth the followng characterstcs: (1) an actve gray market, (2) a manufacturer that nvests n marketcreatng nvestments to ncrease demand n an emergng market, (3) postve externaltes to nvestment that enhance an emergng market opportunty for not only the frm but also ts rvals, and (4) a manufacturer that has a muted response to gray market actvty. We choose the example of Apple s Phone. Frst, the Phone s gray market s extremely actve. Second, Apple nvests sgnfcantly n buldng emergng markets. Thrd, Apple s market-creatng nvestments for the Phone arguably created postve externaltes for other products n the category. For example, as the frst touch screen smartphone to gan global promnence, Apple spent consderable amounts educatng consumers on how to use the Phone. These nvestments shfted global consumer preferences away from keyboard nterfaces to touch screen nterfaces, and helped buld the touch screen market for not only the Phone but also for ts touch screen compettors lke the Samsung Galaxy and Google Androd. Importantly, we also observe gray market actvty across the entre range of Phone compettors. Fnally, we note that popular press artcles have commented on Apple s lack of nterference wth gray market Phone sales. For example, Apple doesn t appear to be dong much to combat ts gray market success; n fact, f anythng, t has taken steps to encourage off-contract busness n recent years, by sellng factory unlocked devces drectly through ts own store (Etherngton 2011). To assess the mpact of gray markets on frm profts when a frm s nvestments confer postve externaltes on ts rvals, we present a model of Cournot competton where two frms choose producton quanttes n both a larger domestc market (where retal prces are hgher) and a smaller emergng market (where retal prces are lower). Addtonally, we ncorporate a gray market compettor a Stackelberg follower n the game that purchases volume from the smaller, less expensve emergng market, and resells ths volume n the hgher prced domestc market. Fnally, we allow each frm to make market-creatng nvestments n the frst stage of the game. These nvestments ncrease emergng market demand for the nvestng frm and, when nvestment spllovers exst, the nvestng frm s rval. We fnd that both frms can be better off wth gray markets when a frm s nvestments confer postve externaltes on a rval s demand. Ths result arses from several forces that affect each frm s profts n the two markets. Frst, because of lost domestc sales resultng from the gray market s dverson, frm profts n the domestc market are always lower when gray markets exst. Ths fndng echoes the anecdotal and emprcal evdence of domestc manufacturers observng reduced profts due to ncreased gray market cannbalzaton (e.g., KPMG 2008). However, each frm s nvestment n the emergng market s strctly larger when gray markets exst. Ths outcome arses because gray markets provde each frm wth an added ncentve to ncrease emergng market demand. Specfcally, by nvestng more to ncrease demand, not only does each frm ncrease emergng market consumpton for ts product, t also lmts the gray market s arbtrage opportunty by ncreasng emergng market prces. These larger nvestments have both postve and negatvempactsoneachfrm sprofts.ononehand,nvestments are costly and the costs are ncreasng n the nvestment s sze. It follows that, as nvestments are strctly larger n a gray market settng, so too are ther costs, and these hgher costs lead to lower frm profts when gray markets exst. On the other hand, the larger the nvestment n the emergng market, the greater the emergng market consumpton, retal prces, and profts for each frm. Thus, larger nvestments also have a postve mpact on frm profts when gray markets exst. In a settng where frms make nvestments wth no spllovers, the aforementoned costs outwegh the benefts, and frms are better off wthout gray markets. Conversely, n a settng where frms make nvestments that do have spllover effects on a rval s Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

3 Autrey, Bova, and Soberman: When Gray s Good Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety 3 demand, ether the negatve or postve forces dscussed above can domnate. The postve forces may domnate because a frm ncreases demand for ts product n the emergng market more effcently when nvestments confer postve spllovers. Sad dfferently, the return on nvestment, measured as the rato of ncreased demand to the cost of the nvestment, ncreases n the magntude of the spllover effect. Because gray markets nduce larger nvestments, and nvestments are more effcent when they confer spllovers, frms can be better off wth gray markets than wthout them provded the spllover effect s suffcently large. Ths nference helps to explan why ndustres where postve nvestment externaltes are common, lke the technology sector, appear to allow gray market actvty to thrve. Conversely, t also explans why some ndustres vgorously crack down on gray market actvty. For example, relatve to the technology sector, nvestments n the North Amercan auto ndustry tend to be very asset specfc. In turn, these nvestments have ether a neglgble or lttle postve effect on a compettor s demand. Interestngly, n order to reduce (or elmnate) the gray market dstrbuton of Amercan cars to Canadan consumers, auto manufacturers have recently begun to not honor US warrantes when cars are purchased n the Unted States and exported to Canada. Ths strategy seems to be consstent wth the model s predcton of a strct preference for frms to control gray markets when nvestments yeld muted demand