go upscale? quality competition between national brand … · with the proximity to market and the...

Go Upscale? Quality Competition BetweenNational Brand and Store Brand

Tulika Chakraborty, Satyaveer S. Chauhan, Xiao HuangJohn Molson School of Business, Concordia University, Montreal, QC

[email protected], {satyaveer.chauhan, xiao.huang}@concordia.ca

It is commonly assumed in private label literature that store brands are of lower quality than competing

national brands. In this paper, we contest this notion by studying quality competition between a national-

brand manufacturer and a store-brand retailer. The manufacturer sells its national-brand products through

the retailer who produces a competing store brand at the same time. The two parties first invest in their

brand qualities, after which the manufacture determines the wholesale price for the national brand and

the retailer decides the retail prices for both brands. With a general quality-dependent cost structure, we

explicitly characterize the equilibrium in both price and quality levels under various channel power structures.

The results suggest that the store brand could possibly be of higher quality than the national brand even

in absence of cost disparity; however, the store brand will charge a lower retail price whether its quality

is superior to the national brand or not. Further, price competition and quality competition bear opposite

implications on equilibrium solutions as well as profitability levels. Surprisingly, the manufacturer may benefit

from a more costly production or quality investment scenario, while both the retailer and the supply chain

will su↵er from the same. The paper highlights the importance of accounting for quality decisions in the

study of private label products.

Key words : private label, store brand, game theory, competition, quality, distribution channels, power

structure;

This version : April 18, 2018

1. Introduction

With the proximity to market and the awareness of recurring economy cycles, giant retailers become

increasingly inclined to establish their own store brands, also known as the “private labels.” 1 Both

Target and Walmart have their private label products, “Market Pantry” and “Great Value” respec-

tively, in the frozen food aisles. Costco has long held the “Kirkland” and “Kirkland Signature” as

its home brands. Trader Joes and Whole Foods also possess store-brand organic co↵ee and yogurt

in alluring savvy store-addicted customers. Beyond groceries, store brand has long reached the

fashion end as well. The cosmetic Sephora exclusively carries its “Sephora Collection.” Department

stores from Macy’s, Bloomingdale’s to Saks, all hold private brands that are available “Only At”

1 We will use “store brand” and “private label” interchangeably throughout the rest of the paper.

1

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their chain stores. At the time of this paper being written, the online guru Amazon also join this

wave by developing its own private-label apparels (Bloomberg.com 2017).

The boom of store brand is far from an illusion. According to recent statistics from the Private

Label Manufacturers Association, consumers’s choices are shifting from national brands to store

brands. In 2015, store brands sales in the US reached a record revenue of 118.4 billion, capturing

a record of 17.7% of the total market. The same number increased by 2.2 billion in 2016, also the

highest mark ever. And in 2015, nearly one of every four items sold in US supermarkets was a store

brand (PLMA 2016).

Running one’s own store brand o↵ers numerous benefits, such as closer monitoring of promo-

tional events, more leeway on pricing strategies, and deeper control over product qualities. Among

all, one of the most compelling reasons connects to competition. It is well recognized that store

brand reduces a retailer’s dependency on national brands, which are usually produced by upstream

manufacturers. Store brand inevitably cannibalizes national brands’ demand, thus forcing the man-

ufacturers to lower the wholesale prices of their products (Raju et al. 1995, Narasimhan and Wilcox

1998, Wall Street Journal 2002, Choi and Coughlan 2006).

In this competition, the key advantage of the national brands lies in the brand quality that

the consumers realize and trust (FoodDive.com 2016). This gap was indeed evident decades ago,

when private labels was generally considered generic and of poorer quality comparing to similar

national brands. Subsequently, the assumption that store-brand products are of lower quality than

national-brand has been commonly held among many studies concerning private labels (e.g., Choi

and Coughlan 2006, Chen et al. 2011, Fang et al. 2013, just to name a few). However, it is yet

unexamined to what extent such assumption holds true. On one hand, this notion is clearly chal-

lenged by the rise of premium store brands such as the “President’s Choice” of Loblaw (Quelch and

Harding 1996). On the other, consumers are becoming more hesitant in linking brand names with

qualities. In 2010, 57% of consumers agreed that good brand names do not always imply better

quality, and this figure keeps rising in recent years (Time.com 2012).

