Interaction between channel strategy and store brand decisions

Accepted Manuscript

Interaction Between Channel Strategy and Store Brand Decisions Yannan Jin, Xiaole Wu, Qiying Hu PII: DOI: Reference:

S0377-2217(16)30538-0 10.1016/j.ejor.2016.07.001 EOR 13827

To appear in:

European Journal of Operational Research

Received date: Revised date: Accepted date:

10 September 2015 21 April 2016 1 July 2016

Please cite this article as: Yannan Jin, Xiaole Wu, Qiying Hu, Interaction Between Channel Strategy and Store Brand Decisions, European Journal of Operational Research (2016), doi: 10.1016/j.ejor.2016.07.001

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Highlights • We consider two price schemes depending on manufacturer’s pricing flexibility.

CR IP T

• The firms’ strategic interactions differ significantly under the two price schemes.

• Fewer retailer may introduce a store brand as store brand becomes more competitive. • Retailer may even decrease the price of the increasingly competitive store brand.

AC

CE

PT

ED

M

AN US

• Manufacturer’s pricing flexibility never brings more profit for it.

1

ACCEPTED MANUSCRIPT

Interaction Between Channel Strategy and Store Brand Decisions

CR IP T

Yannan Jin School of International Business Administration, Shanghai University of Finance and Economics, Shanghai 200433, China [email protected]

Xiaole Wu*

School of Management, Fudan University, Shanghai 200433, China [email protected]

Qiying Hu

AN US

School of Management, Fudan University, Shanghai 200433, China [email protected]

Motivated by the prevalent store brand entry and the differing legal environments for pricing flexibility, this paper studies the interaction between a manufacturer’s channel strategy and retailers’ store brand decisions, under both flexible wholesale price (FWP) scheme (where the manufacturer can charge different prices to the retailers) and uniform wholesale price (UWP) scheme (where a uniform price should be offered). Under

M

FWP scheme, a retailer has a lower incentive to introduce a store brand under single channel than under dual channel, and thus, single channel can be a strategy to prevent store brand entry. This strategy is effective when the store brands are moderately competitive. Conversely, under UWP scheme, a retailer has a lower

ED

incentive to introduce a store brand under dual channel. As a result, the manufacturer prefers dual channel, and single channel is rarely adopted under UWP scheme. Under FWP scheme, the retailers’ store brand introduction decisions are mostly symmetric under dual channel due to the less dependent wholesale prices charged by the manufacturer and their ex ante symmetric roles. But under UWP scheme, a retailer may

PT

gain more profit by not introducing a store brand if its competitor has already introduced one, which gives rise to a much larger region of asymmetric dual-channel setting. We also identify two interesting impacts of increasing competitiveness of store brand. First, under UWP scheme, fewer retailers should introduce

CE

a store brand regardless of its increasing competitiveness under certain conditions. Second, in contrast to the existing literature that shows the retailer should increase the price of the increasingly competitive store brand, we find that the retailer should, instead, decrease the price of store brand when its base demand

AC

is large. Finally, we show that although the manufacturer has greater pricing flexibility under the FWP scheme, he never earns a larger profit than under the UWP scheme. Whereas the retailer’s profit can be either larger or smaller under the FWP scheme. Keywords: Store brand, Channel strategy, Pricing flexibility.

1

ACCEPTED MANUSCRIPT

2

1.

Introduction

The marketplace for store brands has evolved dramatically in the past two decades, representing $115.3 billion of current retail businesses in the U.S. and achieving new levels of growth every year (Private Label Manufacturers Association (PLMA), 2015 Yearbooks). The Nielsen data for PLMA’s 2014 Private Label Yearbook shows that market shares of store brands exceed 40% in six countries in Europe: Switzerland (53%), Spain (51%), UK

CR IP T

(45%), Germany (42%), Belgium (41%), and Portugal (44%). Another study, commissioned by PLMA in 2013 and entitled “Today’s European Shoppers”, shows that store brand plays a fundamental role in the lives of shoppers across Europe, with 46% of consumers purchasing store brand products “frequently”.

As store brands become more acceptable to consumers, they are threatening national brands. The Chief Procurement Officer of Walmart’s Sam’s club in China said that after

AN US

manufacturers launch their products in the market, Sam’s club will analyze sales data to figure out which product is popular and worth introducing a similar store brand product (Le 2015). The beauty and personal care retailer Watsons also imitates hot sellers in this way. By data analysis, Watsons finds out top 10 popular products on a regular basis and introduces store brands in these categories (Le 2015). Due to retailers’ such follow-up store

M

brand introduction practice, it is necessary for national brand manufacturers to take them into account in their strategic decisions such as channel selection. It is well known that multiple-channel strategy has the advantage of helping a product to

ED

reach more consumers. Indeed, most products we are familiar with are distributed through multiple channels. However, we can also observe that many manufacturers choose to dis-

PT

tribute some products through single channel. For example, Procter & Gamble (P&G)’s hair care range Physique is exclusively distributed through Tesco in the UK (Euromonitor International 2003). Recently, P&G chooses Target as the single channel for its new

CE

designed diapers.1 In other categories, Whole Foods is the single channel for PepsiCo’s new energy drink Fuelosophy (Thompson 2006); Whirlpool distributes home appliances exclusively through Suning in China;2 One of Lego’s toys named Lego Mace Windu Fighter

AC

can be found only in Walmart.3 * Corresponding author. Tel.: +86-21-25011172. 1

http://www.storebrandsdecisions.com/news/2010/07/13/procter-and-gamble-responds-with-exclusive-brands

2

http://investors.whirlpoolcorp.com/releasedetail.cfm?ReleaseID=658134

3

http://news.walmart.com/news-archive/2011/10/05/walmart-unwraps-its-top-20-holiday-toys-exclusive-offers

ACCEPTED MANUSCRIPT

3

Will a manufacturer’s channel strategy and retailers’ store-brand-introduction decisions have an impact on each other? The following example delivers a point. In China, the famous beauty chain store Sephora is the single retailer for nearly 1000 items from manufacturer brands such as Esthederm, Eisenberg, Rexaline, ELLEgirls, WEI.4 Meanwhile, she sells about 330 items under her own brand.5 Another famous beauty and personal care chain store Watsons, on the contrary, develops nearly 2000 products under its own brand (Le

CR IP T

2015), but she is the single channel for only about 300 items.6 In this example, the retailer, which is more likely to be chosen as the single channel, less likely introduces store brands, and vice versa. Review of both channel and store brands literature shows a lack of study of the interaction between manufacturers’ channel decisions and retailers’ store-brandintroduction decisions. This paper investigates this topic by considering one national brand manufacturer and two retailers. The manufacturer chooses between single channel and

AN US

dual channel and the retailers each decide whether to introduce a store brand. We do not consider more than two retailers for analytical tractability, but in terms of insights interpretation, we can view dual channel as a representative of multiple channel. When facing multiple retailers, an important issue for the manufacturer is whether it can charge different prices. The manufacturer’s pricing flexibility is contingent on the legal

M

environment of the target market. In many countries and regions, there are laws or acts to prohibit price discrimination practices in order to protect smaller businesses from the

ED

buying leverage of larger competitors, e.g., the Robinson-Patman Act in the U.S., the Competition Law in the EU, and the Anti-Monopoly Law in China. However, the RobinsonPatman Act is gradually losing its regulatory power according to Luchs et al. (2010).7

PT

In contrast, the Anti-Monopoly Law in China was just enacted in 2008 and the Chinese government is enforcing the law increasingly tighter these years. According to Article 17 of

CE

Chapter III, a firm with dominant market position is forbidden to “apply dissimilar prices http://www.sephora.cn/exclusive product.html

5

http://www.sephora.cn/brand/sephora 1.html

6

http://www.watsons.com.cn (click menu “Brand Classification” on the webpage, and then by choosing “Exclusive”,

AC

4

all the brands that are distributed only via Watsons are shown. The total number of items under such brands is counted manually.) 7

Luchs et al. (2010) show that the likelihood that a court finds a defendant guilty of violating the act has dropped

drastically as a result of recent Supreme Court rulings, from more than 1 in 3 before 1993 to less than 1 in 20 for the period 2006-2010.

ACCEPTED MANUSCRIPT

4

or other transaction terms to counterparties with equal standing”.8 One landmark case is that in 2011, Huawei, a Chinese telecom company, filed lawsuits in Shenzhen, China, claiming that InterDigital, a U.S.-based licensor of standard-essential patents (SEPs) for mobile phones, had applied a discriminatory royalty rate regarding the licensing of SEPs. In 2013, the Shenzhen Intermediate People’s Court found that the royalty rate charged to Huawei was discriminatory because it was higher than that charged to other compa-

CR IP T

nies such as Apple and Samsung, which constituted an abuse of InterDigital’s dominant marketing position under China’s Anti-Monopoly Law. InterDigital was required to compensate Huawei RMB 20 millions (Zhang 2013). But in some other developing countries, still no such law is put in force to regulate the manufacturer’s pricing flexibility.

Considering the differing legal environments for pricing flexibility in different regions, the

AN US

firms need to understand how the legal environment of the market influences their business activities. Accordingly, this paper investigates the interaction between a manufacturer’s channel strategy and retailers’ store brand decisions under two price schemes: flexible wholesale price scheme (where the manufacturer can charge different wholesale prices to the downstream retailers) and uniform wholesale price scheme (where the manufacturer one-sided partial results.