spllovers on a frm s rvals. Our results are also robust to a number of extensons. In our frst extenson, we assess a dfferent source of nvestment externalty: complementary goods. When products are complements, any nvestment to buld demand for one product also ncreases demand for the other. We fnd that both frms can be better off wth gray markets when products are complements, even f there s no other source of nvestment externalty asde from the complementarty of the products. In a second extenson, we allow each frm to stop ts own gray market wthout cost. Consstent wth the fndngs n the man model, we fnd a unque, pure strategy equlbrum where both frms are better off allowng ther respectve gray market to operate, provded the emergng market s large enough. Fnally, we confrm that our results are robust to makng the gray market more compettve and to changng the nature of competton n the market. The study proceeds as follows. We revew the lterature on frm outcomes and gray markets n secton 2. Secton 3 ntroduces the man model and analyzes the results. In secton 4, we present several extensons for robustness. In secton 5, we conclude. 2. Lterature Revew The lterature assessng gray markets and ther mpact on frms fnds the nearly unanmous result that gray markets make orgnal manufacturers less proftable. For example, Anta et al. (2006), Assmus and Wese (1995), Autrey and Bova (2012), Cavusgl and Skora (1988), Cespedes et al. (1988), L and Robles (2007), Ahmad and Yang (2000), Maskus and Chen (2004) and Wegand (1991) take the poston that gray markets are a problem for manufacturers for reasons that nclude the followng: ncreased competton whch leads to narrower manufacturer proft margns, losng control of dstrbuton, a decreased ablty to prce dscrmnate, a mtgated ncentve to nvest n research and development and the eroson of brand equty. We note that our model shares some common features wth a dual dstrbuton setup (see Arya and Mttendorf 2013a, b), n whch a focal frm n essence dvdes nto two frms and competes as two franchses (e.g., a tradtonal retaler and an onlne store). Both a gray market compettor and an extra authorzed channel (e.g., an onlne store) ncrease competton n the market. For example, f a frm orgnally competes n a duopoly, the ncluson of ether a gray market compettor or an addtonal authorzed dstrbutor ncreases the number of compettors n the market from two to three. However, n the dual dstrbuton setup, the ntatng frm can often be better off, even f dual dstrbuton does not lead to an ncrease n the sze of the market. For example, n a Cournot model of dual dstrbuton, although a frm dvdng tself nto two compettors makes competton more ntense and thus lowers total ndustry profts, the focal frm now enjoys a larger share of the ndustry profts, and s ultmately better off enjoyng a larger share of a smaller pe (see Baye et al. 1996). Unlke the dual dstrbuton settng, the focal frm s strctly worse off f the new compettor n the market s the gray market. Whle a focal frm earns hgher proft n the emergng market on sales to the gray marketer, these addtonal sales are not enough to -offset the mpact that the gray market has on both erodng total ndustry profts and reducng the frm s share of total ndustry profts. Specfcally, the focal frm now obtans less than half of a smaller domestc proft pe (wth a gray marketer) vs. half of a larger domestc proft pe (wthout a gray marketer). The conventonal wsdom, then, s that dual dstrbuton leads to frms beng better off whle gray markets lead to frms beng worse off. In ths lght, t s nterestng that gray markets persst even when frms have the ablty to elmnate them by mplementng comparatvely nexpensve control mechansms. These mechansms may nclude Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

4 Autrey, Bova, and Soberman: When Gray s Good 4 Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety the systematc testng of all ncentvzed transactons, montorng the Internet and other sources for prce anomales, and nsstng that channel partners assess ther own nternal control envronments (Delotte 2011). The observaton that frms are not mplementng these sorts of control mechansms s especally puzzlng, gven evdence that management control systems are typcally effectve at preventng undesred behavor (see Abernethy et al. 2004, Abernethy and Llls 1995, Chenhall 2003, Ittner and Larcker 1997, Langfeld-Smth 1997). We beleve that our model of market-creatng nvestments wth postve externaltes provdes a plausble explanaton for ths unexpected behavor. 3. Man Model Our model conssts of a settng wth two dstnct markets; we refer to the larger market as the domestc market, and the smaller as the emergng market. In our analyss, we model the gray market product as a perfect substtute for the authorzed product (.e., the sze of the market, the slope for demand, and the substtutablty of the two products are dentcal). Whle t s plausble that consumers may have a lower wllngness to pay for some gray market products, we also beleve that, ncreasngly, gray market goods are vewed as perfect substtutes for ther authorzed counterparts. For example, gray markets provde well-known retalers such as Wal-Mart, Target, and Costco the opportunty to offer a perfect substtute for the manufacturer s authorzed product (Stohr 2012). Further, a common justfcaton for the nferorty of gray market products s that they lack warranty protecton (e.g., Ahmad and Yang 2000). However, ncreasngly retalers such as Costco offer ther own warrantes for products sourced through the gray market when the manufacturer