Quality in Supply Chain Encroachment

Transcription

1 Quality in Supply Chain Enroahment Albert Ha, Xiaoyang Long, Javad Nasiry Shool of Business and anagement, Hong Kong University of Siene and Tehnology, Clear Water Bay, Kowloon, Hong Kong. imayha, xlongaa, We study a supply hain with manufaturer enroahment in whih prot quality is endogenous and ustomers have heterogeneous preferenes for quality. It is known that, when quality is exogenous, enroahment ould make the retailer better-off. Yet when quality is endogenous and the manufaturer has enough flexibility in adjusting quality, we find that enroahment always makes the retailer worse-off in a large variety of senarios. We also establish that, while a higher manufaturer s ost of quality hurts the retailer in absene of enroahment, it ould benefit the retailer with enroahment. In addition, we show that a manufaturer offering differentiated prots through two hannels prefers to sell its high-quality prot through the diret hannel. Contrary to onventional wisdom, quality differentiation does not always benefit either manufaturer or retailer. Our results may explain why, despite extant theoretial preditions, retailers almost always resent enroahment. These findings also suggest that firms must be autious when adopting quality differentiation as a strategy to ease hannel onflit aused by enroahment. Key words : enroahment, quality differentiation, al-hannel supply hain 1. Introtion Enroahment ours when the upstream manufaturer in a supply hain sells diretly to onsumers, thereby ompeting with its retail partners in the downstream market. Given the reent advanes in e-ommere, enroahment is now a viable strategy for manufaturers to inrease profit. If ill managed, however, enroahment ould severely damage the relationship between supply hain partners (Wall Street Journal 1995). For example, when Bass Ale launhed a home delivery program, the supplier s top distributer retaliated by pulling all Bass prots off its shelves (Kinsey 1997). To reassure retail partners of Hewlett-Pakard s ommitment to them, the ompany s CEO promised that diret selling behavior will not be tolerated (The Channel 2013). To mitigate hannel onflit, a manufaturer rather than forgoing the diret hannel entirely may offer different prots through different hannels (Kinsey 1997). any manufaturers implement this strategy via quality differentiation. Eureka Forbes Ltd., 1

2 2 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment whih proes vauum leaners, sells its premium brand diretly and its base models through retailer hannels (Sridharan et al. 2012). Kendall-Jakson uses its online hannel to sell high-end wines, suh as Artisans & Estates, that are usually of higher quality than those available in retail stores (Kinsey 1997). Dell and Toshiba have developed exlusive high-end personal omputers, whih are generally of higher quality than their regular prot offerings, for retail partners like Best Buy and Ciruit City (Wall Street Journal 2007). In the apparel instry, retailers inreasingly demand exlusive prots from designers who also reate items for their own boutique stores (Wall Street Journal 2011). Clothing ompanies suh as Ralph Lauren, the Armani Group, Hugo Boss, and Baravade have all developed exlusive lines for department stores or their own stores. In the literature, the enroahment problem is usually studied under the assumption that quality is exogenous and uniform aross hannels (e.g., Chiang et al. 2003, Arya et al. 2007, Cai 2010, Li et al and 2015). A wholesale prie ontrat is ommonly adopted in a manufaturer-retailer relationship. It is known that a lower wholesale prie inreases the retailer hannel s profit by reating a higher demand, but it alloates a smaller portion of that hannel profit to the manufaturer. While assuming that the enroahing manufaturer s selling ost is higher than that of the retailer, Arya et al. (2007) show that enroahment ines the manufaturer to lower the wholesale prie in order to stimulate demand in the retailer hannel, even though this omes at the expense of extrating a smaller portion of hannel profit. This wholesale prie effet is more pronouned when the manufaturer s ost disadvantage is greater. Due to ompetition, enroahment rees the retailer hannel s profit; however, it gives the retailer a larger share of that profit beause of the wholesale prie effet. When the manufaturer s ost disadvantage is large, enroahment ould lead to a win win outome beause the wholesale prie effet dominates the ompetition effet for the retailer. Yet when the ost disadvantage is small, enroahment hurts the retailer and a win lose outome ours. Enroahment involves signifiant manufaturer investments in establishing the diret hannel and adopting retail praties. Hene it is a longer-term deision than the quality deision, whih is made more frequently (for instane, in eah prot life yle). It is therefore possible that quality is endogenous when a manufaturer deides whether or not to enroah. In pratie, many manufaturers have adopted quality differentiation as