We thereby retreat to ask ourselves the very fundamental question: do private labels necessarily

have to compromise on quality? More specifically, how would factors such as competition, channel

power and cost structure, drive the pricing and quality levels of the national- and store-brands? And

how would such further impact the profitability of each stakeholder as well as the supply chain? In

this paper, we tackle these questions by analyzing a stylized supply chain with a national-brand

manufacturer and a store-brand retailer. The retailer procures national-brand products at the

wholesale price set by the manufacturer, and determines retail prices for both the national-brand

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and its store-brand products. Even though each party can promptly adjust prices with respect to

the other’s actions, quality investments are made ahead of time and costly to revise hence bearing

more strategic implications. In investigating the strategic quality decisions, we adopt a general

quality-dependent cost structure and let the two parties competitively set quality levels of their

products before any pricing decision is made. Depending on the channel power between the two

parties – whether the manufacturer or the retailer being the Stackelberg leader or the two making

decisions simultaneously, we characterize the equilibrium quality levels of the store- vs. national-

brand products explicitly. Through both analytical characterization and numerical simulation, our

findings deliver the following insights:

1. It is possible that the retailer would set a higher quality for its store brand than the man-

ufacturer does for the national brand, even when there is little cost disparity between the two;

however, the store brand in general charges a lower retail price than the national brand;

2. The national-brand manufacturer may benefit from a more costly quality investment or quality

production scenario, while such is always detrimental to the retailer and the supply chain.

3. Quality competition has opposite impact than price competition on a number of important

measures. Specifically, intense quality competition reduces pricing and quality levels for both the

national- and store-brand products, making the retailer as well as the supply chain less profitable.

However, the national-brand manufacturer may benefit more out of ferocious quality competition;

4. Greater channel power disincentives quality investment without compromising the price; in

particular, a first-mover retailer fosters premium national brand and higher pricing along the supply

chain.

Therefore, the consideration of quality decisions brings significant insights to existing knowledge

of private label and relevant competitions. It is thus highly valuable for both researchers and

practitioners to account for quality implications in the study of store brand and national brand.

The remainder of the paper is organized as follows: Section 2 reviews the most relevant litera-

ture. Section 3 describes model formulation and characterizes the benchmark centralized decision.

Section 4 solves the pricing and quality equilibrium under di↵erent channel power structures. Sec-

tion 5 discusses the impact of competition, channel power and cost parameters on equilibrium

solutions and profitability. Section 6 concludes the paper. All proofs and notations are relegated

to the appendix.

2. Literature Review

This paper is relevant to two streams of literature: those related to the competition between national

brands and store brands, and those that consider channel/power structures between manufacturers

4

and retailers.

The first stream of research captures the study of private label products and subsequently the

competition between national brand and store brand. A detailed review can be found in Steiner

(2004) and Sethuraman (2009). Private label was originally developed as a low-cost alternative for

low-income customers (Quelch and Harding 1996). For this reason, literature normally assumes

store brands of lower quality than national brands (e.g., Mills 1995, Raju et al 1995, Narasimhan

and Wilcox 1998, Choi and Coughlan 2006, Chen et al 2011, Fang et al 2013, Ru et al 2015,

Jin et al. 2017), even though empirical evidence suggested otherwise might happen (Aplebaum

et al 2003). Among the limited number of papers that take into account of quality decisions in

private label literature (e.g., Dunne and Narasimhan 1999, Choi and Coughlan 2006, Heese 2010),

store brands still turn out inferior to national brands due to direct (e.g., quality of store brand

is capped by national brand) or indirect assumptions (e.g., store brand is cost ine�cient). Our

paper complements the literature by analyzing factors that may drive the quality di↵erence in

the opposite direction. Specifically, we apply a general quality-dependent cost structure for both

products without sacrificing the branding e↵ect, and identifies scenarios where the retailer may

o↵er higher quality store-brand products than the manufacturer would do with its national brand.

The second contribution of our paper to consider joint pricing and quality design for both store-

and national-brands in the context of competition. Most of the previous works in private label have

been focusing on the rationale of introducing the store brand and respective pricing strategies,

while keeping the quality of one or more of the products as given (e.g., Raju et al. 1995, Narasimhan

and Wilcox 1998, Sayman et al. 2002, Groznik and Heese 2010, Chen et al 2011 for single channel

and Jin et al. 2017 for dual channels). It was not until recently that researchers became interested

in the competition among multiple national- and store-brands. While many still focus on the issue

of pricing (Choi and Fredj 2013, Jin et al. 2017), Amaldoss and Shin (2015) study the equilibrium

quality levels and find that it is possible for a store brand to o↵er the top quality. Nevertheless,

among private label literature, the study of quality competition between the national- and store-

brands is still rare. Further, the joint impact of the price vs quality competition is unknown in the

same area. For this purpose, we allows the national brand and store brand to compete on both

price and quality on a general basis.

Another distinction of our paper is to accommodate various channel/power structures between

the manufacturer and the retailer. Channel structures reflecting the parties’ market power have

been widely considered in di↵erent context (see Choi 1991 and its referenced papers; specifically,

Nagarajan and Sosic 2009 for assembly systems, Shi et al 2013 for supply chains). However, few

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applies to private label products. Most studies in private label either assume the manufacturer

to be the Stackelberg leader (Raju et al 1995, Narasimhan and Wilcox 1998, Sayman et al 2002,

Yao et al 2008, Groznik and Heese, 2010, Heese, 2010, Jin et al 2017) or equal power among

channel members (Vertical Nash) (Kurata et al 2007, Corstjens and Lal 2000). That being said,

little attention has been given to the scenario where store-brand retailer is the Stackelberg leader.