does not offer a warranty for these goods. Fnally, by assumng that the gray market product s a perfect substtute for the authorzed product, we allow for the gray market to have ts maxmum mpact on cannbalzng the orgnal manufacturer s domestc sales and, accordngly, on erodng ts global profts. Ths modelng choce should, n turn, bas our results away from fndng evdence that orgnal manufacturers prefer gray markets to not preferrng them. The tmelne s shown n Fgure 1. In the frst stage of the model, each frm chooses ts level of market-creatng nvestments, x 0, at a cost of x 2, followng the standard quadratc cost functon. Examples of market-creatng nvestments nclude buldng dstrbuton networks, creatng marketng partners, and advertsng that nforms or educates potental consumers about benefts assocated wth the category. These nvestments ncrease the sze of the emergng market by x for the nvestng frm but also ncrease the sze of the emergng market by bx, where b 2 (0, 1], for ts rval. The parameter b represents the extent of nvestment spllovers, or the ncrease n the rval s emergng market demand that results from the nvestng frm s market-creatng nvestments. In the second stage, the two frms engage n dfferentated Cournot quantty competton smultaneously n both markets. Demand curves n each market are generated from quadratc consumer utlty preferences as n Sngh and Vves (1984). We defne c 2 (0, 1) as the degree of substtutablty between the frms products. As c? 0, the products become perfectly dfferentated. As c? 1, the products become perfect substtutes. In the domestc market, each frm chooses the quantty q 0 to produce for sale n ts domestc market at prce p 0, gven the followng nverse demand curve ( 6 j 2 {1, 2}): p 1 ðq þ q G cðq j þ q Gj : ð1 Each frm s nverse demand curve n the emergng market s as follows ( 6 j 2 {1, 2}): p E E þ x þ bx j ðq E q G cðq Ej q Gj : ð2 The emergng market s smaller as reflected by the demand ntercept, E, whch we assume to be less than 1. In the emergng market, each frm chooses quantty Q E 0 to sell n the emergng market at prce p E 0. Ths Q E ncludes both sales to the gray marketer, q G 0, and sales to consumers n the emergng market, q E = Q E q G 0. Addtonally, we assume that emergng market consumers and the gray marketer pay the same retal prce, p E, for product purchased n the emergng market. We also note that the q G unts dverted to the domestc market do not satsfy demand n the Fgure 1 Tmelne Each frm chooses x, the amount by whch to grow emergng market demand. Each frm smultaneously chooses q, the quantty to be sold n the domestc market and Q E, the total quantty to be sold n the emergng market. The gray marketer chooses q G1 and q G2, the quantty of gray market product to be bought n the emergng market and sold n the domestc market. Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

5 Autrey, Bova, and Soberman: When Gray s Good Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety 5 emergng market. Only the q E unts that are not sphoned off by the gray marketer are avalable to satsfy the demand of the local end users. As q E determnes the retal prce, p E, that emergng market consumers are wllng to pay n a Cournot market, and because we assume that the gray market and local consumers pay the same prce, q E n turn determnes the market prce that clears the emergng market. Importantly, the quantty consumed by emergng market consumers, q E, s strctly lower when a gray marketer s present, ceters parbus (a pont we expand on below). In turn, the emergng market retal prce that clears that market s hgher when a gray market exsts, because emergng market consumers procure fewer products for consumpton. Fnally, n the game s thrd stage, the gray market frm chooses the quantty q G of each frm s product to dvert from the emergng market to the domestc market. We solve the model by backward nducton. The gray marketer s objectve functon s: Max qg1 ;q G2 p G q G1 ðp 1 p E1 þq G2 ðp 2 p E2 ; ð3 subject to Equatons (1) and (2). Substtutng these constrants nto Equaton (3), takng frst order condtons wth respect to q G1 and q G2, and solvng, we obtan the followng best response functon ( 6 j 2 {1,2}): q G ðq ; Q E 1 c ðq Q E ð1 c 2 ½Eð1 cþx ð1 bcþx j ðb cš 4ð1 c 2 : ð4 We also assess settngs where no gray market exsts. In these settngs, q G = 0( = 1, 2). Antcpatng the gray market demand, n the second stage each frm s objectve s as follows ( = 1,2): Max q ;q E p q ðp þq E ðp E x 2 ; ð5 subject to Equatons (1) and (2), and ether Equaton (4) or q G = 0, dependng on whether the gray market exsts or not, respectvely. To solve, we take the frst order condtons wth respect to q 1, q 2, Q E1 and Q E2, whch creates a system of four equatons and four unknowns. The resultng equlbrum quanttes are as follows ( 6 j 2 {1, 2}): q 1 2 þ c ; Q E Eð2 cþx ð2 bcþx j ð2b c 4 c 2 : ð6 Interestngly, we note that for a gven set of nvestment levels, x and x j, the equlbrum quanttes n the domestc and emergng markets, q and Q E, are dentcal and strctly postve whether gray markets are actve or not. An explanaton for ths outcome can be gleaned from an example n Trole (1988, p. 316). In the example, a Stackelberg leader sets the same quantty n a Cournot economy rrespectve of whether a Stackelberg follower exsts or not, provded (a) demand s lnear, (b) the Stackelberg leader and Stackelberg follower produce perfect substtutes, and (c) the Stackelberg leader commts to ts quantty decson. All of these provsons are also assumed n our model (where the Stackelberg leaders and the Stackelberg follower are