3 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 3 a strategy to mitigate hannel onflit e to enroahment. To the best of our knowledge, neither the role of quality in enroahment nor the issue of quality differentiation in a al-hannel setting has been explored in the literature. We hope to fill these gaps by addressing the following researh questions: (1) how would quality being endogenous affet the manufaturer s enroahment deision and its impat on firm profits? (2) how should an enroahing manufaturer differentiate in terms of quality? (3) how would quality differentiation affet firm profits? We onsider a supply hain with a manufaturer (she) selling to a retailer (he). If the manufaturer enroahes, she has a selling ost disadvantage and engages in Cournot ompetition with the retailer. Our model extends Arya et al. (2007) by allowing the onsumers to have heterogeneous preferenes for quality, whih is an endogenous deision made by the manufaturer. In the basi model, we assume that the quality ost funtion is quadrati and the manufaturer has the flexibility of hoosing any quality level. We onsider two ases depending on whether she an quality differentiate aross the two hannels. Suppose the manufaturer annot quality differentiate. When quality is endogenous, besides the ompetition and wholesale prie effets that exist in Arya et al. (2007), enroahment has a quality distortion effet: it ines the manufaturer to distort quality to shift demand to the retailer hannel. Similar to the ase of exogenous quality, wholesale prie effet here means that enroahment ines the manufaturer to adjust the wholesale prie to stimulate the retailer hannel s demand at the expense of extrating a smaller portion of hannel profit, but the wholesale prie is not always lower than that without enroahment beause quality may hange too. When the manufaturer an distort quality, she relies less on adjusting the wholesale prie to influene the retailer s demand and sets it more aggressively for hannel profit extration. Therefore the wholesale prie effet beomes weaker. When the manufaturer s selling ost disadvantage is small, the negative ompetition effet dominates and makes the retailer worse-off. When the manufaturer s selling ost disadvantage is large, the negative ompetition and quality distortion effets together again make the retailer worse-off. Therefore, when quality is endogenous, enroahment always hurts the retailer in the basi model. This result is robust and holds regardless of whether firms make quantity deisions sequentially or simultaneously, whether the manufaturer an segment the market through only the retailer, and whether the ost of quality is fixed or variable.

4 4 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment It is optimal for the manufaturer to enroah when either she has a small ost disadvantage or her ost of quality is low. oreover, if there is enroahment then the retailer is better-off when either the manufaturer has a larger selling ost disadvantage or her ost of quality is higher. The effet of the selling ost disadvantage is intuitive. As the manufaturer s ost of quality inreases, she must rely more on adjusting the wholesale prie to stimulate the retailer s demand and the wholesale prie effet beomes stronger. This hinders the manufaturer s ability in extrating hannel profit and makes it more ostly for her to enroah; hene she prefers not to do so unless her ost of quality is low. A stronger wholesale prie effet benefits the retailer, whih explains why he is better-off if the manufaturer s ost of quality is higher. This setting ontrasts with that of no enroahment, where the retailer is always worse-off if the manufaturer s ost of quality inreases. Now suppose the manufaturer an quality differentiate. In pratie, many enroahing manufaturers quality differentiate aross hannels, whih is onsistent with the onventional wisdom that hannel onflit an be eased when different prots are offered in different hannels (Kinsey 1997). Yet we show that quality differentiation aross hannels does not always benefit the manufaturer or the retailer, and it is not a panaea for hannel onflit resulting from enroahment. Consider first the manufaturer. If it is optimal to quality differentiate, the manufaturer always prefers to sell the high-quality prot (whih has a higher profit margin) diretly beause in that way she aptures all the revenue of the high-quality prot. A higher level of quality differentiation enables the manufaturer to ahieve a higher supply hain profit via market segmentation, but it also diminishes her ost disadvantages and shifts demand from the retailer hannel to the diret hannel. In determining the level of quality differentiation, the manufaturer faes a tradeoff between the benefit of market segmentation and the ost of selling less through the more effiient retailer hannel. As the manufaturer s selling ost disadvantage inreases, she lowers the level of quality differentiation to shift demand to the retailer hannel. When her selling ost disadvantage is large enough, the hannel ineffiieny effet dominates and it is optimal for her not to quality differentiate at all. When the manufaturer s ost of quality inreases, market segmentation via quality differentiation beomes more expensive and it is optimal for her not to quality differentiate. Now onsider the effet of quality differentiation on the retailer. Suppose the manufaturer s selling ost disadvantage is small. Without quality differentiation, the manufaturer

5 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 5 uses the wholesale prie to nullify her selling ost disadvantage and aptures most of the demand. Quality differentiation benefits the retailer beause it allows him to inrease his demand by fousing on the low-end market segment. Suppose the manufaturer s selling ost disadvantage is large. Quality differentiation now hurts the retailer beause his demand is lowered e to the quality disadvantage. Our results imply that quality differentiation eases hannel onflit aused by enroahment (though not eliminating it entirely beause enroahment still hurts the retailer) when the manufaturer s selling ost disadvantage is small, but exaerbates it otherwise. By having quality differentiation as another lever, the manufaturer relies less on adjusting the wholesale prie to influene the retailer s demand and sets it more aggressively for hannel profit extration. As a result, the wholesale prie effet is weakened and, as before, enroahment always hurts the retailer. Finally, we onsider an extension where the manufaturer an hoose only quality levels that are not lower than a base level. If the manufaturer s ost of quality is low, the retailer always loses from enroahment. Otherwise, similar to Arya et al. (2007), enroahment ould lead to a win win outome when the manufaturer s selling ost disadvantage is neither too small nor too large. Based on numerial examples, we show that a win win outome is more unlikely to our when either the base quality level or the base unit protion ost (i.e., the unit ost of proing the base quality level) is low. Our results altogether demonstrate that the retailer always loses from enroahment if the manufaturer has enough flexibility in hanging quality (i.e., ost of quality, base quality level or base unit protion ost is low). These are settings where the prot quality an vary greatly and where the basi prot funtion as well as the assoiated protion ost are low. We believe that this applies to many instries. The apparel instry is a partiularly suitable example beause the protion ost an be extremely low whereas the quality range ould be very wide. For instane, the ost of making a polo shirt an be from as low as $1 or $2 to over $29 (Wall Street Journal 2012). Another example is the onsumer eletronis instry. The unit protion ost of a smartphone has fallen so muh that a fully funtional one osts just about $43 (The Telegraph 2014, Daily ail 2014). Lenovo, whih sells smartphones through both retail and online hannels, offers phones that vary widely in quality and prie (a budget model at less than $100 to a high-end model at about $560). Other onsumer eletroni prots (e.g., tablets