M

has to set a uniform wholesale price). Restricting to one price scheme at best delivers only The existing literature has shown that retailers’ store brand decisions are influenced

ED

by the product and store characteristics. In our study we also take these factors into consideration, specifically, the competition between store brand and national brand (also

PT

interpreted as the competitiveness of store brand as a substitute of national brand), the store brand’s base demand, and the competition between stores. Since the recent industry reports reveal that store brands are increasingly popular and acceptable among consumers,

CE

we particularly study the impact of increasing competitiveness of store brands, and provide insights for firms to better adapt to this trend.

AC

In summary, this paper pursues answers to the following questions: (1) How do the retailers’ incentives to introduce a store brand affect the manufacturer’s channel strategy? What are the retailers’ optimal store-brand-introduction decisions? (2) What are the impacts of increasing competitiveness of store brand on channel strategy and store brand decisions? 8

http://english.mofcom.gov.cn/aarticle/policyrelease/announcement/200712/20071205277972.html

ACCEPTED MANUSCRIPT

5

(3) Whether does the differing legal environment for pricing flexibility have an impact on firms’ decisions? If so, what are the differences? The remainder of this paper is organized as follows. §2 reviews the related literature and

§3 presents the model. We analyze the setting where the manufacturer has the flexibility

to set different wholesale prices in §4. §5 analyzes the setting where the manufacturer has to set a uniform wholesale price, and compares the results under the two price schemes to

CR IP T

draw managerial implications. This paper concludes with §6. All proofs are given in the online supplement.

2.

Literature Review

This paper is related to the streams of literature on channel selection and store brand.

AN US

Research to date, however, has studied these two topics in isolation: The channel selection literature takes a static view that the selected channel will only sell the national brand manufacturer’s product, barring the possibility that the selected channel may potentially introduce competing store brands. The store brand literature frequently assumes a given channel structure. To the best of our knowledge, this paper is the first to study the introduction decisions.

M

interaction between the manufacturer’s channel strategy and the retailers’ store-brandIn the channel selection literature, Choi (1996) has summarized three main retailing

ED

channel structures and extended these to a fourth one. The first is the Exclusive Dealer Channel (Jeuland and Shugan 1983, 1988, Shugan 1985, Lal and Staelin 1984, Moorthy 1988, Coughlan 1985, Coughlan and Wernerfelt 1989). The second is the Monopoly Com-

PT

mon Retailer Channel, with two manufacturers selling to a common retailer (Choi 1991). The third is the Monopoly Manufacturer Channel, with one manufacturer selling to mul-

CE

tiple exclusive retailers (Ingene and Parry 1995, Marx and Shaffer 2007). The fourth is the Duopoly Common Retailers Channel, with two common retailers competing with each other (Choi 1996). The second and fourth structures involve two manufacturers, whereas

AC

this paper considers one manufacturer. Our single channel is similar to the first one and our dual channel is similar to the third one. The retailers’ store-brand-introduction decisions on top of single-channel and dual-channel strategies lead to five channel settings in our model (formally presented in Figure 2 of Section 3). There has been much research discussing the optimal channel structure for manufacturers and retailers among the above four retailing

ACCEPTED MANUSCRIPT

6

channels and the direct channel (Chiang et al. 2003, Arya et al. 2007, Cai et al. 2012). But none of these studies consider the retailers’ store-brand-introduction decisions. Taking this into account, this paper contributes to the channel literature by revealing how the downstream retailers’ store brand decisions influence a manufacturer’s channel choice. In addition, it provides a new rationale to use single-channel strategy and characterizes the conditions when such a strategy works.

CR IP T

The store brand literature has been growing as store brands become increasingly popular. Store brand entry may alter the market players’ interactions. For a comprehensive review of store brands’ impacts on retailers, manufacturers, and consumers, please refer to Pauwels and Srinivasan (2004). Most studies focus on the retailers’ store-brand-introduction strategy, i.e., whether to introduce a store brand (Raju et al. 1995, Groznik and Heese 2010,

AN US

Chen et al. 2011), positioning issues (Sayman et al. 2002, Morton and Zettelmeyer 2004, Kuo and Yang 2013), pricing behavior (Chintagunta et al. 2002, Bonfrer and Chintagunta 2004, Choi and Fredj 2013), quality level (Dunne and Narasimhan 1999, Apelbaum et al. 2003, Heese 2010), category issues (Sayman and Raju 2004), and store loyalty issues (Seenivasan et al. 2015).

Different from the above papers, some consider from the national brand manufacturers’

M

perspective how they should confront store brands (Quelch and Harding 1996, Rao 1991, Lal 1990, Wu and Wang 2005, Nasser et al. 2013, Fang et al. 2013, Amrouche and Yan

ED

2015). Quelch and Harding (1996) offer manufacturers a set of ideas to deal with the store brand threat, such as investing in brand equities, innovating wisely, managing the price spread and category, exploiting sales-promotion tactics, and so on. In contrast, Wu and

PT

Wang (2005) suggest that national brand manufacturers can cooperate with store brands. They provide an economic rationale for national brand manufacturers to provide store

CE

brands to their retailers: A store brand mitigates the promotion competition between two national brands, which benefits all three members in the channel. Nasser et al. (2013) have summarized national brand manufacturers’ three strategies against the threat from store

AC

brands (accommodate, displace, or buffer), and clarified the incentives for each strategy. From a different perspective, Fang et al. (2013) propose a new contract for the manufacturer to coordinate the supply chain considering store brands. Ru et al. (2015) study the impact of a store brand on national brand manufacturers’ profitability and find that a store brand may benefit the manufacturer when the interaction between the manufacturer and retailer

ACCEPTED MANUSCRIPT

7

Retailers decide retail prices

Retailers decide whether to introduce a store brand

Manufacturer chooses one or two retailers

Manufacturer sets wholesale price

Figure 1

Pricing stage

CR IP T

Channel –setting stage Sequence of events

is modeled as a retailer-led Stackelberg game. Our paper also considers a national brand manufacturer’s perspective, but in contrast to these studies that assume a given channel

AN US

structure, we consider the manufacturer’s channel selection decision taking into account potential competition from store brands, and provide insights for firms on how to adapt to the trend of increasingly popular store brands.

3.

Model

The market consists of a national brand manufacturer and two ex ante symmetric com-

M

peting retailers (A and B). The manufacturer (he) who is a leader in the market produces the product at a constant marginal cost and needs to choose one or two retailers (she)

ED

to distribute his product. The retailers may introduce a store brand to compete with the national brand if it brings additional benefits. Since the supply of store brand products is often perfectly competitive in the market (McMaster 1987, Narasimhan and Wilcox 1998),

PT

we assume that the retailers can purchase a store brand product from an alternative manufacturing source at a fixed unit price that equals the marginal production cost (Raju

CE

et al. 1995, Sayman et al. 2002, Choi and Fredj 2013). For ease of exposition, the marginal production costs of both the national brand and store brand products are set to zero.9 The manufacturer and the retailers engage in a two-stage game. The first stage is called

AC

channel-setting stage where the manufacturer first chooses one or two retailers to distribute his product and then each retailer decides whether to introduce a store brand. The second stage is called pricing stage where the manufacturer sets a wholesale price for each selected 9

When this assumption is relaxed by allowing the production cost of national brand product to be greater than zero,

we have numerically shown that the only difference is the retailers’ greater incentives to introduce a store brand.

ACCEPTED MANUSCRIPT

8

channel and then each retailer decides the retail prices for the national brand product and/or her own store brand product, if any. Since pricing is a shorter-term decision and is much easier to adjust compared to the strategic-level store-brand-introduction decision, we consider the more relevant case where the retailers’ store-brand-introduction decisions are made ahead of the manufacturer’s wholesale price decision. Figure 1 depicts the sequence of events.

CR IP T

In the channel-setting stage, if the manufacturer implements single-channel strategy, we assume without losing generality that retailer A is the selected channel. It is not clear if it is beneficial for retailer A to introduce a store brand because the competition between her store brand and the national brand may erode her revenue from the national brand. However, retailer B, who is not a national brand distributor, can always benefit from introducing a store brand because the purchase cost from an outside manufacturing source

AN US

is quite low (normalized to 0 in our model). Therefore, under single-channel strategy, there are two possible settings, denoted by N (retailer A does not introduce a store brand) and I (retailer A introduces a store brand).

If the manufacturer implements dual-channel strategy, then based on the retailers’ storebrand-introduction decisions, there are four possible settings, denoted by NN (neither of

M

them introduces a store brand), IN (only retailer A introduces a store brand), NI (only retailer B introduces a store brand), and II (both introduce a store brand). By symmetry, NI is the same as IN, and without losing generality we only consider IN hereafter.