represented by the competng frms and the gray market, respectvely). These model assumptons provde some nsght as to why the frms quantty choces are nvarant to the gray market s exstence. Thus, when no gray market exsts, Q E q E, and all of the product produced n the emergng market s consumed locally. When gray markets are actve, Q E q G q E, and part of the emergng market quantty s sphoned off by the gray market leavng less product avalable for emergng market consumers. As we note above, the emergng market prcng functon n Equaton (2) s decreasng n the amount of product consumed locally by emergng market consumers, q E. Thus, we should expect strctly hgher emergng market prces, p E, for a gven set of nvestment levels x and x j when gray markets are actve, gven that the product consumed locally, q E, s strctly lower n a gray market settng. We obtan the equlbrum gray market quanttes by substtutng the second-stage solutons nto the best response functons n Equaton (4), whch yelds ( 6 j 2 {1, 2}): q G ð1 Eð2 3c þ c2 x ð2 3bc þ c 2 x j ð2b þ bc 2 3c 4ð4 5c 2 þ c 4 : ð7 Our man analyss proceeds as follows. We begn wth the followng two benchmark cases. (1) Frms cannot nvest to ncrease emergng market demand (.e., x = 0, = 1, 2). In ths settng, we calculate and compare frm profts when gray markets exst and when gray markets do not exst. (2) Market-creatng nvestments are possble, but there s no spllover (.e., b = 0). In ths settng, we complete the backward nducton by calculatng optmal nvestment levels n the frst stage of the game. We then calculate and compare frm profts when gray markets exst and when gray markets do not exst. Fnally, n our focal case, we analyze a stuaton wth both nvestments and spllovers. As n the prevous settng, we complete the backward nducton by calculatng optmal nvestment levels n the frst stage of the game, and then calculate and compare frm profts across dfferent settngs. We frst demonstrate that frms are strctly better off wthout gray markets Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

6 Autrey, Bova, and Soberman: When Gray s Good 6 Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety unless nvestment spllovers exst. We then characterze the condtons under whch both frms are better off wth gray markets when nvestments confer postve spllovers No Market-Creatng Investments and No Spllovers In the frst benchmark scenaro, frms cannot make market-creatng nvestments. To determne the mpact of gray markets n ths settng, we derve the equlbrum profts when gray markets are actve and when they are not. To facltate comparsons, we use the superscrpt GB to desgnate the benchmark settng wth gray markets and the superscrpt B to desgnate the benchmark settng wth no gray markets. We obtan the equlbrum quanttes for each frm by substtutng x = x j = 0 nto Equatons (6) and (7). We then substtute these equlbrum quanttes nto Equaton (5) to yeld the equlbrum proft: p GB 3 þ 2E þ 3E2 4ð2 þ c 2 ; 1; 2: ð8 When there s no nvestment or gray markets (.e., q G = 0, = 1, 2), the model s smply the standard dfferentated Cournot model, wth the followng well-known equlbrum profts: p B 1 þ E2 ; 1; 2: 2 ð2 þ c ð9 It s straghtforward to show that p B [ p GB for all c 2 (0, 1) and E 2 (0, 1). Therefore, n the absence of market-creatng nvestments, frms are strctly better off wthout gray markets Market-Creatng Investments and No Spllovers For the next benchmark scenaro, frms have the opton to nvest n market-creatng actvtes such as developng dstrbuton networks, lstngs, relatonshps wth foregn partners or perhaps smply advertsng. However, here, a frm s market-creatng nvestments have no effect on the compettor s demand (.e., b = 0). We denote the settng wth market-creatng nvestments but no spllovers wth the superscrpts GX and X, respectvely, to ndcate actve gray markets or no gray markets. To obtan the proft-maxmzng level of marketcreatng nvestment, we contnue wth backward nducton. Antcpatng the optmal quanttes obtaned n the second stage of the game wth actve gray markets, each frm now maxmzes Equaton (5) wth respect to x, subject to the equlbrum quanttes from Equatons (6) and (7). Substtutng n these constrants and takng frst-order condtons wth respect to x 1 and x 2, we solve to obtan the followng optmal nvestment level ( = 1, 2): x GX 2ð1 þ 3E 26 þ 4cð4 2c c 2 [ 0: ð10 The equlbrum quanttes for each frm are found by substtutng x GX 1 and x GX 2 nto the second-stage solutons n Equatons (6) and (7). Although q and Q E are strctly postve, for some parameter values q G can be negatve; these parameter values correspond to the stuaton n whch E þ x GX [ 1. In other words, for these parameter values the marketcreatng nvestment causes the emergng market to become larger than the domestc market. In that stuaton, the avalable arbtrage opportunty would be for the gray marketer to dvert product from the domestc market to the emergng market. To rule out ths possblty and ensure that q G 0, we make the techncal assumpton that E \ E GX 6þ4c 2c2 c 3. ð2 cð2þc 2 At the other end of the parameter contnuum, the arbtrage opportunty mght be so appealng that the gray marketer would lke to dvert more unts than are avalable n the emergng markets. To represent the upper bound of quantty avalable for dverson (.e., ), we make the addtonal techncal assump- q G Q E ton that E [ E GX 2 c 2. Another way to nter- ð5þ4cð4 c 2 pret ths assumpton s that the frm wll not enter an emergng market that supples only a gray marketer. Fnally, we obtan the equlbrum profts for each frm by substtutng n the optmal nvestment from Equaton (10) and all equlbrum quanttes nto Equaton (5): p GX 2 ð1 þ 3E 2 ð13 8c 2 þ c 4 þ ; 1; 2: 2 3ð2 þ c 3ð13 þ 8c 4c 2 2c 3 2 ð11 When there s no gray market dverson, each frm solves the frst-stage game for optmal nvestment as above, but usng q G = 0( = 1, 2) n place of Equaton (7). Ths yelds the optmal market-creatng nvestments and profts wthout gray markets ( = 1, 2): x X 2E 6 þ 4c 2c 2 [ 0; ð12 c3 p X 1 ð2 þ c 2 þ E2 ð12 8c 2 þ c 4 ð6 þ 4c 2c 2 c 3 2 : ð13 Our frst result compares the equlbrum levels of market-creatng nvestments and the equlbrum frm profts, wth and wthout actve gray markets. The feasble regon n ths settng conssts of all E 2ðE GX ;E GX ; c 2ð0;1; and b = 0. Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