6 6 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment and blue-ray players) and small home applianes (e.g., hair dryers, eletri heaters and vauum leaners) also display similar harateristis. Our model, however, would not be appliable to prots with high base quality levels and osts suh as eletri ars and ompressor-driven refrigerators. 2. Literature Review Our paper relates to the literature on al-hannel supply hains. Chiang et al. (2003) find that, when onsumers do not strongly prefer the diret hannel over the retailer hannel, the manufaturer s threat of launhing its own diret hannel ould lead to gains for both hannels. Tsay and Agrawal (2004) show that the introtion of a diret hannel an benefit both manufaturer and retailer, provided the former is not too ineffiient in stimulating demand through sales effort. Cattani et al. (2006) demonstrate that the manufaturer ould use priing strategies (e.g., promising not to underut the retailer) as a means of mitigating ompetition and inreasing benefits for both firms, espeially when the diret hannel is ostly. Dumrongsiri et al. (2008) find that the manufaturer may be better-off establishing a diret hannel when demand variability is low. Finally, Arya et al. (2007) show that if an enroahing manufaturer has a selling ost disadvantage relative to the retailer, then the manufaturer has an inentive to lower the wholesale prie to maintain the retailer hannel s demand; if the selling ost disadvantage is large enough, the downstream retailer would also benefit from enroahment a win win outome. Similarly, Cai (2010) finds that a win win outome arises when the retailer hannel has a suffiient advantage in base demand or operational ost over the diret hannel. Li et al. (2014 and 2015) extend Arya et al. s model to inorporate asymmetri information and show that, when the retailer has private information about demand, enroahment ould lead to win win, win lose, lose win, or lose lose outomes. Our work differs from these papers in two aspets. First, we onsider prot quality as an endogenous deision and show that it leads to qualitatively different results. Seond, these papers assume that hannel differentiation is exogenous. For instane, onsumers may have a given preferene for one hannel over the other, or a hannel may be assoiated with higher osts. We onsider endogenous hannel differentiation; that is, the manufaturer an hoose to differentiate the hannels by varying the prot quality offered through eah hannel. Our work also relates to the literature on a firm s quality deision in the presene of heterogeneous onsumers. oorthy (1988) studies firms vertial positioning strategies in a

7 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 7 opoly with variable quality ost. Chambers et al. (2006) provide a review of the extensive work in eonomis and marketing on quality-based ompetition; these authors observe that the defining harateristi of quality is that the marketplae onsists of indivials who all agree that a higher level is always preferable to a lower level. We onsider vertial differentiation with either variable or fixed quality ost in a framework similar to that used in otta (1993). There are a number of papers addressing the effet of hannel deentralization on prot quality. Jeuland and Shugan (1983) and Eonomides (1999) were the first to establish that quality should be lower (or the same) in deentralized hannels. Xu (2009) extends this result to show that the reverse may hold depending on the marginal revenue funtion. Shi et al. (2013) examine the ase of vertial and horizontal onsumer heterogeneity. They find that the effet of hannel deentralization on prot quality is sensitive to the distribution of onsumer preferenes. Our work differs from these papers in that, instead of omparing entralized versus deentralized hannels, we examine the ase where both hannels exist simultaneously for one manufaturer and show that prot quality under enroahment ould be either higher or lower depending on the selling ost in the diret hannel. 3. odel and Benhmark Analysis In this setion, we outline the basi model and investigate a benhmark ase with no enroahment. We study enroahment in Setions 4 and 5 and ompare the results with the benhmark ase Basi odel Consider a market, with size normalized to 1, that onsists of onsumers with heterogenous preferenes for quality. A manufaturer (she) sells a prot through a retailer (he) but may also establish her own hannel to sell diretly to onsumers. A onsumer s surplus from purhasing the prot with quality u > 0 and prie p is U(u, p; θ) = θu p, where θ represents the onsumer s sensitivity to quality. We model onsumer heterogeneity by assuming that θ is uniformly distributed on [0, 1] (Ronnen 1991, Lehmann-Grube 1997). If there is only one prot of quality u in the market, then a onsumer with sensitivity θ is indifferent between buying and not buying when θu p = 0. Therefore, all ustomers with θ p/u would buy the prot. Hene demand is q = 1 p/u, whih yields the inverse demand funtion p = u(1 q).

8 8 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment We assume that the manufaturer s unit ost for making a prot with quality level u is ku 2, where k > 0 aptures the manufaturer s ost of quality. This funtional form implies that the manufaturer an hoose any quality level, and it has been extensively used in the literature (e.g., oorthy and Png 1992). In Setion 6.4, we onsider a more general ost funtion under whih the manufaturer has less flexibility in hoosing the quality level. Similarly to Arya et al. (2007), we assume that the manufaturer inurs a selling ost 0 for every unit of prot sold through the diret hannel and normalize the retailer s selling ost to 0. This diret selling disadvantage ould be e to inexperiene, lak of onsumer knowledge, or the additional ost of e-ommere (The Eonomist 2013, Wall Street Journal 2014). Finally, we assume that onsumers an aurately pereive prot quality. The timeline is as follows: (i) the manufaturer deides on the quality level(s) of the prot and the wholesale prie w; (ii) after observing the quality level(s) and w, the retailer deides on his order quantity q R ; (iii) if a diret hannel exists, then the manufaturer deides on the quantity q that she will sell diretly. This deision sequene entails three models: no enroahment, enroahment with uniform quality, and enroahment with quality differentiation. Without enroahment, the manufaturer sells the prot of quality u through the retailer hannel only. If a diret hannel exists and only one type of prot is sold (enroahment with uniform quality) then, after reeiving the retailer s order, the manufaturer deides on the quantity she wants to sell diretly. Both firms fae the same market-learing prie. We assume that quantity deisions are made sequentially beause the manufaturer an observe the retailer s order deision whereas the manufaturer s own quantity deision is usually unknown to the retailer. In other words, the manufaturer annot redibly ommit to not hanging her quantity after reeiving the retailer s order. (In Setion 4.2, we study the ase in whih the manufaturer and the retailer make simultaneous quantity deisions.) Finally, the manufaturer an deide to quality differentiate by offering prot of quality u through the diret hannel and prot of quality tu, t > 0, through the retailer (enroahment with quality differentiation). The model of enroahment with uniform quality orresponds to the ase where it is not pratial for the manufaturer to offer a variety of prots in the supply hain for instane, owing to the high prot development ost or high protion ost assoiated with a small volume. This model also serves as a base ase for understanding the role of quality in enroahment when quality differentiation aross hannels is not an important issue.