ED

The five possible channel settings under both single and dual channel are summarized in Figure 2. Let a denote the number of retailers that sell the national brand product. Therefore, under settings I and N , a = 1, and under all dual-channel settings, a = 2. Let

PT

b denote the number of retailers that sell a store brand. For example, b = 1 under N and IN , because under N only retailer B sells a store brand and under IN only retailer A sells

CE

a store brand. Under settings I and II, both retailers sell a store brand and thus b = 2. As in Raju et al. (1995), we use a linear demand function to specify the dependence of demand on price. To suppress the effect of reaching more consumers by using more

AC

channels and ensure the comparability across different channel settings, we assume that the total category demand is the same and normalized to one unit under all settings when all the retail prices are set to zero. This assumption is common in papers on store brands such as Sayman et al. (2002) and Sayman and Raju (2004) and those that conduct crosssetting comparison such as Arya et al. (2007) and Kumar and Ruan (2006). Specifically,

ACCEPTED MANUSCRIPT

9 •NBM: national brand manufacturer •SB: store brand

•A: retailer A •B: retailer B NBM

NBM

A

B

SB

SB

NBM

A

NBM

SB

B (NN )

A

NBM

B (IN )

Five possible channel settings

SB

SB

A

B

SB

(II )

AN US

Figure 2

B (I )

(N )

Dual channel

A

CR IP T

Single channel

for a given channel setting k, k ∈ {I, N, II, IN, N N }, let pkij and qijk denote the retail price

and the demand of retailer i’s product j (j = n for national brand, j = s for store brand),

respectively. Retailer −i denotes the retailer other than retailer i. Then under setting II,

M

for i ∈ {A, B}

1 [1 − pin + θ(p−in − pin ) + δ(pis − pin ) + τsn (p−is − pin )], a + λb 1 = [λ − pis + δ(pin − pis ) + τsn (p−in − pis ) + τss (p−is − pis )], a + λb

II qis

ED

II qin =

(1) (2)

where λ ∈ (0, 1) measures the store brand’s base demand, and the assumption of λ ∈ (0, 1)

PT

implies that the base demand of store brand is lower than the national brand’s. This is consistent with our intuition that the perceived quality difference between the national

CE

brand and store brand leads to preference asymmetry, as explained in Hoch and Banerji (1993). θ, δ, τsn , and τss ∈ (0, 1) measure respectively the cross-price sensitivity between the two retailers for the national brand, between the national brand and a store brand

AC

within the same retailer, between the national brand at one retailer and a store brand at the other retailer, and between two store brands. As mentioned in Choi (1996) and Choi and Fredj (2013), compared with the competition between the same brand in different stores or that between different brands in the same store, the competition between different brands in different stores is very weak. Intuitively, different brands in the same store are

ACCEPTED MANUSCRIPT

10

all readily available for a consumer that visits the store, and hence they compete directly with each other. Competition between the same national brand in different stores is further intensified by the emerging cellphone applications such as “RedLaser” and “ShopSawy” that enable consumers to scan the barcode of the national brand product and compare its prices in different stores. Compared to them, the competition between a store brand in one retailer and another store brand or the national brand in a different retailer is much

CR IP T

weaker. For brevity, we set τsn = τss = 0.10 Correspondingly, the demand function under setting II becomes

1 [1 − pin + θ(p−in − pin ) + δ(pis − pin )], a + λb 1 [λ − pis + δ(pin − pis )], = a + λb

II qin = II qis

(3) (4)

AN US

where θ is hereafter referred to as parameter for cross-store competition or national brand competition, and δ parameter for competition between store brand and national brand. Note that, under settings other than II, there is at least one retailer that either does not sell the national brand product or does not introduce a store brand. Then, the corresponding term should be removed from the demand functions (3) and (4). This treatment is also

M

1 IN = 2+λ adopted in papers such as Arya et al. (2007). For example, qBn [1−pBn +θ(pAn −pBn )],

i.e., the term δ(pBs − pBn ) is removed from demand function (3), because retailer B does

not introduce a store brand under setting IN and in her store there is no competition

ED

between the national brand and store brand. Furthermore, the coefficient

1 a+bλ

needs to be

adjusted by setting b = 1 because only one retailer introduces a store brand. Similarly, we

PT

can derive demand functions under other channel settings. For an exhaustive list of such demand functions, please refer to Appendix A1. Let subscript M denote the manufacturer, and Πki denote firm i’s (i = M, A, B) equilib-

CE

rium profit under channel setting k. In the pricing subgame, the manufacturer first sets wholesale prices wA for retailer A and wB for retailer B, and then the retailers set retail

AC

prices to maximize their profits as follows:

10

Manufacturer : ΠkM = max

wA ,wB

P

 k w q i in , i=A,B

k k Retailer i ∈ {A, B} : Πki = max (pin − wi )qin + pis qis . pin ,pis

Nevertheless, the qualitative results in this paper still hold when τsn or τss is non-zero but very small.

(5)

ACCEPTED MANUSCRIPT

11

That is, the manufacturer’s profit is the sum of each selected channel’s wholesale price multiplied by the demand of the national brand, and each retailer benefits from the national k brand and/or store brand products. Note that qin = 0 if retailer i is not the selected channel k for the national brand, and qis = 0 if retailer i does not introduce a store brand under

setting k. We solve this subgame backward by first deriving the retailers’ retail prices given wA and wB , and then optimizing wA and wB to maximize the manufacturer’s profit.

CR IP T

Note that under single channel, retailer A is the selected channel and the manufacturer only needs to set a single wholesale price, wA . However, under dual channel, depending on the legal environment, we consider two schemes for the manufacturer’s wholesale price decisions. In the first scheme, there is no regulation over pricing and the manufacturer has the flexibility to set any wholesale prices for the two retailers, referred to as flexible

AN US

wholesale price (FWP) scheme. That is, there is no constraint over wA and wB , which can be either different or equal to each other. In the second scheme, regulation over pricing is present and the manufacturer has to set a uniform wholesale price for both retailers, i.e., wA = wB . This scheme is referred to as uniform wholesale price (UWP) scheme. For each scheme, we solve the equilibrium wholesale prices and retail prices, and further

M

derive the manufacturer’s and the retailers’ profits under any channel setting. The results are summarized in Appendices A2 and A3. With these profits, we are ready to analyze the first-stage channel-setting game, i.e., the manufacturer chooses between single and dual

ED

channel, and the retailers decide whether to introduce a store brand. Section 4 analyzes the first-stage game under FWP scheme, allowing wA 6= wB in the second stage, and Section

PT

5 is dedicated to the UWP scheme, imposing the constraint wA = wB . In this paper, the

4.

CE

terms increasing and decreasing are used in the weak sense.

Analysis Under Flexible Wholesale Price Scheme

By backward induction, we have already derived the pricing decisions and further the firms’

AC

profits under any channel setting shown in Appendices A2 and A3. Based on these results, in this section, we consider the FWP scheme where the manufacturer can set different wholesale prices under dual channel. We first derive the retailers’ store-brand-introduction decisions in Section 4.1 and then the manufacturer’s optimal channel strategy in Section 4.2.

ACCEPTED MANUSCRIPT

12 1 0.9 0.8 0.7

λ

0.6 0.5

I

0.4 0.3

λ s(δ)

0.2 0.1

N 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

δ

Figure 3

4.1.

0.8

0.9

1

CR IP T

0

Retailer A’s store-brand-introduction decision under single channel (the curve represents ΠIA = ΠN A)

Retailers’ Store-Brand-Introduction Decisions

4.1.1.

Store-Brand-Introduction Decisions Under Single Channel As we have

AN US

argued, under single channel, retailer B, which is not the selected channel, always benefits from introducing a store brand. Also, intuitively, a larger base demand of store brand (λ) provides retailer A with greater incentives to introduce a store brand. Whereas the impact of δ on retailer A’s store brand introduction is not clear a priori. As the competition becomes stronger (i.e., δ is larger), it is easier for a store brand to gain demand, but meanwhile the negative impact on the national brand is also more evident. Nevertheless,

M

we show in Lemma 1 that increasing δ also favors introducing a store brand, as illustrated in Figure 3. This is consistent with Raju et al. (1995).11

ED

Lemma 1. Under single channel, it is optimal for retailer A to introduce a store brand (i.e., ΠIA > ΠN A ) if and only if either (i) δ ≥ 1/2, or (ii) λ is greater than a threshold λs (δ).

PT

It is worth noting two effects of increasing δ. First, for large δ, i.e., intense price competition between national brand and store brand, the national brand manufacturer has to

CE

set a low wholesale price in order to induce a low national brand retail price to compete with the store brand. This is referred to as the “wholesale-price-down” effect of increasing δ. Second, larger δ means store brand can substitute national brand to a larger extent,

AC

which allows the retailer to gain profit from store brand more easily. This is referred to as “positive-store-brand” effect of increasing δ. Both wholesale-price-down and positivestore-brand effects provide retailer A with greater incentives to introduce a store brand. 11

However, we will show in Section 5 that in contrast to Raju et al. (1995), under the uniform wholesale price scheme

increasing δ does not necessarily increase the retailers’ incentives to introduce a store brand.

ACCEPTED MANUSCRIPT

Figure 4

AN US

CR IP T

13

Retailers’ profits under dual-channel settings

4.1.2.

Store-Brand-Introduction Decisions Under Dual Channel Since retailers A

M

and B are symmetric ex ante, we assume under dual channel, they simultaneously decide whether to introduce a store brand. Out of their decisions, there are three possible channel settings: II, IN, and N N. We derive the equilibrium of the pricing subgame for each

ED

channel setting. This gives us the retailers’ profits in the 2 × 2 matrix in Figure 4 (for the detailed expressions of profits, please refer to Appendix A2).