7 Autrey, Bova, and Soberman: When Gray s Good Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety 7 In a settng wthout nvestment spllovers: 1. Each frm spends more on market-creatng nvestments when gray markets are actve (.e., x GX [ x X ; 1; 2). 2. Each frm s strctly worse off when gray markets are actve (.e., p GX \ p X ; 1; 2). PROPOSITION 1. PROOF. All proofs are n the Onlne Appendx. Note that each frm s nvestment n the emergng market s strctly larger when gray markets exst. Ths outcome arses because gray markets provde each frm wth an added ncentve to ncrease emergng market demand. By nvestng more to ncrease demand, not only does each frm ncrease the emergng market consumpton for ts product, t also lmts the gray market s arbtrage opportunty by ncreasng ts cost base. Whle these larger nvestments result n greater emergng market profts for each frm, these ncreased profts are not enough to outwegh the costs related to gray market cannbalzaton n the domestc market. Ths leads to both frms beng strctly worse off n an economy wth gray markets when nvestments confer no spllovers on a rval s demand Market-Creatng Investments and Spllovers In ths subsecton, we present the man model. Here, both frms can nvest n market-creatng actvtes n the emergng market, and nvestments ncrease not only the focal frm s demand but also the compettor s demand. Specfcally, we defne the spllover effect for Frm as an ncrease n the emergng market demand ntercept of b 2 (0, 1] tmes the nvestment choce of ts rval, x j. We solve the frst-stage game exactly as n the prevous subsecton, except that we do not restrct the spllover parameter b to zero. We denote the settngs wth market-creatng nvestments and spllovers wth the superscrpts Gb and b, respectvely, to ndcate actve gray markets or no gray markets. When gray markets are actve, the optmal nvestment level s as follows ( = 1, 2): x Gb ð1 þ 3Eð2 bc 26 3bð2 cþ3b 2 c þ 4cð4 2c c 2 [ 0: ð14 Smlar to the prevous subsecton, we agan mpose two techncal assumptons to ensure that equlbrum gray market quanttes are non-negatve (.e., q G 0), and that they do not exceed the avalable supply (.e., q G Q E ). Accordngly, we restrct and E\E 2ð3 bþð1 þ bbc þ cð4 2c c2 ð2 cð2 þ c 2 E [ E 2 2b þ bcð1 þ b c2 ð5 þ 4cð4 c 2 respectvely. Fnally, we obtan the equlbrum profts for each frm by substtutng n the equlbrum nvestment and all equlbrum quanttes nto Equaton (5): p Gb 2 3ð2 þ c 2 þ ð1 þ 3E2 ½52 þ 12bc c 2 ð32 þ 3b 2 þ4c 4 Š 3½26 3bð2 cþ3b 2 c þ 4cð4 2c c 2 Š 2 ; 1; 2: ð15 When there s no gray market dverson (.e., q G = 0, = 1, 2), the optmal market-creatng nvestments and profts are as follows ( = 1, 2): x b Eð2 bc 6 bð2 cþb 2 [ 0; ð16 c þ cð4 2c c 2 p b 1 ð2 þ c 2 þ E 2 ½12 þ 4bc c 2 ð8 þ b 2 þc 4 Š ½6 bð2 cþb 2 c þ cð4 2c c 2 Š 2 : ð17 Comparng the equlbrum levels of market-creatng nvestments wth and wthout actve gray markets, we agan fnd that each frm nvests more when facng actve gray markets. However, n contrast to subsecton 3.2, profts can be hgher or lower when there are gray markets. We characterze the parameter regon n whch frms are better off wth gray markets n Proposton 2. The feasble regon n ths settng conssts of all E 2 (E, E), c 2 (0, 1), and b 2 (0, 1]. PROPOSITION 2. Let b * = c/2. In a settng wth marketcreatng nvestments and spllovers: 1. Each frm spends more on market-creatng nvestments when gray markets are actve (.e., x Gb [ x b ; 1; 2). 2. Provded b > b *, there exsts a boundary E * such that each frm s strctly better off wth gray markets (.e., p Gb [ p b ; 1; 2) for all feasble E>E *. When b b *, the frms are weakly worse off wth gray markets (.e., p Gb p b ; 1; 2) for all feasble E. Proposton 2 presents the overall effect of several competng forces. On one hand, the gray market Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

8 Autrey, Bova, and Soberman: When Gray s Good 8 Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety ncreases the number of compettors n the domestc market, whch lowers each frm s profts n the domestc market. In addton, each frm nvests more n the emergng market when gray markets are present, and those market-creatng nvestments are both costly and ncreasng n the nvestment sze. On the other hand, market-creatng nvestments help the frm n two ways. Frst, frm nvestments ncrease the market-clearng prce n the emergng market, whch ncreases proft n the emergng market. Second, frm nvestments also ncrease the gray market s cost base whch reduces ts compettveness n the domestc market and leads to less cannbalzaton of domestc profts. When nvestment spllovers are non-exstent, as n Proposton 1, the negatve forces domnate, and frms are strctly better off n an economy wthout gray markets. Conversely, n a settng where each frm s market-creatng nvestments have spllover effects, ether the negatve