Recently, Ru et al (2015) study a retailer-Stackelberg game and show that the entry of store

brand can actually benefit the national-brand manufacturer. Choi and Fredj (2013) consider one

national-brand manufacturer and two store-brand retailers and study their pricing strategies under

all possible channel structures. For as far as we know, the consideration of quality is still scarce in

this line of research.

In summary, this paper adds another block to private label literature by considering 1) a general

quality-dependent cost structure, 2) joint price and quality competitions, and 3) various chan-

nel/power structures between the channel members.

3. Model

Consider a supply chain with one manufacturer and one retailer. The retailer procures national-

brand products (NB) from the manufacturer and at the same time, produces its own store-brand

products (SB) in-house. The two products, NB and SB, serves the same market thus the manufac-

turer and the retailer are market competitors and channel partners at the same time (Choi 2015).

For the rest of the paper, we will use subscript “n” for NB, subscript “s” for SB, and the generic

subscript i2 {n, s} for terms that apply to both.

Let µ denotes the total market size, ↵i the market fractions, pi the retail prices, and xi the

quality levels for NB and SB respectively. The demand functions of the two products, dn and ds,

are characterized by

di = µ↵i ��pi + �pj + �xi ��xj, i, j 2 {n, s}, i 6= j (1)

where � and � measure one’s own price and quality sensitivity, and � and � measure the cross price

and quality sensitivity between the brands, and �, �,�,� 2 R+. We assume that � > � and � > �.

These give the assurance that the demand for one brand is a↵ected more by the changes in the

price and the quality of its own brand than those of the competitors. This is also consistent with

our existing notion. Similar demand functions have been widely used in literature considering both

price and quality competition, such as Banker et al(1998), Xie et al (2011) and Giri et al (2015),

just to name a few. In modeling brand asymmetry, we further assume that ↵n > ↵s in reflecting

that NB is of higher brand value than SB (Dawes and Nenycz-Thiel 2013).

6

Contrary to most private label literature where production costs are often ignored (e.g., Raju

1995, Sayman 2002, Choi and Fredj 2013, Jin et al 2017, with an exception of Chen et al 2011),

we allow the two brands to carry di↵erent production costs. Further, such production costs are

primarily comprised of two components. The first is a lump-sum cost ⌘ix2i , which arises from

technology or facility investment in maintaining brand line i at quality level xi. Consistent with the

relevant literature, such cost quadratically increases with the quality level, representing diminishing

returns on investment. The second is a marginal cost ci + ✓xi, where ci > 0 and 0 < ✓ < 1, that

applies to each unit of output. Thus the quality level has a positive impact on both the fixed

cost and marginal cost. To the best of our knowledge, this is the first paper in private label that

explicitly models quality-driven fixed and variable costs.

The timeline of the game is as follows:

• Stage 1 (Quality competition): the manufacturer determines the quality level of NB, xn, and

the retailer determines the quality level of SB, xs;

• Stage 2 (Price competition): the manufacturer determines the wholesale price of NB to the

retailer, wn, and the retailer determines the retail margin for both products (mn,ms), which imme-

diately implies the retail prices pn =mn +wn and ps =ms + cs + ✓xs.

We let quality decisions take place before pricing decisions as revising quality can be rather

time-consuming compared to adjusting price (Olbrich and Jansen 2014). For the same reason, we

assume that the price competition will take place on a simultaneous basis – that the manufacturer

and the retailer can promptly adjust their prices based on the observation of the other party’s

decision since the two brands are competing in the same market.

Thus at Stage 2, the profit of the manufacturer and the retailer are

⇧M(wn|pn, ps, xn, xs) =⇥wn � (cn + ✓xn)

⇤dn � ⌘nx

2n, (2)

⇧R(pn, ps|wn, xn, xs) = (pn �wn)dn +�ps � (cs + ✓xs)

ds � ⌘sx

2s. (3)

The equilibrium prices are thereby denoted as w⇤n(xn, xs), p⇤n(xn, xs) and p

⇤s(xn, xs).

Back to Stage 1, we consider several game sequences that can arise due to di↵erent power

structures:

• Manufacturer Stackelberg Vertical Nash (MSV): Under MSV, the manufacturer is the Stackel-

berg leader in quality setting, and the retailer decides the quality level of SB based on that of NB.