PT

To derive the retailers’ equilibrium store-brand-introduction decisions, we first analyze one retailer’s incentive to introduce a store brand given the other’s decision, characterized ˜ I and λ ˜ N . Suppose one retailer has introduced a store brand, then the by two thresholds, λ

CE

˜I ; other retailer will also introduce one if and only if the store brand base demand λ > λ

AC

given that no retailer has introduced a store brand, then one will introduce a store brand ˜ N . These results together lead to the retailers’ equilibrium store-brandif and only if λ > λ

introduction decisions under dual channel in Lemma 2. ˜I , λ ˜ N ∈ [0, 1), such that II Lemma 2. Under dual channel, there exist two thresholds, λ ˜ I , IN is an equilibrium when λ ˜N ≤ λ ≤ λ ˜ I , and N N is an is an equilibrium when λ ≥ λ ˜N . equilibrium when λ ≤ λ

ACCEPTED MANUSCRIPT

14 HaL Θ = 0.005

HbL Θ = 0.5

HcL Θ = 0.995

0.30

0.30

0.30

0.25

0.25

0.25

II

0.20

0.20

0.20

0.10

0.15

Λ

0.15

Λ

Λ

II

0.10

0.15

IN

0.10

0.05

0.05

0.00

0.05

NN

NN

NN

0.00 0.0

0.2

0.4

0.6

0.8

1.0

0.00

0.0

0.2

0.4

∆

Figure 5

CR IP T

IN

0.6

∆

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

∆

Retailers’ store-brand-introduction decisions under dual channel and flexible wholesale price scheme

AN US

˜ I can be either greater or less than λ ˜ N depending on problem It is worth noting that λ ˜I > λ ˜ N , then introducing a store brand at one retailer decreases the other parameters. If λ ˜ N is easier to satisfy than retailer’s incentive to also introduce a store brand, because λ > λ ˜ I . Otherwise, one retailer has a greater incentive to introduce a store brand if the λ>λ ˜I ≤ λ ≤ λ ˜ N , both II and N N are equilibrium other has introduced one. In this case, if λ

M

settings. When multiple equilibria exist, we use the Pareto optimality concept to refine the equilibrium outcome. For example, when both II and N N are equilibria under dual NN 12 channel, II is taken as the refined equilibrium if ΠII A > ΠA , and vice versa.

ED

Lemma 2 implies the number of retailers who introduce a store brand increases in the

PT

store brand base demand λ. As for the effects of the other two parameters, we can show ˜ N and λ ˜ I decrease in δ and θ, implying an increase of δ or θ also improves numerically that λ retailers’ incentives to introduce a store brand. This is because both wholesale-price-down

CE

and positive-store-brand effects of increasing δ identified under single channel carry over to dual channel. More intense national brand competition (larger θ) makes the national brand less attractive and hence the retailers more likely introduce a store brand, shifting

AC

demand from the national brand to store brand to mitigate the negative impact of intense national brand competition. 12

Pareto-optimal subgame equilibrium under dual channel may not be unique only for boundary cases such as

ΠII A

N II NI II NI = ΠN A , or ΠA = ΠA and ΠB = ΠB . For those cases, we have shown no matter which Pareto-optimal subgame

equilibrium is taken, the manufacturer’s choice over single or dual channel will be invariant.

ACCEPTED MANUSCRIPT

15

For better illustration, Figure 5 shows the retailers’ strategies under dual channel for each combination of (δ, λ) at three representative values of θ. The regions with λ > 0.3 not shown in Figures 5-8 correspond to dual-channel setting II.13 When national brand competition is very weak (e.g., θ = 0.005), the two retailers are almost monopolists in each market. Then by their ex ante symmetry, the retailers’ strategic decisions are also symmetric. Only when national brand competition is above some level will there emerge

4.2.

CR IP T

the asymmetric channel setting IN for a very small region with low λ and intermediate δ. Equilibrium Channel Strategy

Section 4.1 has discussed the equilibrium channel setting, or called emerging setting, under both single and dual channel. If the manufacturer’s payoff under the emerging singlechannel setting is greater than that under the emerging dual-channel setting, then single-

AN US

channel strategy is preferred by the manufacturer, and vice versa. To derive the manufacturer’s optimal channel strategy, we first compare his profits under the five settings (N , I, N N , IN , II) in Lemma 3.

N N NN IN II I Lemma 3. (i) ΠN M > ΠM ; (ii) ΠM > ΠM > ΠM > ΠM .

Lemma 3 (i) shows given that the selected channels do not introduce a store brand,

M

introducing downstream national brand competition by adopting dual-channel strategy benefits the manufacturer. There are two sources of this benefit: First, intense national

ED

N NN N brand competition pulls down the retail price (pN An = pBn < pAn ) and hence expands the

national brand demand. Second, under setting N , retailer B introduces a store brand to gain profit from this category, reducing the market share of the national brand. In contrast,

PT

under setting N N , there is no store brand and the national brand takes the whole market NN NN N share (qAn + qBn > qAn always holds).

CE

Lemma 3 (ii) tells that under dual channel, the manufacturer’s profit is lower if more retailers introduce a store brand. The single channel with a store brand leads to a lower In our model with store brand base demand equal to λ, if all retail prices are set to zero, the store brand unit

AC

13

market share in one retailer equals

λ . 1+λ

IRI (1988, 1998) show that the average unit market share of store brand is

around 20%; PLMA (2015) shows that in the U.S. store brand unit market share is 23.1% in supermarkets. Since in practice store brand products are typically priced lower than national brand products,

estimator of store brand unit market share. with λ less than 0.3.

λ 1+λ

λ 1+λ

is approximately a lower

< 23.1% leads to λ < 0.3, i.e., it is reasonable to focus on the region

ACCEPTED MANUSCRIPT

16

profit than any dual channel. Note that cross-store competition under dual channel and no store brand introduction are two desirable features for the manufacturer. Setting I deviates from both of the features, and thus leads to a lower profit. This result implies that, although I may be the equilibrium under single channel, it can never be the equilibrium channel setting for the whole game, because if the manufacturer foresees the equilibrium setting is I under single channel, he can always improve his profit by using dual-channel

CR IP T

strategy. Alternatively speaking, the manufacturer may choose single channel only if he foresees the selected retailer will not introduce a store brand; but if the selected single channel introduces competing store brands, the manufacturer should turn to dual-channel strategy. This provides an interpretation for the contrasting phenomenon between Sephora and Watsons in China: Sephora is chosen as the single channel for nearly 1000 items considering that it sells only 370 items under its own brand, whereas Watsons is the single

AN US

channel for only about 300 items considering that it sells 2000 products under its own brand; that is, Sephora is known to less likely introduce store brands than Watsons, and hence Sephora is more likely chosen as the single channel.

Recall that Lemma 1 has shown if either λ or δ is sufficiently large, I is the emerging setting under single channel. Therefore, under the same conditions in Lemma 1, the manu-

M

facturer adopts dual-channel strategy to avoid the single-channel setting I. That is, when store brand base demand is large or highly substitutable with the national brand, dual

ED

channel is the equilibrium strategy (Proposition 1 (i)). Proposition 1. The manufacturer prefers dual-channel strategy if either of the follow-

PT

ing two conditions holds: (i) δ ≥ 1/2 or λ is greater than the threshold λs (δ), where λs (δ) ˜N , λ ˜ I } and δ is less than a threshold. is introduced in Lemma 1; (ii) λ < min{λ Proposition 1 (ii) provides another sufficient condition for the manufacturer to adopt

CE

dual-channel strategy. For sufficiently small λ and δ, store brand will not be introduced under either single or dual channel, in which case it is preferable for the manufacturer to use dual channel to foster cross-store competition. To summarize, for either small or large

AC

λ, δ, it is optimal for the manufacturer to adopt dual-channel strategy. Single channel can be the equilibrium strategy only with non-extreme values of λ, δ.

Proposition 2 characterizes a sufficient condition. Proposition 2. The single-channel setting N is the equilibrium if δ is greater than a ˜I , λ ˜ N } < λ < λs (δ). threshold but less than 1/2, and max{λ

ACCEPTED MANUSCRIPT

17 HaL Θ = 0.005

HbL Θ = 0.5

HcL Θ = 0.995

0.30

0.30

0.30

0.25

0.25

0.25

II

0.20

0.20

0.20

0.15

Λ

0.15

Λ

Λ

II II

0.15

N 0.10

0.05

0.10

0.05

NN 0.00

IN

N

NN

0.2

0.4

0.6

0.8

1.0

NN

N

0.00

0.0

0.2

0.4

∆

Figure 6

IN

0.05

0.00 0.0

CR IP T

0.10

0.6

∆

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

∆

Equilibrium channel setting in δ − λ space for three values of θ under flexible wholesale price scheme

AN US

The condition λ < λs (δ) guarantees that N is the emerging setting under single channel, ˜I , λ ˜ N } < λ guarantees that II is the emerging setting under dual and the condition max{λ

channel. If the manufacturer’s profit under N is greater than that under II, single channel will be the equilibrium channel strategy. In choosing between N and II, the manufac-

turer makes a tradeoff: more national brand distributors but with competition from store brand (II), or one national brand distributor but without threat from store brand (N ).

M

If substitution between national brand and store brand is strong (i.e., δ is greater than a threshold), the manufacturer is better off by distributing via a single channel to avoid the

ED

store brand threat, i.e., N is the equilibrium channel setting. Figure 6 depicts the whole game’s equilibrium channel setting in the δ − λ space for three

representative θ values. Comparing the three plots, we find the equilibrium setting is also

PT

influenced by θ. For larger θ, II becomes more desirable for the manufacturer compared to N , because more intense cross-store competition leads to a larger national brand demand.