9 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment Benhmark: No Enroahment Here we establish a benhmark ase with no diret hannel. The problem is solved by bakward intion. Given wholesale prie w and quality u, the retailer hooses order quantity q R to maximize his profit: Π N R (q R, w, u) = (u(1 q R ) w) q R, from whih it follows that qr N(w, u) = 1 w. Antiipating the retailer s order deision, the manufaturer solves 2 2u ( 1 max (w w,u ku2 )qr N (w, u) = max (w w,u ku2 ) 2 w ) ; 2u this expression yields w N (u) = ku2 2 + u 2, (1) and hene qr N(u) = 1 ku. The manufaturer s and the retailer s profits as a funtion of 4 4 quality u are, respetively, Π N (u) = u(1 ku)2 8 and Π N R (u) = u(1 ku)2. (2) 16 Finally, the manufaturer determines the optimal quality by maximizing Π N (u), whih yields u N = 1, 3k wn = 2, and 9k qn R = 1. The equilibrium profits under no enroahment are 6 Π N = 1 54k and Π N R = 1 108k. Without a diret hannel, the two firms interests are perfetly aligned for the quality deision: aording to (2), the quality level u N that maximizes the manufaturer s profit Π N (u) also maximizes the retailer s profit ΠN R (u). 4. Enroahment with Uniform Quality In this setion, we onsider the ase where the manufaturer sells diretly to onsumers and there is no quality differentiation aross hannels Sequential Quantity Deisions Following the timeline in the basi model (Setion 3.1), we assume that the retailer determines his order quantity before the manufaturer determines her selling quantity. In the last stage, the manufaturer s optimization problem (given u, w, and q R ) is max q (w ku 2 )q R + (u uq uq R ku 2 )q,

10 10 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment whih gives her best response quantity q U (q R, w, u) = ( 1 q R ) +. ku 2 2 2u 2 Antiipating this, the retailer determines his order quantity by maximizing his own profit: max q R ( u(1 qr q U (q R, w, u)) w ) q R, whih, assuming q R 1 u ku, simplifies into max q R 1 2 uq2 R + ( 1 2 u ku2 + 2 w)q R. Solving this optimization problem and substituting the retailer s optimal quantity into the manufaturer s best response quantity q U (q R, w, u) yields the following solution for the quantity ompetition subgame when w and u are given: q U R(w, u) = 1 2 w u + ku 2 + 2u and qu (w, u) = w 2u 3ku 4 3 4u. (3) In the first stage, by antiipating the equilibrium quantities qr U(w, u) and qu (w, u), the manufaturer solves the following optimization problem: ( max ) w ku 2 qr(w, U u) + ( u uq(w, U u) uqr(w, U u) ku 2) q(w, U u). w,u It is straightforward to show that, for a given u, the optimal wholesale prie is w U (u) = ku2 2 + u 2 6 (4) with the orresponding quantities q U R(w U (u), u) = 2 3u and qu (w U (u), u) = ku 2 5 6u The profit funtions then beome Π U (u) = k2 u ku u ku2 2 + u 4 2 and Π U R(u) = 22 9u. (5) Comparing the retailer s profit under enroahment Π U R (u) in (5) with the benhmark profit under no enroahment Π N R (u) in (2), we see that the retailer is better-off with enroahment if and only if 3(u ku 2 ) 4 2 < < 3(u ku2 ), (6) 5 where the left inequality follows from Π U R (u) ΠN R (u) > 0 and the right inequality is the onstraint for enroahment to our: q U (u) = ku > 0. Condition 6 is exatly 2 6u 2 the same as that in Proposition 2 of Arya et al. (2007) with a = u ku 2. In their model,