This is also the game sequence that has been most often considered in private label literature. The

MSV model can be formulated as

maxxn

⇧M

⇣xn,w

⇤n

�xn, x

⇤s(xn)

�, p

⇤n

�xn, x

⇤s(xn)

�, p

⇤s

�xn, x

⇤s(xn)

�⌘

7

s.t. x⇤s(xn) = argmax

xs⇧R

⇣xn, xs,w

⇤n(xn, xs), p

⇤n(xn, xs), p

⇤s(xn, xs)

⌘

• Retailer Stackelberg Vertical Nash (RSV): Under RSV, the retailer is the Stackelberg leader in

quality setting. This scenario arises when the retailer has more control of the channel power and

the manufacturer is of less impact. And the RSV model is be formulated by

maxxs

⇧R

⇣xs,w

⇤n

�x⇤n(xs), xs

�, p

⇤n

�x⇤n(xs), xs

�, p

⇤s

�x⇤n(xs), xs

�⌘

s.t. x⇤n(xs) = argmax

xn⇧M

⇣xn, xs,w

⇤n(xn, xs), p

⇤n(xn, xs), p

⇤s(xn, xs)

⌘

• Vertical Double Nash (VDN): Under this VDN game it is assumed that both the manufacturer

and the retailer are of equal power in the quality setting and will determine the quality levels

simultaneously. The equilibrium qualities in the VDN model satisfy

x⇤n = argmax

xn⇧M

⇣xn, x

⇤s,w

⇤n(xn, xs), p

⇤n(xn, xs), p

⇤s(xn, xs)

⌘

x⇤s = argmax

xs⇧R

⇣x⇤n, xs,w

⇤n(xn, xs), p

⇤n(xn, xs), p

⇤s(xn, xs)

⌘

For the rest of the paper, we use subscript to denote supply chain member and superscript for the

game type, e.g., ⇧MSVR (·) denotes the profit of the retailer under Manufacturer Stackelberg Vertical

Nash (MSV) game.

Before getting into the game analysis, we first characterize the first best solution, namely the

optimal decision for a centralized supply chain.

3.1. Centralized supply chain

Consider a central planner that sets the quality levels and retail prices with the goal of maximizing

total profit of the supply chain. Essentially, it needs to solve the following optimization problem:

maxpn,ps,xn,xs

⇧C(pn, ps, xn, xs) =X

i2(n,s)

hpi � (ci + ✓xi)

idi � ⌘ix

2i . (4)

For the rest of the paper, we denoteA1: �� 0,A2: 0< �4�

< ✓<��,A3: ↵n > ↵s � (�2��2)cs

�µ,

A4: ⌘i >maxn⌘1,⌘2,⌘3

ofor i2

�n, s

. These conditions sustain a wide range of reasonable model

parameters and are su�cient for many subsequent analytical results. For technical purpose, we

consider these conditions as global assumptions albeit they are not necessary, as the same results

may still hold in violation of some or all of these conditions.

Proposition 1. There exists a unique line of optimal retail prices and quality levels that satisfies

the following optimality conditions:

@⇧C

@pn= �2�pn +2�ps +(�+�✓)xn � (�+ �✓)xs +T1 = 0,

8

@⇧C

@ps= 2�pn � 2�ps � (�+ �✓)xn +(�+�✓)xs +T2 = 0,

@⇧C

@xn= (�+�✓)pn � (�+ ✓�)ps � 2(⌘n + �✓)xn +2�✓xs �T3 = 0,

@⇧C

@xs= �(�+ ✓�)pn +(�+�✓)ps +2�✓xn � 2(⌘s + �✓)xs �T4 = 0,

where the expression of Ti’s are given in the appendix.

Note that @2⇧C@pn@ps

= 2� > 0 and @2⇧C@xn@xs

= 2�✓> 0. These imply the complementarity between the

two retail prices and the same between the two quality levels. That is, retail price (resp. quality) of

the national brand always enhances the value of the retail price (resp. quality) of the store brand,

and vice versa. The complementarity between retail prices (resp. quality levels) also increase with

the cross-price (resp. cross-quality) sensitivity parameter. Thus the interaction between the prices

(resp. quality levels) of two brands and cross-sensitivity parameters have a significant impact on

the supply chain profit.

4. Equilibrium Analysis

In this section, we characterize the equilibrium that arises from the three games, MSV, RSV, VDN,

respectively. We first discuss pricing equilibrium based on given quality levels, which is common

across the three games.

Proposition 2. At given quality levels (xn, xs), there exists a unique Nash equilibrium in the

pricing stage. Further, the equilibrium of the wholesale price and retail prices for the national brand

and the store brand are given by:

w⇤n(xn, xs) =

1

3�

h(2�✓+ �)xn � (�� ✓)xs +µ↵n +2�cn + �cs

i, (5)

p⇤n(xn, xs) =

⇣1xn + ⇣2xs +(4�2 � �2)µ↵n +3��µ↵s +(�2 � �

2)(2�cn + �cs)

6�(�2 � �2), (6)

p⇤s(xn, xs) =

(��)xn +�✓(�2 � �

2)+�� xs + �µ↵n +�µ↵s +(�2 � �

2)cs2(�2 � �2)

, (7)

where ⇣1 = �(2�2+�2)�3��+2(�2��

2)(�+�✓)> 0 and ⇣2 = 3��(�+�✓)� (�+ ✓�)(2�2+�2)�2�(�2�

�2)< 0.