CE

In order for setting N to outperform II for the manufacturer, the required δ value is larger so that II becomes less attractive due to greater threat from store brand. For the region where N is the equilibrium setting in Figure 6, under single channel the

AC

selected retailer finds it not profitable to introduce a store brand (Figure 3), but under dual channel both retailers will introduce a store brand (Figure 5). That is, the retailers have greater incentives to introduce a store brand under dual channel than under single channel. As a result, single channel can be a strategy to avoid the selected channel introducing a store brand, and this serves as one rationale to use single-channel strategy besides those

ACCEPTED MANUSCRIPT

18

identified in Tsay and Agrawal (2004) and Cai et al. (2012). Proposition 2 has taken this argument one step further by characterizing when this strategy works. Many real world examples echo our theory’s prediction. Narasimhan and Wilcox (1998) have designed a survey to measure the “expected penalty” level of 110 categories, and expected penalty is defined as the disutility a consumer suffers if she buys an improper

CR IP T

product in a specific category multiplied by the probability she buys an improper one. They assume that when a category has high expected penalty level, consumers are less likely to switch to store brand in that category, i.e., substitution between store brand and national brand is low. Therefore, expected penalty is a measurement similar to what the parameter δ in our model captures. A large δ means high substitution level between store brand and national brand, which corresponds to low expected penalty. They find

AN US

that the expected penalty values are extremely high (low δ) in the three categories: baby food, frozen fish, and feminine protection. Same as our theory predicts, these products are typically distributed via multiple channels and it is difficult to find store brand products in these categories. On the other hand, they find that expected penalty values are extremely low (high δ) in the three categories: dried noodles, canned beans, and ice cream

M

cones. Again, we see that most of the national brand products in these categories are distributed through multiple retailers and store brands are quite prevalent. For example,

ED

Brilla spaghetti is distributed through supermarkets like Walmart and Tesco. Meanwhile, it is easy to find store brand spaghetti in these supermarkets, such as Great Value spaghetti

PT

in Walmart and Tesco Everyday Value spaghetti in Tesco. This paper shows that single channel becomes a possible equilibrium setting only with intermediate values of δ, which corresponds to categories such as disposable diaper and many beauty and personal care

CE

products according to the measurement of Narasimhan and Wilcox (1998). Indeed, it is easier to find national brand products that are distributed through single channel in these

AC

categories. For instance, P&G’s designed diaper, including pastel-colors with choices of madras, stripes and printed ruffles, is distributed exclusively through Walmart. For the beauty and personal care category, as mentioned before, nearly a thousand products are distributed through single channel at Sephora China, and hundreds of products are distributed through single channel at Watsons.

ACCEPTED MANUSCRIPT

19

4.3.

Pricing Tactics

As store brands become more competitive, they are substituting national brands to a greater extent. Next, we study how retailers should adjust their prices in response to this trend, captured by increasing δ. Raju et al. (1995) find that store brand retail price increases in δ. In contrast to their finding, we show in Proposition 3 that store brand retail prices decrease in δ when the store brand base demand is above a certain level. This implies the store brand becomes more competitive.

CR IP T

that the retailer should not necessarily increase its store brand retail price even though

Proposition 3. Under settings IN and II, store brand retail prices decrease in δ if and only if λ is greater than a threshold.

Decreasing store brand retail price has two effects: The store brand demand will expand,

AN US

which is the positive effect; meanwhile it decreases the demand for the national brand product and forces setting a lower national brand retail price, which is the negative effect. The two effects will be more evident as δ increases. In Raju et al. (1995), there is a single retailer and there is no cross-store competition. The negative effect of decreasing store brand price on the national brand always dominates the positive effect due to the

M

high margin of the national brand product, and hence they find the store brand retail price always increases in the competition intensity between the national brand and store

ED

brand. Whereas in our paper, there is cross-store competition over the national brand. The profitability from the national brand becomes less important compared to that in Raju et al. (1995). When the store brand base demand is sufficiently large, the positive effect of

PT

expanding store brand demand dominates the latter negative effect on the national brand,

5.

CE

in which case it is optimal for the retailer to decrease the store brand retail price.

Analysis Under Uniform Wholesale Price Scheme

Section 4 has derived firms’ channel and pricing decisions under the flexible wholesale price

AC

scheme. However, when there is regulation over price discrimination, it is not feasible for the manufacturer to charge different wholesale prices. Similar to Yoshida (2000), Vakharia and Wang (2014) and Lu and Liu (2013), we also study the setting that the manufacturer has to set a uniform wholesale price for both retailers, i.e., the uniform wholesale price (UWP) scheme. We go through the steps in Section 4 with the constraint wA = wB , and

ACCEPTED MANUSCRIPT

20

focus on reporting the different results between the two price schemes. For exposition simplicity, we omit the subscript of the wholesale prices under UWP scheme. ˆ , I, ˆ NˆN , IN ˆ and II) ˆ represent those To avoid confusion, the settings with a hat (N under UWP scheme. The equilibrium results under single-channel settings or symmetric dual-channel settings are the same under the two price schemes, because under singlechannel settings, the manufacturer only needs to set a single wholesale price, and under

CR IP T

symmetric dual-channel settings, the manufacturer’s optimal wholesale prices for the two retailers are the same even under FWP scheme. Therefore, among the five settings, only ˆ and IN lead to different equilibrium results. The equilibrium wholesale prices, retail IN ˆ are summarized in Appendix A3. In the following, prices, and firms’ profits under IN we characterize the results under UWP scheme, and compare them with the counterparts

5.1.

AN US

under FWP scheme. Retailers’ Store-Brand-Introduction Decisions

Similar to Section 4, we study each retailer’s store-brand-introduction decision before deriving the equilibrium channel setting. Under single channel, Lemma 1 still holds because the ˆ and I, ˆ respectively. Under dual channel, we find that settings N and I are the same as N

M

˜ ˆ and λ ˜ ˆ , such that II ˆ is an equilibrium similar to Lemma 2, there are two thresholds λ I N ˜ ˆ, and NˆN is an equilibrium when ˜ˆ ≤λ≤λ ˜ ˆ, IN ˆ is an equilibrium when λ when λ ≥ λ I

N

I

ED

˜ ˆ . Comparing these thresholds under the two schemes, we derive Proposition 4. λ≤λ N

Proposition 4. Under dual channel, the retailers have lower incentives to introduce a

PT

store brand under UWP scheme than under FWP scheme. ˜ˆ > λ ˜ I and λ ˜ˆ ≥λ ˜ N , i.e., the threshProposition 4 follows from the analytical result of λ I N

CE

olds under UWP scheme are larger and the retailers are less likely to introduce a store

brand. This is because with a uniform wholesale price, the wholesale-price-down benefit that a retailer achieves by introducing a store brand is also enjoyed by her competitor. Such

AC

a free-rider problem on one hand discourages a retailer from introducing a store brand if the other retailer has not introduced one, and on the other hand also reduces a retailer’s need to introduce a store brand if the other retailer has introduced one. This free-rider problem is a major feature that distinguishes the UWP scheme from the FWP scheme, and drives most of the different results between the two schemes.

ACCEPTED MANUSCRIPT

21 HaL Θ = 0.005

HbL Θ = 0.5

0.30

HcL Θ = 0.995

0.30

` II

0.25

0.30

0.25

0.25

` II 0.20

0.15

0.15

` IN

0.10

` NN 0.05

0.00

0.10

` NN

0.05

0.2

0.4

0.6

0.8

1.0

` IN

0.00

0.0

0.2

0.4

∆

Figure 7

` NN

0.05

0.00 0.0

` II

CR IP T

0.10

0.20

Λ

` IN

0.15

Λ

Λ

0.20

0.6

∆

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

∆

Retailers’ store-brand-introduction decisions under dual channel and uniform wholesale price scheme

AN US

Figure 7 depicts the emerging dual-channel setting in the δ −λ space under UWP scheme.

Compared to Figure 5, there are several different observations.

Observation 1. Under dual channel, as δ increases, more retailers introduce a store brand under FWP scheme, whereas under UWP scheme, retailers’ incentives to introduce a store brand can be dampened.

M

As mentioned under FWP scheme, both the positive-store-brand and wholesale-pricedown effects of increasing δ make introducing a store brand more desirable, and hence more

ED

retailers will do so as δ increases. In contrast, under UWP scheme, when national brand competition is weak (Figure 7 (a)), as δ increases the emerging dual-channel setting may ˆ to IN ˆ for a certain range of λ. This implies that as the store brand becomes switch from II

PT

more competitive, under certain conditions one retailer might benefit from abandoning its store brand. The free-rider problem of the wholesale-price-down benefit explains this

CE

result. Suppose retailer A has introduced a store brand. As δ increases, retailer B can free ride on the more evident wholesale-price-down effect. This, together with the very low cross-store competition, allows her to enjoy a large profit margin from the national brand.

AC

As a result, retailer B prefers not to introduce a store brand considering that introducing a store brand will erode the demand of the high-margin national brand. Another observation follows from the comparison between Figures 5 and 7. Observation 2. The region of asymmetric dual-channel setting is extremely small under FWP scheme, but relatively large under UWP scheme.