11 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 11 the demand funtion is a bq and the unit protion ost is normalized to zero. When u is exogenously given, our model is the same as theirs with a = u ku 2 and b = u. Similar to the wholesale prie effet identified by Arya et al. (2007), from (1) and (4), w N (u) w U (u) = 6 0 and wn (u) w U (u) is inreasing in. When quality is endogenous, the above analysis no longer applies beause the manufaturer s quality deision depends on whether there is a diret hannel or not. The following proposition haraterizes the manufaturer s quality deision under enroahment and shows that, unlike the ase of exogenous quality, a win win outome is no longer possible (all proofs are in Appendix). Proposition 1. (i) There exists a threshold suh that the manufaturer enroahes if and only if <. (ii) Under enroahment, (a) the prot quality u U is first inreasing and then dereasing in, and (b) there exists a threshold u suh that u U u N, if u and u U < u N otherwise. (iii) When enroahment happens, the manufaturer always wins, Π U ΠN > 0, and the retailer always loses, ΠU R ΠN R < 0. Here, as in the rest of the paper, enroahment means that the manufaturer atually sells through her diret hannel (q U > 0). In Appendix, we onsider the ase of qu = 0 (i.e., no sales through the diret hannel) when we haraterize the threshold value. Note that this latter ase differs from the benhmark ase, in whih no diret hannel exists. As the diret selling ost inreases, the manufaturer would like to shift more sales to the retailer hannel. Proposition 1 states that she an do so by first inreasing u when is small, and then dereasing it when is large. By setting = 0 in (5), we an show that the optimal quality level for the entralized system (i.e., the manufaturer owns the retailer hannel) is 1 3k, whih is the same as un. Proposition 1 states that the manufaturer distorts quality upward (u U u N ) when is small and downward (u U < u N ) when is large. These results an be explained as follows. In (3), the third and fourth terms of qr U(w, u) are positive whereas those of qu (w, u) are negative. This shows that given w and u, the manufaturer has ompetitive disadvantages e to her protion ost ku 2 and selling ost. A larger u inreases her protion ost and makes this disadvantage more signifiant (ku in the third term beomes larger). However, a larger u improves the market profitability and makes the selling ost disadvantage less signifiant ( u in the fourth term beomes smaller). These effets are reversed when u beomes smaller. When is small, the

12 12 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment protion ost disadvantage effet dominates the selling ost disadvantage effet, and a larger u shifts demand from the diret hannel to the retailer hannel. When is large, however, the selling ost disadvantage effet dominates and a smaller u shifts demand from the diret hannel to the retailer hannel. By distorting quality, the manufaturer an rely less on the wholesale prie to influene the retailer s demand and uses it more aggressively to extrat profit from the retailer hannel. It is intuitive that the retailer is now more unlikely to benefit from enroahment. Proposition 1, however, shows a stronger result: the retailer no longer wins. This an be explained as follows. Enroahment has three effets on the retailer: a ompetition effet (a portion of the retailer hannel s profit is lost to the diret hannel), a wholesale prie effet (the retailer reeives a larger portion of the hannel profit beause the manufaturer adjusts wholesale prie to boost retailer hannel s demand) and a quality distortion effet (quality is distorted to boost retailer hannel s demand at the expense of a lower hannel profit). The first two effets are similar to those in Arya et al. (2007), exept wholesale prie does not always go down beause enroahment ould ine a higher quality level. When is small, the negative ompetition effet dominates the other two effets. When is large, the negative quality distortion effet is strong and, together with the negative ompetition effet, makes the retailer lose from enroahment. Figure 1 illustrates the results and shows that quality distortion e to enroahment an be as large as 16%. Our result that enroahment always hurts the retailer depends ritially on the assumed quality ost funtion. Obviously it is valid only if the assumed ost funtion is realisti (i.e., the marginal quality ost is inreasing in the urrent quality level and the manufaturer an hoose any quality level). Nevertheless it is onsistent with what we observe in pratie where retailers almost always resent enroahment (see the examples of Bass Ale and Hewlett-Pakard in Setion 1). In Setion 6.4, we onsider a more general quality ost funtion to further investigate the onditions under whih the result holds. Corollary 1. The threshold is dereasing in k. Given > 0, the retailer s profit under enroahment is inreasing in k. Without enroahment, the retailer s profit dereases in k beause it beomes more expensive for the supply hain to use quality to inrease onsumers willingness to pay (see Setion 3.2). With enroahment, when k is lose to 0, market profitability is very high

13 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment u U u N R N w U w N (a) Wholesale prie and quality level (b) anufaturer s profit () Retailer s profit Figure 1 Firms Deisions and Profits versus anufaturer s Selling Cost Disadvantage (k = 1). N U R U e to inexpensive quality and the manufaturer s selling disadvantage beomes insignifiant. Therefore the retailer s demand is very small when k is lose to 0. As k inreases, it benefits the retailer in two ways. First, his demand inreases beause his selling ost advantage beomes more signifiant. Seond, the manufaturer relies less on distorting quality and more on adjusting the wholesale prie to stimulate the retailer s demand. Hene, the wholesale prie effet beomes more pronouned, whih benefits the retailer. When the wholesale prie effet is stronger, enroahment is more ostly to the manufaturer; hene the threshold for enroahment is dereasing in k. Figure 2 shows how k affets firms profits. Unsurprisingly, the manufaturer s profit is dereasing in k U N k (a) anufaturer s profit Figure 2 Firms Profits versus Cost of Quality k ( = 1). R U R N k (b) Retailer s profit