As the quality of NB (xn) increases, the manufacturer will increase its wholesale price and the

retailer will raise the retail price of the NB accordingly. The retail price of SB increases with either

quality level, whether it is of the competing product NB (xn) or its own (xs). However, the quality

level of SB (xs) has negative impact on the retail price of NB product.

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4.1. Manufacturer Stackelberg Vertical Nash (MSV)

In the MSV game, the pricing follows Proposition 2 for any given quality levels, and the national

brand manufacturer is the Stackelberg leader in the quality-setting stage. To derive the equilibrium

quality levels, we first characterize the retailer’s optimal reaction to the manufacturer’s quality

decision:

Lemma 1. (a) In the MSV game, given manufacturer’s quality decision xn, the optimal reaction

of the retailer is

x⇤s(xn) =

V1xn +U1

�1, (8)

where the expression of V1, U1 and �1 are given in the appendix.

(b) @x⇤s/@xn > 0.

Thus in the scenario of MSV, the retailer enhances the quality level of its store brand when

the manufacturer increases the quality level of its national brand. The existence of the unique

Stackelberg solution in the quality-setting stage is secured by the following proposition:

Proposition 3. There exits a unique subgame perfect equilibrium in the quality-setting stage

where the manufacturer is the Stackelberg leader. Specifically, the equilibrium quality levels of the

national brand and the store brand in MSV are given by:

xMSV ⇤n =

h(��✓)�1 � (�� ✓)V1

ih(µ↵n ��cn + �cs)�1 � (�� ✓)U1

i

�3(9)

xMSV ⇤s =

V1

h(��✓)�1 � (�� ✓)V1

ih(µ↵n ��cn + �cs)�1 � (�� ✓)U1

i+U1�3

�1�3(10)

where �3 > 0 and the expression is given in the appendix.

From these quality equilibrium solutions, it can be observed that initial market demand of NB has

a positive influence on the quality levels of both NB and SB products. Hence, higher initial market

size of the NB encourages the retailer to invest more in the quality improvement e↵orts of his own

store brand (SB) product.

4.2. Retailer Stackelberg Vertical Nash (RSV)

In RSV, the retailer is the Stackelberg leader in the quality setting stage. Manufacturer’s reaction

function given retailer’s quality of the SB product can be found in the following lemma:

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Lemma 2. (a) In the RSV game, given the retailer’s quality decision xs, the optimal reaction of

the manufacturer is

x⇤n(xs) =

V2xs +U2

�2, (11)

where the expression of V2, U2 and �2 are given in the appendix.

(b) @x⇤n/@xs > 0.

Similar to the MSV game, we can also show that if the retailer increases the quality level of its

store brand, the national brand manufacture will follow suit accordingly. The equilibrium quality

levels under the RSV game can subsequently be obtained from the following proposition.

Proposition 4. There exits a unique subgame perfect equilibrium in the quality-setting stage

where retailer is the Stackelberg leader. Specifically, the equilibrium quality levels of the national

brand and the store brand in RSV are given by:

xRSV ⇤s =

F4U2V2 +F5U2�2 +F6V2�2 +F7�22

�4(12)

xRSV ⇤n =

V2

nF4U2V 2+F5U2�2 +F6V2�2 +F7�2

2

o+U2�4

�2�4(13)

where the expression of Fi’s and �i’s are listed in the appendix.

4.3. Vertical Double Nash (VDN)

Under VDN, the optimal quality reaction functions are the same as characterized in MSV and

RVS. However, in the VDN game the manufacturer and the retailer set their quality levels in a

simultaneous basis. The equilibrium quality levels are characterized in following proposition.

Proposition 5. There exists a unique Nash equilibrium in the quality-setting stage. Specifically,

the equilibrium quality levels of the national brand and the store brand in VDN are given by:

xV DN⇤n =

�1U2 +V2U1

V1V2 +�1�2and x

V DN⇤s =

�2U1 +V1U2

V1V2 +�1�2. (14)

Thus far, we managed to prove the existence of NE for all three games and obtained closed

form solutions for both the quality and pricing equilibrium. In what follows, we proceed to inves-

tigate the impact of competition, power structure and cost structure on equilibrium solutions and

channel profitability. Given the complex structure of the equilibrium solutions, not all results are

analytically tractable. We thereby conduct extensive numerical analysis in complementing relevant

studies.

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5. Numerical Analysis

In the section, we study the impact of various factors on the equilibrium solutions and profitability

levels. We first focus on the competition itself and investigate how the quality vs price competition

a↵ects equilibrium decisions and subsequently the benefit of each stakeholder as well as the entire

supply chain. We then look into the impact of the channel/power structure, namely how the pricing

and quality levels vary across the MSV, RSV and VDN scenarios. Lastly, we analyze how the cost

parameters may contribute to the profitability variation under di↵erent scenarios.