ACCEPTED MANUSCRIPT

22

Observation 2 implies that asymmetric dual-channel setting is more likely the equilibrium under the symmetric pricing environment (UWP scheme), but is rarely the equilibrium under the environment that allows asymmetric pricing (FWP scheme). This can be explained as follows. The retailers’ received wholesale prices and decisions are less dependent on each other under FWP scheme. Since the retailers are ex ante symmetric, the strategies they adopt tend to be symmetric as well. However, under UWP scheme, one

CR IP T

retailer’s decision, such as introducing a store brand, directly affects the other retailer’s wholesale price, and both retailers share the same reduced wholesale price. Due to such free-rider benefit, the other retailer may find it desirable to sell only the national brand ˆ product. This explains that compared to the FWP scheme, the asymmetric setting IN emerges under dual channel for a much larger region and the region of the symmetric setˆ shrinks under UWP scheme. As a result, a retailer should be careful on whether to ting II

AN US

follow its competitor’s store-brand-introduction decision. Under UWP scheme, diversified strategy should be pursued by the retailers for a wide range of parameter settings. 5.2.

Equilibrium Channel Strategy

To derive the equilibrium channel strategy, we compare the manufacturer’s profit under

M

the emerging dual-channel setting with that under the emerging single-channel setting. The results in Lemma 3 and Propositions 1, 2 derived under FWP scheme carry over to the UWP scheme. That is, single channel will be the equilibrium strategy only with non-

ED

extreme values of λ, δ. For a thorough understanding, Figure 8 depicts the equilibrium channel setting under UWP scheme in the δ − λ space for three θ values.

PT

Comparing Figures 8 and 6, we find a feature specific to the UWP scheme. Observation 3. Under UWP scheme, the region where single-channel strategy is opti-

CE

mal for the manufacturer becomes extremely small, and disappears when θ exceeds a certain value (less than 0.15).

AC

To understand this result, first note that under UWP scheme, for the shaded area in Figure 8, the emerging setting is Iˆ under single channel, but NˆN under dual channel; i.e.,

the retailers have higher incentives to introduce a store brand under single channel than under dual channel. But recall that under FWP scheme, the retailers always have greater incentives to introduce a store brand under dual channel, which serves as a driving force for the manufacturer to use single-channel strategy. The contrasting result under UWP scheme

ACCEPTED MANUSCRIPT

23 HaL Θ = 0.005

HbL Θ = 0.1

0.30

` II

0.30

` II

0.25

0.20

` N

0.20

` N

0.20

` IN

` IN

0.10

0.15

Λ

Λ

0.15

0.10

` NN

` NN

` NN

` NN

0.05

0.00 0.4

0.6

0.8

1.0

0.00

0.0

0.2

0.4

∆

Figure 8

` NN

0.05

0.00 0.2

` IN

0.15

0.10

` NN

0.05

0.0

` II

0.25

CR IP T

0.25

Λ

HcL Θ = 0.15

0.30

0.6

∆

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

∆

Equilibrium channel setting in δ − λ space for three values of θ under uniform wholesale price scheme

AN US

is again due to the free-rider problem of the wholesale-price-down benefit, which dampens each retailer’s incentive to introduce a store brand under dual channel. But under single channel, the wholesale-price-down benefit is only enjoyed by the retailer that introduces a store brand, which gives a higher incentive to introduce a store brand than under dual channel. To avoid store brand entry, the manufacturer chooses dual channel for such cases.

M

Proposition 4 has shown that under dual channel, the retailers have lower incentives to introduce a store brand under UWP scheme. Then not surprisingly, NˆN is the equilibrium

ED

setting for a much larger set of parameters under UWP scheme than under FWP scheme. ˆ is always dominated by From the manufacturer’s perspective, the single-channel setting N

PT

the dual-channel setting NˆN (Lemma 3). The expansion of the region NˆN erodes the region ˆ . Therefore, the region where single-channel strategy is optimal for the manufacturer for N becomes extremely small. As cross-store competition exceeds a level, the manufacturer’s

CE

incentive to use dual channel becomes stronger so that the region of single-channel strategy disappears.

AC

Recall that under FWP scheme, single channel is the optimal strategy for the manufac-

turer for a non-small region for all levels of θ values. But under UWP scheme, for the vast

majority of parameter settings, the manufacturer should use dual-channel strategy. This, together with other contrasting results under the two price schemes, implies the importance for the firms to recognize the legal environment of the market for pricing flexibility.

ACCEPTED MANUSCRIPT

24

5.3.

Profit Implications

Since the regulation over price discrimination varies across regions, when a manufacturer wants to launch a new product, should it choose a potential target market with tight regulation or no regulation? Motivated by this question, we compare the manufacturer’s profit under the UWP scheme with that under the FWP scheme by assuming all else being equal in two potential markets except their legal environment. Note that this compari-

CR IP T

son is meaningful under the assumption that in the environment without regulation, the manufacturer’s commitment to a uniform wholesale price is not credible among retailers, which must lead to the FWP scheme. Otherwise, if the manufacturer has the commitment power, the environment without regulation is always preferred, simply because it allows the manufacturer to credibly choose either uniform pricing or flexible pricing. However, it is arguably reasonable to assume that the manufacturer’s commitment is not credible

AN US

in situations where the contract terms offered to one retailer is not observable to other retailers.

For simplicity, let FM and UM denote the manufacturer’s equilibrium profit under the FWP and UWP schemes, respectively. As shown in Proposition 5 (i), when λ is sufficiently large or small, the manufacturer is indifferent between the two price schemes. For large

M

λ, both retailers introduce a store brand under both schemes; for sufficiently small λ, neither introduces a store brand. Under symmetric dual-channel settings, the manufacturer’s

ED

optimal wholesale prices for both channels are the same even under the FWP scheme, so the two price schemes do not make any difference. However, if the two schemes lead to different channel settings, then the manufacturer may prefer one scheme over the other.

PT

Proposition 5 (ii) provides a sufficient condition that guarantees the manufacturer to earn a larger profit under the UWP scheme.

CE

Proposition 5. (i) When λ > max{ ˜ N < λ < min{λ ˜ ˆ, λ ˜ ˆ }, FM < UM . When λ I

√

2−1 ˜ ˜ , λIˆ, λNˆ } 2

or λ < min{λI , λN }, FM = UM ; (ii)

N

˜ N < λ, under the FWP scheme, at least one retailer will introduce a store Given λ

AC

brand under dual channel, so N N cannot be the equilibrium setting. Whereas given λ < ˜ ˆ, λ ˜ ˆ }, under the UWP scheme no retailer will introduce a store brand (i.e., NˆN will min{λ I N

be the emerging setting) under dual channel. It has been proved in Lemma 3 that among all channel settings, NˆN (same as N N ) leads to the largest profit for the manufacturer. Therefore, under the condition in Proposition 5 (ii), the manufacturer achieves a larger

ACCEPTED MANUSCRIPT

25 HaL Manufacturer

HbL Retailer

0.30

0.30

0.25

0.25

FR =U R

0.20

0.20

0.15

0.15

Λ

Λ

F M =U M

FR
0.10

F M
FR =U R

F M =U M 0.00

0.00 0.0

0.2

0.4

0.6

0.8

1.0

∆

Figure 9

0.0

0.2

CR IP T

FR >U R

0.05

0.4

0.6

0.8

1.0

∆

Comparison of firms’ profits under the two price schemes when θ = 0.5

leads to settings other than N N .

AN US

profit under the UWP scheme that leads to setting NˆN than under the FWP scheme that To obtain a thorough understanding, we conduct a numerical study. Figure 9 (a) shows the results in the δ − λ space for a representative θ value. Meanwhile, our extensive numerical study reveals there is no parameter setting in which FM > UM holds. This implies that

M

the manufacturer’s pricing flexibility to set different wholesale prices for the two retailers never strictly benefits him in our setting. The underlying reason is that without free-rider problem, more retailers introduce a store brand under the FWP scheme and such strate-

ED

gic response actually hurts the manufacturer’s profitability. From this perspective, when choosing the target market, the manufacturer does not need to avoid the environment with

PT

strict regulation over price discrimination.14 The implication of legal environments on the retailers’ profits might be of interest to those multi-national retailers that are choosing locations to open new stores. There is no

14

CE

doubt that every firm prefers to be treated fairly. Paradoxically, the environment that We conducted a numerical study to investigate the profit difference under the two price schemes. We consider the

AC

following combinations of parameters: both δ and θ from 0.01 to 1 with step size of 0.01, and λ from 0.01 to 0.3 with step size of 0.01 (because when λ exceeds 0.3, the two price schemes make no difference). Then there are totally 300,000 numerical experiments. We use the term

UM −FM FM

to measure the profit difference for the manufacturer. Based

on the 131,507 experiments that lead to positive profit difference, the difference is between 10% and 100% in most cases (for 130,274 experiments). When θ and λ are small and δ is large, the difference can be larger than 100%. When θ and λ are small and δ is intermediate, the difference can be less than 10%.

ACCEPTED MANUSCRIPT

26

guarantees uniform pricing (i.e., UWP scheme) can even lead to lower profits for retailers compared to the environment where the manufacturer can implement differential pricing (i.e., FWP scheme), as Proposition 6 shows. FR and UR denote the retailers’ equilibrium profits under the FWP and UWP schemes, respectively. ˜ ˆ, λ ˜ ˆ } and δ exceeds a threshold, FR > UR . Proposition 6. When λ < min{λ I N

CR IP T

Under the conditions in Proposition 6, the equilibrium setting is II under the FWP scheme, but NˆN under the UWP scheme due to lower store-brand-introduction incentives. When the substitution effect between store brand and national brand is sufficiently strong, the retailers earn more profits under II (with store brand) than under NˆN (without store brand). As a more complete illustration, Figure 9 (b) compares a retailer’s profit under the two schemes in the δ − λ space for a representative θ value. Note that when the two

AN US

retailers are asymmetric, the retailer considered in Figure 9 (b) is the chosen one under

single channel or the one introducing a store brand under the asymmetric setting IN or ˆ . The figure shows that the retailer’s profit can be either larger or smaller under the IN FWP scheme.15 This implies that no regulation over price discrimination can represent

6.