14 14 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 4.2. Simultaneous Quantity Deisions In the basi model with uniform quality, we assumed the firms make quantity deisions sequentially. Here we examine the ase where they make their deisions simultaneously; in other words, the retailer no longer has a first-mover advantage. The following proposition haraterizes the onditions under whih enroahment ours as well as its effets on the manufaturer and retailer profits. Proposition 2. (i) When both firms hoose quantities simultaneously, there exists a threshold suh that the manufaturer enroahes if and only if <. Under enroahment, there exists L suh that the retailer always loses (Π S R < ΠN R ), whereas the manufaturer loses (Π S < ΠN ) if and only if L < <. (ii) The manufaturer is more likely to enroah under simultaneous than under sequential quantity deisions: <. Proposition 2 states that enroahment may hurt the manufaturer under simultaneous quantity deisions. So when it is optimal for the manufaturer to enroah, she ould be better-off if enroahment were not an option (i.e., if the diret hannel did not exist). Figure 3 illustrates this result. The lose lose outome arises beause the simultaneous game intensifies ompetition in the downstream market, whih hurts both the retailer and the manufaturer. Arya et al. (2007) find that, when quality is exogenous, enroahment with simultaneous quantity deisions yields win lose, lose win, or lose lose outome. In omparison, our results show that endogenizing quality eliminates the possibility of a retailer benefitting from enroahment. With or without endogenous quality, the manufaturer is more likely to enroah under simultaneous quantity deisions (i.e., < ) beause the retailer no longer has the first-mover advantage. For the rest of this paper, we maintain the assumption of sequential quantity deisions beause in most instries, it is more likely that the manufaturer an revise her protion quantity after reeiving the retailer s order. 5. Enroahment with Quality Differentiation In this setion, we study the ase where the manufaturer an enroah by offering prots of different quality levels through the two hannels. This is motivated by the onventional wisdom that hannel onflit an be eased when different prots are offered in different hannels.

15 Ha,, Long, and Nasiry: Quality in Supply Chain Enroahment R N S N R S Figure (a) anufaturer s profit (b) Retailer s profit Comparison of Firms Profits with and without Enroahment under Simultaneous Quantity Deisions (k = 1). Suppose the manufaturer distributes a prot of quality u through the diret hannel and a prot of quality tu through the retailer hannel. Beause the demand funtions are different depending on whih hannel arries the higher-quality prot, we distinguish two ases: 0 < t 1 (high-quality enroahment) and t 1 (low-quality enroahment). If 0 < t 1 then onsumers for whom θ p p R u tu θ < p p R u tu hoose quality u while those for whom p R tu hoose quality tu, where p and p R orrespond to the market-learing pries of (respetively) the diret- and retailer-hannel prots. The market is thus segmented, and the respetive inverse demand funtions are p = u(1 q tq R ) and p R = tu(1 q q R ). The demand funtions when t 1 an be derived similarly. We first establish that if it is optimal for the manufaturer to offer two qualitydifferentiated prots, she prefers to offer the high-quality prot through the diret hannel. This is onsistent with the Eureka Forbes example in Setion 1. Proposition 3. Under enroahment, the manufaturer never offers a prot of stritly lower quality through the diret hannel. Beause the high-quality prot aters to onsumers with greater willingness to pay for quality, the total surplus that ould be extrated is larger, whih leads to a higher margin for the higher-quality prot (oorthy 1988). Then, beause the manufaturer reeives only a part of the retailer hannel s revenue, she prefers to distribute the high-quality prot through the diret hannel while selling the low-quality prot through the retailer hannel. But is quality differentiation always optimal? Without a diret hannel, it is known that quality differentiation benefits a monopoly (ussa and Rosen 1978, oorthy

16 16 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment Table 1 anufaturer s Equilibrium Deisions. t u q 0 < 1 t = < 1 u 4 > 5 5 ku 2 3k q > 0 1 < 2 t = 1 u 4 < 3k q > 0 > 2 N/A N/A q = ) or two ompeting firms (oorthy 1988, otta 1993) beause it enables firms to segment the market and extrat more onsumer surplus. Yet we an show that, under ertain onditions, a uniform quality poliy is preferred by the enroahing manufaturer. Proposition 4. (i) There exist two thresholds 1 < 2 that haraterize the manufaturer s equilibrium deisions as given in Table 1. (ii) When enroahment happens, the manufaturer always wins (Π > ΠN ) and the retailer always loses (Π R < ΠN R ). When is relatively small (i.e., < 1 ), the manufaturer sells a lower-quality prot through the retailer. However, when the selling disadvantage is suffiiently large (i.e., 1 < 2 ), the enroahing manufaturer is better-off by not quality differentiating at all. To see why, we first look at the effet of quality differentiation on the retailer hannel s demand. In the quantity ompetition subgame, given w, u and t, where t < 1, the equilibrium quantities are: 1 q R (w, u, t) = 2(2 t) w t(2 t)u + ku 2(2 t) + 2(2 t)u, q (w, u, t) = 4 3t 4(2 t) + w (4 t)ku (4 t) 2(2 t)u 4(2 t) 4(2 t)u. (7) Similar to the ase of no quality differentiation, given w, u and t, the manufaturer has ompetitive disadvantages e to her protion ost ku 2 and selling ost. (In (7), the third and fourth terms of q R (w, u, t) are positive whereas those of q (w, u, t) are negative.) Inreasing the level of quality differentiation (i.e., lowering t) has two effets. On the one hand, it allows the manufaturer to inrease onsumers willingness to pay and ahieve a higher supply hain profit via market segmentation. On the other hand, it diminishes her protion and selling ost disadvantages and shifts demand from the more effiient retailer hannel to the less effiient diret hannel (the magnitude of eah of the third and fourth terms of q R (w, u, t) and q (w, u, t) is inreasing in t). In determining the level of quality differentiation, the manufaturer must trade off the benefit of market segmentation