or postve forces can domnate, as shown n Fgure 2. Ths outcome s drven by the postve externalty conferred on each compettor s demand n the emergng market. Ths postve nvestment externalty not only makes the emergng market demand larger for each frm than n a settng wth no nvestment spllovers (e.g., x Gb þ bx Gb j [ x GX, for all feasble c, b, E) but, mportantly, allows each frm to more effcently buld ts own market. In other words, the return on nvestment, measured as the rato of the ncrease n market demand relatve to the cost to ncrease demand, s hgher when nvestments confer spllovers than when nvestments confer no spllovers (e.g., ðx Gb þ bx Gb j =ðx Gb 2 [ x GX =ðx GX 2 ; for all feasble c, b, E). As b ncreases, so does the effcency of the frm s nvestment, and the benefts of gray markets (.e., hgher emergng market consumpton and gray market cost base) eventually outwegh the costs of gray markets (.e., cannbalzaton of domestc Fgure 2 E Wth Investment Spllover of b = 1, the Feasble Regon s Between the Sold Lnes. Frms are Better Off wth Gray Markets Between E * (Dashed Lne) and E Gb Infeasble Regon Prefer Gray Market Prefer No Gray Market E Gβ Infeasble Regon 0.0 γ E Gβ E product and larger nvestments costs). When the spllover effect s suffcently large (.e., b > b * = c/2), each frm may be better off wth gray markets than wthout them. Thought of n economc terms, each frm nvests untl the margnal return from nvestment equals the margnal cost of nvestment. When a gray market s ntroduced wth no spllovers, the margnal return for a gven nvestment level ncreases because the nvestment reduces cannbalzaton n the domestc market. When there are spllovers, the margnal return for a gven nvestment level ncreases not only because of cannbalsm reducton but also because the other frm nvests more and that makes the focal frm s nvestment more valuable. We note that the threshold b * ncreases n the substtutablty parameter, c. The ntuton behnd ths result s straghtforward. Because hgher c (.e., the level of substtutablty between the competng frms products) leads to more cannbalzed domestc sales for both the focal frm and ts rval, as c approaches 1 (.e., each frm produces a near perfect substtute), the aggregate negatve forces assocated wth gray markets ncrease, resultng n a correspondngly hgher threshold b * over whch the benefts from gray markets wll outwegh the costs from the gray market. Fnally, condtonal on b > b *, both frms are better off wth gray markets provded the emergng market s large enough (.e., E > E * ). The smaller the emergng market, the lower the emergng market retal prce and, n turn, the lower the gray market s cost base. A lower cost base allows the gray marketer to be more compettve n the domestc market leadng to more cannbalzed sales from the domestc frm. For suffcently low E, the larger market-creatng nvestments brought on by the gray market s exstence do not ncrease the gray market s cost base enough to outwegh the negatves of gray market cannbalzaton. Once E > E *, however, the emergng market s large enough such that, followng each frm s nvestment, the gray market becomes suffcently uncompettve and both frms are better off wth gray markets. 4. Model Extensons 4.1. Complementary Goods and Investments In the prevous secton, our results show that frms are better off wth gray markets provded there are suffcent postve externaltes (.e., spllovers) generated when frms make market-creatng nvestments n the emergng market. In our frst extenson, we demonstrate the model s robustness to a dfferent source of postve externalty, complementary goods. Specfcally, we consder a settng n whch the focal frm nvests n the emergng market and the economy s characterzed by products that are complements as Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

9 Autrey, Bova, and Soberman: When Gray s Good Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety 9 opposed to substtutes. When products are complements, any market-creatng nvestment for one frm s product also ncreases demand for the other frm s product. To analyze a settng wth complementary goods and no spllovers, we use the model from subsecton 3.2 (.e., a market where b = 0) but assume that the frms produce complements (.e., c 2 ( 1, 0)) nstead of substtutes. Note that all of the optmal nvestments, quanttes, and profts are dentcal to those n subsecton 3.2, except that we now consder outcomes over the range c 2 ( 1, 0) as opposed to c 2 (0, 1). The feasble regon n ths settng conssts of all E 2ðE GX ;E GX ; c 2ð 1; 0; and b = 0. PROPOSITION 3. In a settng wth complementary products and market-creatng nvestments wth no nvestment spllovers: 1. Each frm spends more on market-creatng nvestments when gray markets are actve (.e., x GX [ x X ; 1; 2). 