5.1. Impact of Price and Quality Competition

How would price competition (�� ) and quality competition (��) between two brands impact

the quality levels of the final products, and further, influence the prices and profitabilities? We

describe such impacts in the following observations, which hold true across di↵erent channel power

structures.

• Price competition has positive impact on the quality levels of both brands. Moreover, it has

positive influence on prices and profits for both the manufacturer and the retailer, as well as the

supply chain profit in total.

Higher price competition (smaller ��) implies higher product substitutability. Hence, in order

to di↵erentiate themselves from the competing brands, channel members would increase the quality

levels of their own brands (Figure 1-a and 1-c). The higher quality levels of both brands subse-

quently force the manufacturer and the retailer to set higher prices for both brands (Figure 2-a,2-c

and 2-e).

On the other hand, however, it appears that price competition has positive e↵ect on the demand

function of SB product but not so much on that of the NB product. In the same line of numerical

analysis, we find that a 20% change in price competition level results in an average 0.6% change in

the demand of NB product and 3.5% for the SB product. Thus, profits of both the manufacturer

and the retailer rise due to higher margin and more-or-less stable demand (Figure 3-a,3-c and 3-e)

. Consequently, the supply chain profit increases with the price competition as well (Figure 4-a).

• Quality competition has negative impact on the quality level of the both brands. Moreover, it

has negative impact on prices, retailer’s profit, and total channel’s profit, but positive impact on

the profit of the manufacturer.

Similar to price competition, higher quality competition (smaller ��) also implies that brands

are more substitutable. Such forces the retailer to reduce prices for both the NB and SB prod-

ucts (Figure 2-b and 2-d). Further, we find that quality competition has negative impact on the

demand of the SB product but little influence on that of the NB product. For this reason, intense

12

0

5

10

15

20

25

1 . 5 2 2 . 5 3 3 . 5

Qua

lity

leve

l

Quality Competition (δ-λ)

( b ) Q u a l i t y L e v e l o f N a t i o n a l B r a n d

xn(Cent) xn(VDN)

xn(RSV) xn(MSV)

0

5

10

15

20

1 . 5 2 2 . 5 3 3 . 5

Qua

lity

leve

l


( d ) Q u a l i t y L e v e l o f S t o r e B r a n d

xs(Cent) xs(VDN)

xs(RSV) xs(MSV)

2468

10121416

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Qua

lity

leve

l

Price Competition (β-γ)

( a ) Q u a l i t y L e v e l o f N a t i o n a l B r a n d

xn(Cent) xn(VDN)

xn(RSV) xn(MSV)

456789

101112

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Qua

lity

leve

l

Price competition (β-γ)

( c ) Q u a l i t y L e v e l o f S t o r e B r a n d

xs(Cent) xs(VDN)

xs(RSV) xs(MSV)

Figure 1 Equilibrium quality levels under di↵erent channel power structures (µ= 1000, cn = 6, cs = 6, ↵n = 0.8,

↵s = 0.2, ⌘n = 8, ⌘s = 8, ✓ = 0.3, � = 10.5, � = 8 for quality competition and � = 7, � = 5 for price

competition)

quality competition lowers the profit of the retailer (Figure 3-d and 3-f). On the other hand, since

quality competition has little impact on the demand of the NB product, the manufacturer will

only set a slightly higher or even lower wholesale price for the NB product (Figure 2-f). Hence,

the manufacturer’s profit increases under the influence of quality competition (Figure 3-b). The

aggregated impact on the retailer and the manufacturer leads to a reduced supply chain profit as

quality competition intensifies (Figure 4-b).

• Price competition and quality competition have

(a) opposite influence on equilibrium pricing and quality levels;

(b) opposite influence on the retailer’s profit and the supply chain profit;

(c) similar influence on the manufacturer’s profit.

Comparing the previous two observations, it turns out that price competition and quality com-

petition bear opposite implications to equilibrium solutions. Higher price competition enhances the

equilibrium quality levels and elevated the prices, while more intense quality competition reduces

13

110

115

120

125

130

135

140

1 . 5 2 2 . 5 3 3 . 5

Reta

il pr

ice


( b ) R e t a i l P r i c e o f N a t i o n a l B r a n d

Pn(Cent) Pn(VDN)

Pn(RSV) Pn(MSV)

90

95

100

105

110

1 . 5 2 2 . 5 3 3 . 5

Reta

il pr

ice


( d ) R e t a i l P r i c e o f S t o r e B r a n d

Ps(Cent) Ps(VDN)

Ps(RSV) Ps(MSV)

31

32

33

34

35

36

1 . 5 2 2 . 5 3 3 . 5

Who

lesa

le p

rice


( f ) W h o l e s a l e P r i c e

Wn(VDN) Wn(RSV) Wn(MSV)

110

120

130

140

150

160

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Reta

il pr

ice


( a ) R e ta i l P r i c e o f N a t i o n a l B r a n d

Pn(Cent) Pn(VDN)