M

either a positive or a negative feature for retailers.

Conclusions

ED

This paper studies the interaction between national brand manufacturer’s channel strategy for a product and retailers’ store brand decisions, under both FWP and UWP schemes due to the varying legal environment for pricing flexibility across regions. The main findings

PT

are summarized as follows.

Under FWP scheme, a retailer has a lower incentive to introduce a store brand under

CE

single channel than under dual channel, and thus, single channel can be a strategy to prevent store brand entry. This strategy is effective when the store brands are moderately competitive. However, under UWP scheme, due to the free-rider problem of the wholesale-

AC

price-down benefit, the opposite is true: A retailer has a lower incentive to introduce a store brand under dual channel. Moreover, the retailers’ incentives to introduce a store 15

Based on the same 300,000 numerical experiments, we find that when the considered retailer earns a larger profit

under the UWP scheme, the profit difference

UR −FR FR

is small (less than 6%), but when it earns a smaller profit, the

absolute profit difference can be either small or large (between 0 to −55%).

ACCEPTED MANUSCRIPT

27

brand under dual channel is lower under UWP scheme than under FWP scheme. Therefore, the manufacturer prefers dual channel to avoid store brand entry for the vast majority of parameter settings under UWP scheme. The retailers’ store-brand-introduction decisions also present different pattern under the two price schemes. Under FWP scheme, the retailers’ store-brand-introduction decisions are mostly symmetric under dual channel. This is because the wholesale prices charged to

CR IP T

the retailers are relatively independent, and due to the retailers’ ex ante symmetric roles, their decisions also tend to be symmetric. But under UWP scheme, once a retailer has introduced a store brand, the other retailer can take a free ride of the wholesale-price-down benefit, without the need to also introduce a store brand. This gives rise to a larger region of asymmetric dual-channel setting under UWP scheme.

AN US

A major trend for store brands during the past decade is their increasing competitiveness (i.e., higher capability to substitute the national brand). This paper identifies two interesting impacts. First, as a caveat, the retailers should not always more likely introduce a store brand; our analysis reveals that under UWP scheme, fewer retailer should introduce a store brand as store brand becomes more competitive under certain conditions. Second, although store brands are becoming more competitive, the retailer should not always increase its

M

store brand retail price. When the store brand base demand is large, the retailer may even decrease its price to further exploit its large market potential. This stands in contrast with more competitive.

ED

the existing literature that shows the store brand retail price should increase as it becomes The comparison of each firm’s profit under the two price schemes shows that, although

PT

the manufacturer has greater pricing flexibility under the FWP scheme, he never earns a larger profit but sometimes earns a strictly smaller profit compared to that under the UWP

CE

scheme. This implies the manufacturer does not need to avoid an environment with tight regulation over price discrimination. The retailer’s profit can be either larger or smaller

AC

under the FWP scheme. This implies no regulation over price discrimination can represent either a positive or a negative feature for retailers.

References Amrouche, N., Yan, R., 2015. Aggressive or partnership strategy: Which choice is better for the national brand? International Journal of Production Economics 166, 50–63.

ACCEPTED MANUSCRIPT

28

Apelbaum, E., Gerstner, E., Naik, P., 2003. The effects of expert quality evaluations versus brand name on price premiums. Journal of Product & Brand Management 12 (3), 154–165. Arya, A., Mittendorf, B., Sappington, D., 2007. The bright side of supplier encroachment. Marketing Science 26 (5), 651–659. Bonfrer, A., Chintagunta, P., 2004. Store brands: Who buys them and what happens to 195–218.

CR IP T

retail prices when they are introduced? Review of Industrial Organization 24 (2), Cai, G., Dai, Y., Zhou, S., 2012. Exclusive channels and revenue sharing in a complementary goods market. Marketing Science 31 (1), 172–187.

Chen, L., Gilbert, S., Xia, Y., 2011. Private labels: Facilitators or impediments to supply chain coordination. Decision Sciences 42 (3), 689–720.

AN US

Chiang, W., Chhajed, D., Hess, J., 2003. Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design. Management Science 49 (1), 1–20. Chintagunta, P., Bonfrer, A., Song, I., 2002. Investigating the effects of store-brand introduction on retailer demand and pricing behavior. Management Science 48 (10), 1242– 1267. Science 10 (4), 271–296.

M

Choi, S., 1991. Price competition in a channel structure with a common retailer. Marketing

72 (2), 117–134.

ED

Choi, S., 1996. Price competition in a duopoly common retailer channel. Journal of retailing Choi, S., Fredj, K., 2013. Price competition and store competition: Store brands vs. national

PT

brand. European Journal of Operational Research 225 (1), 166–178. Coughlan, A., 1985. Competition and cooperation in marketing channel choice: Theory and application. Marketing Science 4 (2), 110–129.

CE

Coughlan, A., Wernerfelt, B., 1989. On credible delegation by oligopolists: A discussion of distribution channel management. Management Science 35 (2), 226–239.

AC

Dunne, D., Narasimhan, C., 1999. The new appeal of private labels. Harvard Business Review 77 (3), 41–48.

Euromonitor International, 2003. Private label in the uk (part iii): The changing face of fmcg marketing. URL

http://www.just-food.com/analysis/the-changing-face-of-fmcg-mar

keting_id93544.aspx

ACCEPTED MANUSCRIPT

29

Fang, X., Gavirneni, S., Rao, V., 2013. Supply chains in the presence of store brands. European Journal of Operational Research 224 (2), 392–403. Groznik, A., Heese, H., 2010. Supply chain interactions due to store-brand introductions: The impact of retail competition. European Journal of Operational Research 203 (3), 575–582. Heese, H., 2010. Competing with channel partners: Supply chain conflict when retailers

CR IP T

introduce store brands. Naval Research Logistics 57 (5), 441–459.

Hoch, S., Banerji, S., 1993. When do private labels succeed? Sloan Management Review 34.

Ingene, C., Parry, M., 1995. Channel coordination when retailers compete. Marketing Science 14 (4), 360–377.

AN US

IRI, 1988. Infoscan Supermarket Review. Information Resources Inc, Chicago. IRI, 1998. Marketing Fact Book. Information Resources Inc, Chicago.

Jeuland, A., Shugan, S., 1983. Managing channel profits. Marketing science 2 (3), 239–272. Jeuland, A., Shugan, S., 1988. Note-channel of distribution profits when channel members form conjectures. Marketing Science 7 (2), 202–210.

Kumar, N., Ruan, R., 2006. On manufacturers complementing the traditional retail channel

M

with a direct online channel. Quantititive Marketing and Economics 4 (3), 289–323. Kuo, C., Yang, S., 2013. The role of store brand positioning for appropriating supply chain 88–97.

ED

profit under shelf space allocation. European Journal of Operational Research 231 (1), Lal, R., 1990. Price promotions: Limiting competitive encroachment. Marketing Science

PT

9 (3), 247–262.

Lal, R., Staelin, R., 1984. An approach for developing an optimal discount pricing policy.

CE

Management Science 30 (12), 1524–1539.

Le, Y., 2015. Retailers won by store brands: Depending on mathematical models. (in Chinese).

AC

URL http://www.yicai.com/news/2015/01/4059929.html

Lu, Q., Liu, N., 2013. Pricing games of mixed conventional and e-commerce distribution channels. Computers & Industrial Engineering 64 (1), 122–132.

Luchs, R., Geylani, T., Dukes, A., Srinivasan, K., 2010. The end of the Robinson-Patman Act? Evidence from legal case data. Management Science 56 (12), 2123–2133.

ACCEPTED MANUSCRIPT

30

Marx, L., Shaffer, G., 2007. Upfront payments and exclusion in downstream markets. The RAND Journal of Economics 38 (3), 823–843. McMaster, D., 1987. Own brands and the cookware market. European Journal of Marketing 21 (1), 83–94. Moorthy, K., 1988. Strategic decentralization in channels. Marketing Science 7 (4), 335– 355.

CR IP T

Morton, F., Zettelmeyer, F., 2004. The strategic positioning of store brands in retailer– manufacturer negotiations. Review of Industrial Organization 24 (2), 161–194. Narasimhan, C., Wilcox, R., 1998. Private labels and the channel relationship: A crosscategory analysis. The Journal of Business 71 (4), 573–600. Nasser, S., Turcic, D., Narasimhan, C., 2013. National brand’s response to store brands: Throw in the towel or fight back? Marketing Science 32 (4), 591–608.

AN US

Pauwels, K., Srinivasan, S., 2004. Who benefits from store brand entry? Marketing Science 23 (3), 364–390. PLMA, 2015. Private Label Yearbook. Private Label Manufacturers Association, New York.

M

Quelch, J., Harding, D., 1996. Brands versus private labels: Fighting to win. Harvard Business Review 74 (1), 99. Raju, J., Sethuraman, R., Dhar, S., 1995. The introduction and performance of store brands. Management Science 41 (6), 957–978.

ED

Rao, R., 1991. Pricing and promotions in asymmetric duopolies. Marketing Science 10 (2), 131–144.