2. There exsts a boundary E ** such that each frm s strctly better off wth gray markets for all feasble E>E ** and weakly worse off wth gray markets for all feasble E E ** (.e., p GX [ p X ; 1; 2 f and only f E > E ** ). Ths result s drven by the same forces as the spllover results n Proposton 2. Specfcally, n an economy wth complementary products, when a focal frm nvests n the emergng market, there s a postve externalty generated on ts compettor s demand. Smlar to a settng wth nvestment spllovers, provded the emergng market s large enough, ths postve externalty leads to larger, more cost-effcent nvestments for each frm, and each frm s better off wth gray markets than wthout them. To provde addtonal ntuton for how postve nvestment externaltes can lead to frms beng better off wth gray markets, we contrast the results from Propostons 1 and 3. In both settngs, market-creatng nvestments create no spllovers (.e., b = 0). In the frst settng, frms produce substtute goods. In the second settng, nvestments confer a postve externalty on a rval s demand through the complementary nature of the products. As can be seen n Fgure 3, n a market wth no nvestment spllovers, frms are strctly worse off wth gray markets f they produce substtutes. If frms produce complements, however, there exsts an emergng market sze threshold above whch both frms are better off wth gray markets. These results echo our fndngs n Proposton 2, and broaden the reach of our results from nvestment spllovers n partcular to postve nvestment externaltes n general Endogenzng the Gray Market The orgnal model exogenously determned whether the gray market exsted or not. We now extend the model to consder the outcomes when each frm has the ablty to stop the gray market for ts own product wthout cost. To analyze ths scenaro, we return to our man model of nvestment spllovers from subsecton 3.3, and consder whether a frm mght prefer to stop ts own gray market and free rde on the spllover effects of a compettor s market-creatng nvestments. To endogenze the gray market, we nclude an addtonal decson at the begnnng of the game as shown n Fgure 4. Specfcally, each frm now chooses whether to stop the gray market for ts own product wthout cost. We denote the strategy combnatons of Frms 1 and 2 by superscrpts {s 1, s 2 }, where G mples that the frm has allowed the gray market for ts product and N means that the frm has decded not to allow the gray market for ts product. For tractablty, we fx b n ths settng. We present the analyss for b = 1 because t results n the least cumbersome expressons mathematcally, but note that our results are robust to settng b to other values. Usng backward nducton, we solve the game wth the addton of the new frst stage. Note that all of the optmal nvestments, quanttes, and profts when ether both frms allow or both frms do not allow the gray market are dentcal to those n subsecton 3.3, and thus p Gb j b1 p GG and p b j b1 pnn. The feasble regon n ths stuaton conssts of all E 2 (E, E), c 2 (0, 1), and b = 1. We also analyze the model wth the frms makng asymmetrc decsons n the frst stage. Wthout loss of generalty, we assume that Frm 1 chooses not to allow the gray market and Frm 2 chooses to allow the gray market. We obtan p NG usng the same procedure Fgure 3 Wth No Investment Spllovers, the Feasble Regon s Between the Sold Lnes. Frms are Better Off wth Gray Markets Between E ** (dashed lne) and E GX Prefer Gray Market Infeasble Regon Prefer No Gray Market E E GX Infeasble Regon γ E Prefer No Gray Market E GX Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

10 Autrey, Bova, and Soberman: When Gray s Good 10 Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety Fgure 4 Tmelne for Endogenous Gray Markets Each frm chooses whether or not to costlessly stop the gray market. Each frm chooses x, the amount by whch to grow emergng market demand. Each frm smultaneously chooses q, the quantty to be sold n the domestc market and Q E, the total quantty to be sold n the emergng market. The gray marketer chooses q G1 and q G2, the amount of gray market product to be bought n the emergng market and sold n the domestc market. as before, except that n stage 4, the gray market s constraned to choose q G1 = 0 and chooses only q G2 to maxmze Equaton (3). The resultng equlbrum nvestments and quanttes n the asymmetrc case are as follows: q NG 1 8 c 4c2 þ cð1 cðe þ x 1 þ x 2 ð2 þ cð8 5c 2 ; ð18 q NG c2 c 3 c 2 ð1 cðe þ x 1 þ x 2 2ð2 þ cð8 5c 2 ; ð19 Q NG E1 Q NG E2 cð1 cþð8 c 4c2 ðe þ x 1 þ x 2 ð2 þ cð8 5c 2 ; ð20 c2 ð1 cþð16 9c 2 c 3 ðe þ x 1 þ x 2 2ð2 þ cð8 5c 2 : ð21 Solvng the second-stage game yelds the equlbrum nvestment levels: 16 þ 32c 2c 2 36c 3 22c 4 þ 12c 5 þ 9c 6 x NG þe c 312c 2 þ 56c 3 þ 112c 4 12c 5 9c 6 1 2ð288 þ 544c 244c 2 660c 3 49c 4 þ 202c 5 þ 54c 6 ; x NG 2 ð22 48 þ 32c 102c 2 4c 3 þ 44c 4 8c 5 c 6 þe c 2 16c 3 þ 66c 4 þ 8c 5 þ c 6 2ð288 þ 544c 244c 2 660c 3 49c 4 þ 202c 5 þ 54c 6 : ð23 The resultng equlbrum frm profts for asymmetrc decsons, p NG 1 ð p GN 2 and p NG 2 ð p GN 1, are lengthy expressons and are provded n the Onlne Appendx. Parallelng subsecton 3.3, we agan mpose two techncal assumptons to ensure that the equlbrum gray market quantty for the frm that chooses to allow the gray market s non-negatve (.e., q G2 0), and that the frm s gray market does not exceed the avalable supply n the emergng market (.e., q G2 Q E2 ). The restrctons are E \E NG 2 1 ð2 þ c 2 and E [ E NG 1 þ 1 4ð5 4c þ 2 þ c 9ð8 5c c 231c2 þ 9ð 40 þ 22c 2 þ 3c 3 respectvely. These feasblty regon boundares are somewhat more restrctve than the condtons of subsecton 3.3. In partcular, Ej b1 E NG and Ej b1 \ E NG. Therefore, the feasble regon for the next proposton conssts of all E 2ðE NG ;E NG ; c 2ð0; 1; and b = 1. Wthn the feasble regon, we fnd that each frm s equlbrum proft can be hgher by allowng the gray market to exst, whether ts rval chooses to stop or allow the gray market to operate (.e., there are settngs where both p GG [ p NG and p GN [ p NN ; 1; 2). Proposton 4 characterzes the parameter regon n whch there s a unque, pure strategy equlbrum where both frms are better off allowng gray markets. PROPOSITION 4. There exsts a boundary E / n the feasble regon. For all feasble E > E /, there s a unque, pure strategy equlbrum n whch both frms allow the gray market for ther respectve products to exst. Proposton 4 states that, even f ether frm had the ablty to costlessly stop ts own gray market, provded the emergng market s large enough, each frm has an ncentve to allow ts own gray market to contnue. Ths result obtans because market-creatng nvestments are strctly larger for both frms when gray markets exst for both products, than f gray markets exst for one product or nether product. Note that allowng the gray market to contnue when t could be stopped allows the frm to credbly commt to a hgher nvestment level. In turn, ths allows for better nvestment coordnaton between a frm and ts rval. Fnally, ths result also provdes another perspectve on why frms may not mplement management control systems meant to mtgate gray market dstrbuton, even f mplementng such control systems were costless. Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254

11 Autrey, Bova, and Soberman: When Gray s Good Producton and Operatons Management 0(0), pp. 1 13, 2014 Producton and Operatons Management Socety Competton n the Gray Market To assess whether the lack of competton n the gray market nsttuton drves the results n the man model, we extend the model to allow competng gray market frms. We return to the man settng wth nvestment spllovers and the tmelne of Fgure 1. However, we now assume that two gray marketers exst, and that each gray marketer specalzes n obtanng and resellng the product of a sngle manufacturer. The addtonal gray marketer ntensfes competton n the domestc market, leadng to ncreased cannbalzaton of domestc products compared to a settng where one gray marketer supples both products. To smplfy the expressons for a crsper presentaton, we set c = 1 for ths subsecton; however we note that the results are robust for all c 2 (0, 1). We denote the settng wth multple gray marketers wth the superscrpt 2Gb. We agan analyze the model of subsecton 3.3, usng the same procedure as before, except that n stage 3, each gray marketer smultaneously chooses the quantty q G, as follows: Max qg p G q G ðp p E ; 1; 2 ð24 subject to demand condtons gven n Equatons (1) and (2). The resultng optmal gray market quanttes are as follows ( 6 j 2 {1, 2}): q 2Gb G 1 1 q q ;q j ;Q E ;Q Ej ð Q E q j Q Ej : 6 E þ x ð2 b x j ð1 2b ð25 Usng backward nducton, n the second stage game, we determne the manufacturers equlbrum quanttes to be ( 6 j 2 {1, 2}): q 2Gb 1 6 ð2 3x ð1 bþ3x j ð1 b; ð26 Q 2Gb E 1 6 ð2e þ x ð7 5b x j ð5 7b: ð27 Solvng the frst stage game yelds the followng equlbrum nvestment levels by each manufacturer ( = 1, 2): x 2Gb 1 þ 11E þ b 7Eb 43 4b þ 7b 2 [ 0: ð28 We agan requre two techncal assumptons to ensure that equlbrum gray market quanttes are non-negatve (.e., q G 0), and that they do not exceed the avalable supply (.e., q G Q E ). Accordngly, we compute the feasble regon and restrct E \ 1 9 ð7 b þ b2 E 2Gb and E [ 2 b 21 E 2Gb. The feasble regon for ths settng conssts of all E 2ðE 2Gb ;E 2Gb ; c 1; and b 2 (0, 1]. Proposton 5 confrms that our man model s results do not depend on a sole gray market frm. PROPOSITION 5. Let b * = c/2. In a settng wth two gray marketers, market-creatng nvestments, and spllovers: 1. For all feasble regons, each frm spends more on market-creatng nvestments when gray markets are actve (.e., x 2Gb [ x b ; 1; 2). 2. Provded b > b *, there exsts a boundary E d such that each frm s strctly better off wth gray markets (.e., p 2Gb [ p b ; 1; 2) for all feasble E > Ed. When b b *, the frms are weakly worse off wth gray markets (.e., p 2Gb p b ; 1; 2) for all feasble E Prce Competton The analyss of the man model and extensons consder a standard Cournot Stackelberg game. However, there are stuatons (e.g., dsclosure choce, transfer prcng) where recastng a Cournot model as dfferentated Bertrand competton leads to dfferent conclusons. These alternate conclusons often arse as quanttes are strategc substtutes n a Cournot game whereas prces are strategc complements n a Bertrand game. Thus, t s mportant to assess whether nferences developed under one type of competton contnue to hold under another. We denote the prce competton settng wth the superscrpts Gh and h, respectvely, to ndcate actve gray markets or no gray markets. When gray markets are actve, recastng the model n a Bertrand settng presents practcal challenges. Specfcally, the Bertrand model breaks down because the gray market frm produces a perfect substtute to ts domestc counterpart and has a hgher cost base. In such a settng, the optmal soluton for the orgnal manufacturer would be to lower ts prces n the domestc market to a level margnally below the gray market compettor s cost (.e., the retal prce n the emergng market) to preclude any arbtrage opportunty. Ths reasonng suggests that gray markets should not be observed when frms compete n prces and the gray marketed product s a perfect substtute for the authorzed product. Nevertheless, gray markets are observed n categores characterzed by prce settng competton. Accordngly, we model the gray market n ths context by assumng that the gray marketer s a prce taker rather than a prce setter, smlar to the approach of Gaskns (1971). We model the gray market as a prcetakng, compettve frnge player that ncurs a quadratc cost to purchase stock. Importantly, we confrm that the tenor of the Cournot results contnue to hold n a Bertrand settng. Specfcally, we fnd that: (1) for all feasble regons, each Please Cte ths artcle n press as: Autrey, R. L., et al. When Gray s Good: Gray Markets and Market-Creatng Investments. Producton and Operatons Management (2014), do /poms.12254