Pn(RSV) Pn(MSV)

95

100

105

110

115

120

125

130

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Reta

il pr

ice


( c ) R e t a i l P r i c e o f S t o r e B r a n d

Ps(Cent) Ps(VDN)

Ps(RSV) Ps(MSV)

31

32

33

34

35

36

37

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Who

lesa

le p

rice


( e ) W h o l e s a l e P r i c e

Wn(VDN) Wn(RSV) Wn(MSV)

Figure 2 Equilibrium retail prices and wholesale price under di↵erent channel power structures (µ= 1000, cn = 6,

cs = 6, ↵n = 0.8, ↵s = 0.2, ⌘n = 8, ⌘s = 8, ✓ = 0.3, � = 10.5, � = 8 for quality competition and � = 7,

�= 5 for price competition)

quality levels and equilibrium prices in general. All stakeholders including the supply chain will

benefit from a more intense price competition, however, only the manufacturer will enjoy the same

for quality competition. The joint e↵ect of the two competitions will apparently depend upon the

strength of each and can interestingly be decomposed in these two dimensions.

14

52005400560058006000620064006600

1 . 5 2 2 . 5 3 2 . 5

Man

ufac

ture

r's p

rofit


( b ) M a n u f a c t u r e r ' s P r o f i t

NB manuf-VDN NB manuf-RSV

NB manuf-MSV

1500017000190002100023000250002700029000

1 . 5 2 2 . 5 3 3 . 5

Reta

iler's

pro

fit


( d ) R e t a i l e r ' s P r o f i t f r o m N a t i o n a l B r a n d a n d S t o r e B r a n d

NB-VDN NB-RSV NB-MSV

SB-VDN SB-RSV SB-MSV

41000

42000

43000

44000

45000

46000

47000

1 . 5 2 2 . 5 3 3 . 5

Reta

iler's

pro

fit


( f ) R e t a i l e r ' s P r o f i t

Retailer-VDN Retailer-RSV

Retailer-MSV

5800

6000

6200

6400

6600

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Man

ufac

ture

r's p

rofit


( a ) M a n u f a c t u r e r ' s P r o f i t

NB-Manuf-VDN NB-Manuf-RSV

NB-Manuf-MSV

15000

20000

25000

30000

35000

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Reta

iler's

pro

fit

Pricee Competition (β-γ)

( c ) R e t a i l e r ' s P r o f i t f r o m N a t i o n a l B r a n d a n d S t o r e B r a n d

NB-VDN NB-RSV NB-MSV

SB-VDN SB-RSV SB-MSV

40000

45000

50000

55000

60000

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Reta

iler's

prof

it


( e ) R e t a i l e r ' s P r o f i t


Retailer-MSV

Figure 3 Equilibrium profits of the manufacturer and the retailer under di↵erent channel power structures (µ=

1000, cn = 6, cs = 6, ↵n = 0.8, ↵s = 0.2, ⌘n = 8, ⌘s = 8, ✓ = 0.3, � = 10.5, � = 8 for quality competition

and �= 7, �= 5 for price competition)

5.2. Impact of Channel Power Structure

Recall that in our model, the manufacturer and the retailer can set quality levels in three di↵erent

sequences, reflecting di↵erent channel power structures. However, price setting between the two

members is conducted on a simultaneous basis. This is in contrast to many existing literature (e.g.,

15

Raju et al. 1995, Choi et al. 2013) where power structure is considered for price setting rather

than quality setting purpose. This subsection demonstrates that the insights could be quite distinct

when the notion of channel power applies to quality rather than price setting.

• Impact on equilibrium quality levels:

(a) for NB product, if price competition is high and quality competition is low, then xMSV ⇤n ⇡

xV DN⇤n <x

RSV ⇤n x

C⇤n ; otherwise, xMSV ⇤

n ⇡ xV DN⇤n <x

C⇤n <x

RSV ⇤n ;

(b) for SB product, if quality competition is low, then xRSV ⇤s x

C⇤s <x

V DN⇤s ⇡ x

MSV ⇤s ; otherwise,

xC⇤s <x

RSV ⇤s <x

V DN⇤s ⇡ x

MSV ⇤s .

The above observation on equilibrium quality comparison across di↵erent power structures can

be derived from Figure 1. In general, as the power shifts from the manufacturer to the retailer

(MSV!VDN!RSV), the quality level of the NB product increases and that of the SB product

decreases. Since the quality level impacts both the upfront lump-sum cost (⌘ix2i ) as well as the

marginal production cost (ci + ✓xi), the manufacturer as well as the retailer would set a lower

quality for its own products should it be the game leader.