17 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 17 against the ost of selling less through the more effiient retailer hannel. As inreases, the manufaturer inreases t to get it loser to 1 (i.e. lowers the level of quality differentiation) in order to shift demand to the retailer hannel. When is large enough ( > 1 ), she prefers not to quality differentiate at all. Figures 4a to 4 illustrate these results. As the manufaturer s selling disadvantage inreases, her inentive to enroah dereases. There is a threshold 2 suh that, if > 2, then the manufaturer does not sell anything through the diret hannel. Under enroahment, when the manufaturer an adjust the level of quality differentiation, she relies less on adjusting the wholesale prie to shift demand to the retailer hannel and sets it more aggressively for hannel profit extration. Beause the wholesale prie effet is subed, similar to the ase of uniform quality, enroahment always hurts the retailer q q U t (a) Quality differentiation level (b) anufaturer s quantity q R R 0.05 q R U () Retailer s order quantity (d) Retailer s profit Figure 4 Firms Deisions and Retailer s Profit versus anufaturer s Selling Cost Disadvantage (k = 1). R U Figure 4d shows that under enroahment, quality differentiation benefits the retailer when is small but hurts him otherwise. This finding ontradits onventional wisdom,

18 18 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment whih holds that the retailer is better-off if the enroahing manufaturer sells a different prot. Suppose is small. Without quality differentiation, the manufaturer uses the wholesale prie to nullify his ost disadvantage and aptures most of the sales (q U R is lose to zero). Quality differentiation benefits the retailer beause it allows him to inrease his sales (qr > qu R ) by fousing on the low-end market segment. Now suppose is large. Quality differentiation hurts the retailer beause his sales are lowered (qr < qu R ) e to the quality disadvantage. In pratie, a manufaturer may have to let a powerful retailer sell the high-quality prot (i.e., t > 1). In this ase, our numerial analysis shows that, as inreases, the manufaturer dereases t to get it loser to 1 (i.e., lowers the level of quality differentiation) in order to shift demand to the retailer hannel. It remains true that enroahment always hurts the retailer. However, under enroahment, quality differentiation always benefits the retailer. Finally, we examine how k, the manufaturer s ost of quality, affets her deisions and the retailer s profit. Corollary 2. Given > 0, as k inreases: (i) the manufaturer beomes less likely to enroah or quality differentiate (i.e., both 1 and 2 derease); and (ii) the retailer s profit first dereases and then inreases. Reall from Corollary 1 that, absent quality differentiation, a higher k makes it more ostly for the manufaturer to enroah and the retailer s profit is inreasing in k. It follows that the threshold for enroahment 2 is dereasing in k. From Figure 5, as k inreases, the level of differentiation dereases beause it beomes more expensive to quality differentiate. Therefore the threshold for no quality differentiation 1 is dereasing in k as well. Unlike the ase of no quality differentiation, the retailer an now fous on the low-end market segment and obtain a positive demand even when k is lose to 0. As k inreases, it has two opposing effets on the retailer s profit. On the one hand, market profitability is lower e to the higher ost of quality and this hurts the retailer. On the other hand, it dereases quality differentiation whih benefits the retailer. When k is small, the negative effet of lower market profitability dominates the positive effet of lower quality differentiation, and the reverse is true when k is large. Therefore, under quality differentiation the retailer s profit first dereases and then inreases in k. Figure 5 illustrates the result.

19 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment R 0.6 t k k (a) Quality differentiation level (b) Retailer s profit Figure 5 Quality Differentiation Deision and Retailer s Profit versus Cost of Quality k ( = 1) Extensions We now onsider several variations of the basi model to show that our main insights are robust Segmentation through the Retailer Instead of selling two different prots through two different hannels, the manufaturer might sell both prots through only the retailer hannel. In this setion we develop a model that aounts for this possibility and, by omparing it with the model in Setion 5, show that the win lose outome of enroahment is robust. Suppose that there is no diret hannel and that the manufaturer sells two prots of different quality levels through the retailer. Given w 1, w 2, u 1, and u 2 (without loss of generality, we let u 1 > u 2 ), the retailer hooses q 1 and q 2 to solve max q 1,q 2 (u 2 (1 q 2 q 1 ) w 2 )q 2 + (u 1 u 1 q 1 u 2 q 2 w 1 )q 1, whih yields q 1 (u 1, u 2, w 1, w 2 ) = u 1 u 2 w 1 +w 2 2(u 1 u 2 and q ) 2 (u 1, u 2, w 1, w 2 ) = u 2w 1 u 1 w 2 2u 2 (u 1 u 2. The manufaturer s profit maximization problem is ) then max (w 1 ku 2 w 1,w 2,u 1,u 2 1)q 1 (u 1, u 2, w 1, w 2 ) + (w 2 ku 2 2)q 2 (u 1, u 2, w 1, w 2 ). It is straightforward to show that the optimal solution to the manufaturer s problem is u N2 1 = 2, 5k un2 2 = 1, 5k wn2 1 = 7, 25k wn2 2 = 3, and qn2 25k 1 = q2 N2 = 1. Furthermore, ΠN2 10 = 1 and 50k Π N2 R = 1. The manufaturer learly should prefer to sell two prots of different quality 100k levels (u N2 1 u N2 2 ) through the retailer to benefit from market segmentation (Π N2 = 1 > 50k Π N = 1 ). The retailer also benefits from this strategy (ΠN2 54k R = 1 > 100k ΠN R = 1 ). 108k