PT

Ru, J., Shi, R., Zhang, J., 2015. Does a store brand always hurt the manufacturer of a competing national brand? Production and Operations Management 24 (2), 272–286.

CE

Sayman, S., Hoch, S., Raju, J., 2002. Positioning of store brands. Marketing Science 21 (4), 378–397.

AC

Sayman, S., Raju, J., 2004. How category characteristics affect the number of store brands offered by the retailer: A model and empirical analysis. Journal of Retailing 80 (4), 279–287. Seenivasan, S., Sudhir, K., Talukdar, D., 2015. Do store brands aid store loyalty? Management Science Forthcoming. Shugan, S., 1985. Implicit understandings in channels of distribution. Management Science 31 (4), 435–460.

ACCEPTED MANUSCRIPT

31

Thompson, S., 2006. Pepsi dons disguise in attempt to seduce the whole foods devotees. URL

http://adage.com/article/news/pepsi-dons-disguise-attempt-seduc

e-foods-devotees/112984/ Tsay, A., Agrawal, N., 2004. Channel conflict and coordination in the e-commerce age. Production and Operations Management 13 (1), 93–110. Vakharia, A., Wang, L., 2014. Uniform vs. retailer-specific pricing: Incentive alignment 1176–1182.

CR IP T

to enhance supply chain efficiency. Production and Operations Management 23 (7), Wu, C., Wang, C., 2005. A positive theory of private label: A strategic role of private label in a duopoly national-brand market. Marketing Letters 16 (2), 143–161.

Yoshida, Y., 2000. Third-degree price discrimination in input markets: Output and welfare. American Economic Review 90 (1), 240–246.

AN US

Zhang, A., 2013. Huawei/IDC anti-monopoly litigation. URL HUAWEI/IDCANTI-MONOPOLYLITIGATION

Appendix A: Demand functions and equilibrium results for each channel setting

M

A1: Demand functions for each channel setting under FWP and UWP schemes ˆ (N/N)

ED

1 [1 − pAn ], 1+λ ˆ 1 N N qBs = qBs = [λ − pBs ]. 1+λ (I/ˆ I) 1 I Iˆ qAn = qAn [1 − pAn + δ(pAs − pAn )], = 1 + 2λ 1 I Iˆ qAs = qAs = [λ − pAs + δ(pAn − pAs )], 1 + 2λ ˆ 1 I I qBs = qBs = [λ − pBs ]. 1 + 2λ ˆ (NN/NN) ˆ

CE

PT

N N qAn = qAn =

AC

1 NˆN NN = [1 − pAn + θ(pBn − pAn )], qAn = qAn 2 1 NˆN NN = [1 − pBn + θ(pAn − pBn )]. qBn = qBn 2 ˆ (IN/IN) 1 [1 − pAn + θ(pBn − pAn ) + δ(pAs − pAn )], 2+λ ˆ 1 IN IN qBn = qBn = [1 − pBn + θ(pAn − pBn )], 2+λ ˆ 1 IN IN qAs = qAs = [λ − pAs + δ(pAn − pAs )]. 2+λ ˆ

IN IN qAn = qAn =

ACCEPTED MANUSCRIPT

32 ˆ (II/II) 1 [1 − pAn + θ(pBn − pAn ) + δ(pAs − pAn )], 2 + 2λ ˆ 1 II II qBn = qBn = [1 − pBn + θ(pAn − pBn ) + δ(pBs − pBn )], 2 + 2λ ˆ 1 II II qAs = qAs = [λ − pAs + δ(pAn − pAs )], 2 + 2λ ˆ 1 II II [λ − pBs + δ(pBn − pBs )]. qBs = qBs = 2 + 2λ ˆ

II II qAn = qAn =

CR IP T

A2: Equilibrium wholesale prices, retail prices, and firms’ profits under FWP scheme for each channel setting

(N)

1 3 λ 1 λ2 1 N N wA = , pN , ΠN , ΠN , ΠN . An = , pBs = A = B = M = 2 4 2 16(1 + λ) 4(1 + λ) 8(1 + λ) (I)

(NN)

M

1 3+θ NN NN N NN wA = wB = , pN , An = pBn = 2 4 + 2θ 1+θ 1+θ NN NN NN ΠA = ΠB = , ΠM = . 8(2 + θ)2 4(2 + θ)

AN US

(δ + 1)λ + δ 1 3 + 6δ + 2δ 2 + 2δλ + 2δ 2 λ λ , pIAn = , pIAs = , pIBs = , 2(1 + δ) 4(1 + δ)(1 + 2δ) 2(2δ + 1) 2 1 + 4λ2 + 4δ 2 (1 + λ)2 + 2δ(1 + 2λ)2 I ΠA = , 16(1 + δ)(1 + 2δ)(1 + 2λ) 2 1 λ , ΠIM = . ΠIB = 4(1 + 2λ) 8(1 + δ)(1 + 2λ)

I wA =

(IN)

2 + 4δ + 2(3 + 5δ)θ + [4 + δ(4 + λ)]θ2 , 4(1 + θ)(1 + 2θ) + 2δ 2 [4 + θ(6 + θ)] + 4δ[3 + θ(7 + 3θ)] 2 2 2 + 6θ + 4θ + δ [4 + (3 + λ)θ] + δ[6 + θ(12 + λ + (4 + λ)θ)] IN wB = , 4(1 + θ)(1 + 2θ) + 2δ 2 [4 + θ(6 + θ)] + 4δ[3 + θ(7 + 3θ)] IN IN IN IN IN )] + (1 + θ)wB θ[3 + 2(2 + θ)wA + (1 + θ)wB ] + δ[2 + 2λ(1 + θ) + 4wA + θ(3 + 2(3 + θ)wA pIN An = (2 + θ)(2 + 3θ) + δ[8 + 3θ(4 + θ)] IN ) 2(1 + wA , + (2 + θ)(2 + 3θ) + δ[8 + 3θ(4 + θ)] IN IN IN IN IN IN )] ] + δ[4(1 + wB ) + θ(3 + λ + (2 + θ)wA + 2(3 + θ)wB 2(1 + wB ) + θ[3 + (1 + θ)wA + 2(2 + θ)wB pIN , Bn = (2 + θ)(2 + 3θ) + δ[8 + 3θ(4 + θ)] IN IN λ(2 + θ)(2 + 3θ) + δ[4 + 4λ(1 + θ) + θ(6 + θwA + 2(1 + θ)wB )] pIN , As = 2(2 + θ)(2 + 3θ) + 2δ[8 + 3θ(4 + θ)]

CE

PT

ED

IN wA =

IN IN IN IN IN ΠIN A = (pAn − wA )qAn + pAs qAs , IN IN IN ΠIN B = (pBn − wB )qBn ,

AC

IN IN IN IN IN IN IN ΠIN M = wA qAn + wB qBn , where qAn , qBn , and qAs are provided in Appendix A1.

(II)

2(1 + θ) + δ[4 + (2 + λ)θ] , 2[2(1 + θ) + δ(6 + 4θ + δ(4 + θ))] II II II 1 + wA + θwA + δ[1 + λ + (2 + θ)wA )] II pII , An = pBn = 2 + θ + δ(4 + θ) II λ(2 + θ) + δ(2 + 2λ + θwA ) II pII , As = pBs = 2[2 + θ + δ(4 + θ)] II II wA = wB =

ACCEPTED MANUSCRIPT

33 II II II II II II ΠII A = ΠB = (pAn − wA )qAn + pAs qAs , II II II II ΠII M = 2wA qAn , where qAn and qAs are provided in Appendix A1.

A3: Equilibrium wholesale prices, retail prices, and firms’ profits under UWP scheme for each channel setting

CR IP T

ˆ , I, ˆ NˆN , and II ˆ are the same as those under N , I, N N , and II, respectively. Therefore, The results under settings N ˆ as follows. we only present the equilibrium results under setting IN ˆ (IN)

8 + 16δ + 2[10 + δ(15 + λ)]θ + 3[4 + δ(4 + λ)]θ2 , 8(2 + δ)(1 + 2δ) + 8[5 + δ(10 + 3δ)]θ + 6[4 + δ(6 + δ)]θ2 ˆ ˆ ˆ ˆ (2 + 3θ)(1 + wIN + θwIN ) + δ[2 + 3θ + 2λ(1 + θ) + (1 + θ)(4 + 3θ)wIN ] pIN , An = (2 + θ)(2 + 3θ) + δ[8 + 3θ(4 + θ)] ˆ IN ˆ 2 + 4δ + 3θ + 3δθ + δλθ + (2 + 3θ)[1 + θ + δ(2 + θ)]w pIN , Bn = (2 + θ)(2 + 3θ) + δ[8 + 3θ(4 + θ)] ˆ IN ˆ λ(2 + θ)(2 + 3θ) + δ[4λ(1 + θ) + (2 + 3θ)(2 + θw )] pIN , As = 2(2 + θ)(2 + 3θ) + 2δ[8 + 3θ(4 + θ)] ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

IN IN IN IN ΠIN )qAn + pIN A = (pAn − w As qAs IN IN IN ΠIN )qBn , B = (pBn − w ˆ

ˆ

ˆ

ˆ

ˆ

AN US

wIN =

AC

CE

PT

ED

M

IN IN IN IN IN IN ΠIN (qAn + qBn ), where qAn , qBn , and qAs are provided in Appendix A1. M =w