20 20 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment Without a diret hannel, the manufaturer always prefers selling two qualitydifferentiated prots instead of one prot to ahieve market segmentation. If the retailer has the power to ditate the prot assortment deision and hooses not to arry the full prot line (Villas-Boas 1998), it seems logial for the manufaturer to ounterbalane this power by enroahing and selling some prots through its diret hannel to improve market segmentation. Proposition 4, however, shows that this is not neessarily true beause the manufaturer has an inentive to lower the level of quality differentiation in order to shift demand to the more effiient retailer hannel. Π N2 By omparing with results from the model in Setion 5, we obtain our next proposition. Proposition 5. When enroahment happens, the manufaturer always wins (Π > 0), and the retailer always loses (Π R ΠN2 R < 0). Similar to Proposition 4, enroahment hurts the retailer. This is not surprising beause under enroahment, the retailer now loses the high-quality prot to the diret hannel and the negative ompetition effet of enroahment beomes more signifiant (when ompared with the ase in Proposition 4) Enroahment with Fixed Cost of Quality In some instries, the ost of quality is predominantly driven by a fixed ost that does not depend on protion volume. For example, there is usually a high fixed ost assoiated with researh and development in the high-teh instry and with hiring high-profile designers in the apparel instry. In this setion, we onsider enroahment in a setting where there is a fixed ost assoiated with quality. As in Setion 5, the manufaturer an hoose to quality differentiate between the two hannels with one prot of quality u offered diretly to onsumers and another of quality tu through the retailer. The fixed ost of quality is then given by max(ku 2, kt 2 u 2 ). This orresponds to the ase of a high-quality prot being onvertible to a low-quality one by reing some features, whih in some instries is a ommon way of ahieving quality differentiation. Proposition 6. Under enroahment, (i) quality differentiation is not optimal (i.e., t = 1) and (ii) the manufaturer always wins while the retailer always loses. The intuition is that the ost of improving the quality of the lower-quality prot is zero and onsumers all prefer higher quality to lower quality. The manufaturer is therefore

21 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment 21 inentivized to inrease the quality of the lower-quality prot, resulting in no quality differentiation. Finally, Proposition 6(ii) shows that enroahment always hurts the retailer, whih is onsistent with the ase where quality ost is variable No Quality Commitment for Diret Channel Here we onsider the fast design ase where the manufaturer annot ommit to a partiular level of prot quality in the diret hannel. Lak of ommitment ould be e to design lead times short enough that the manufaturer an adjust the prot s design quality for the diret hannel after reeiving the retailer s order. Beause of this design flexibility, the manufaturer annot redibly ommit to the quality of the diret hannel prot before the retailer plaes an order. The timeline for this model is as follows: (i) the manufaturer announes the prot quality u R and the wholesale prie w; (ii) the retailer hooses the order quantity q R ; (iii) the manufaturer determines the prot quality u and selling quantity q. Proposition 7. If the enroahing manufaturer annot ommit to a level of quality in the diret-hannel prot, then quality differentiation aross hannels is always optimal. Proposition 7 provides an interesting ontrast to Proposition 4. Reall from our disussion of Proposition 4 that, in deiding whether or not to quality differentiate, the manufaturer faes a trade-off between the benefit of market segmentation and the ost of selling less through the more effiient retailer hannel. Without ommitment, the prot quality in the diret hannel an no longer affet the retailer s order diretly and the manufaturer always prefers to quality differentiate and thereby benefit from market segmentation. Beause we are unable to haraterize analytially the optimal quality levels, we investigate the effet of ommitment on firms profits numerially by omputing the optimal enroahment solution for a range of values of in [0, 2 ). The upper bound 2 is hosen suh that we an ompare the results with those under ommitment. Figure 6 illustrates the results in this senario. We find that, as in the Setion 5, enroahment with the highquality prot (u > u R ) is always optimal for the manufaturer. In addition, no quality ommitment in the diret hannel benefits the manufaturer when her ost disadvantage is small but hurts her otherwise (Π F > Π if < in Figure 6a). This result an be explained as follows. No quality ommitment allows the manufaturer to alleviate the

22 22 Ha, Long, and Nasiry: Quality in Supply Chain Enroahment retailer s first-mover advantage in the quantity deision beause she an use quality differentiation afterward to influene ompetition. However, the manufaturer an no longer use the ommitted quality to affet the retailer s order quantity diretly, and the result is insuffiient use of the more effiient retailer hannel. When is small, the manufaturer makes most of her sales through the diret hannel and so the ompetition effet dominates the hannel ineffiieny effet. However, the situation is reversed when is large. Our results imply that, if the manufaturer suffers from a high selling ost disadvantage, then she may be better served by ommitting (if possible) to a strategy of no differentiation rather than maintaining design flexibility. Finally, we disover numerially that the retailer is worse-off when there is no quality ommitment (Π F R < Π R in Figure 6b). The reason is that the retailer s first-mover advantage in the quantity deision is reed owing to the manufaturer s flexibility in hoosing quality differentiation afterward F R R F (a) anufaturer s profit (b) Retailer s profit Figure 6 Comparison of Firms Profits with and without Quality Commitment under Enroahment (k = 1) Generalized Cost Funtion Suppose the unit protion ost is b if u u 0 and b + k(u u 0 ) 2 if u > u 0, where u 0 0 and b 0. Thus the manufaturer annot hoose a quality level that is lower than a base level u 0, whih an be proed at a base unit protion ost b. She an improve quality by an inrement u 1 = u u 0 with an additional unit ost ku 2 1. A larger b means a lower margin for the manufaturer to invest in quality. Therefore the degree of flexibility for the manufaturer to hange quality is lower when either u 0 or b is larger. This ost funtion aptures the model in Arya et al. (2007) with u 0 > 0, b = 0 and k, and our basi model with u 0 = b = 0, and k > 0.