In addition, the finding shed light on the equilibrium quality levels compared to centralized

optimum. To begin with, the manufacturer will always under-set the quality of the NB product

than a centralized system would (xMSV,V DN,RSV ⇤n x

C⇤n ), unless the price competition is mild and

quality competition is immense and the retailer is the Stackelberg leader (RSV). On the other

hand, the retailer will always over-set the quality of the SB product (xMSV,V DN,RSV ⇤s � x

C⇤s ) when

quality competition is low, and it will only under-set the SB quality level when quality competition

is low and retailer is the Stackelberg leader (RSV).

• Impact on the equilibrium prices:

(a) The equilibrium wholesale prices follow: wMSV ⇤n ⇡w

V DN⇤n <w

RSV ⇤n .

(b) The equilibrium retail prices follow: pMSV ⇤s ⇡ p

RSV ⇤s ⇡ p

V DN⇤s < p

MSV ⇤n ⇡ p

V DN⇤n < p

RSV ⇤n .

With regard to equilibrium pricing, we first find that as the power shifts from the manufacturer

to the retailer (MSV!VDN!RSV), the wholesale price of the NB product increases. This more

or less arises from the observations in §5.2, that quality of the NB product is also increasing in

the same process. However, in Choi and Fredj (2013) where the power applies to price rather than

quality setting, the whole sale price of the NB product would actually decrease in the same shift.

This partially reflect why it is crucial to examine quality setting and relevant decision sequence in

the same private label context.

Further, we find that the retailer would always set higher retail price for NB product as compared

to that of SB product. This result conforms to existing findings that retail price of NB is always

16

4600047000480004900050000510005200053000540005500056000

1 . 5 2 2 . 5 3 3 . 5

Supp

ly c

hain

pro

fit


( b ) S u p p l y C h a i n P r o f i tChannel-CentChannel-VDNChannel-RSV

48000500005200054000560005800060000620006400066000

2 2 . 1 2 . 2 2 . 3 2 . 4 2 . 5

Supp

ly c

hain

pro

fit


( a ) S u p p l y C h a i n P r o f i t

Channel-Cent Channel-VDN

Channel-RSV Channel-MSV

Figure 4 Equilibrium profits of the supply chain under di↵erent games (µ= 1000, cn = 6, cs = 6, ↵n = 0.8, ↵s = 0.2,

⌘n = 8, ⌘s = 8, ✓= 0.3, � = 10.5, � = 8 for quality competition and �= 7, �= 5 for price competition)

higher than that of the SB (Choi et al 2013). It is thus more beneficial for the retailers to focus on

its SB brand than the NB brand, by setting a lower retail price for the former and a higher price

for the latter. As the retailer retains more power through MSV!VDN!RSV, the power to entail

such discrepancy is stronger. In addition, the quality of NB product is also increasing throughout

this process. These two factors together lead to the latter half of second observation, that the retail

price of the NB product increases with the power of the retailer.

Finally, the power structure has little impact on the retail price of the SB product. This also

distinguishes our finding from Choi (2013), where power structure applies to price setting only.

It seems that it is su�cient for the retailer to focus on the NB product in responding to the

manufacturer’s various quality and pricing decisions under any power structure.

• Impact across brands:

(a) A centralized decision maker would set a higher quality level for NB product and a lower

quality level for SB product;

(b) A Stackelberg leader may set a lower quality level for its own brand that leads to a higher

quality level for the competing brand.

Given the the fact that we assume the NB product to have a broader market base than SB, it is

natural for the centralized decision maker to assign a higher quality level for NB in accommodating

to the larger base demand. Indeed, through the numerical simulation we find that base demand

di↵erence is the only cause of asymmetric quality levels in centralized decision.

However, as illustrated in Figure 5-c,d,e,f, when the manufacturer is the Stackelberg leader

(MSV), NB product is always of lower quality than the SB product. When the retailer is the

17

0

5

10

15

20

25

2 2 . 5 3 3 . 5 4

Qua

lity

leve

ls


( a ) O p t i m a l Q u a l i t y L e v e l s i n t h e C e n t r a l i ze d S y s t e m

xn(Cent) xs(Cent)

0

5

10

15

20

25

1 . 5 2 2 . 5 3 3 . 5

Qua

lity

leve

ls


( b ) O p t i m a l Q u a l i t y L e v e l s i n t h e C e n t r a l i ze d S y s t e m

xn(Cent) xs(Cent)

0

5

10

15

20

2 2 . 5 3 3 . 5 4

Qua

lity

leve

ls


( c ) Eq u i l i b r i u m Q u a l i t y l e v e l s i n M S V

xn(MSV) xs(MSV)

0

5

10

15

20

1 . 5 2 2 . 5 3 3 . 5

Qua

lity

leve

ls


( d ) Eq u i l i b r i u m Q u a l i t y L e v e l s i n M S V

xn(MSV) xs(MSV)

3

5

7

9

11

13

15

2 2 . 5 3 3 . 5 4

Qua

lity

leve

ls


( e ) E q u i l i b r i u m Q u a l i t y L e v e l s i n R S V

xn(RSV) xs(RSV)

3579

11131517

1 . 5 2 2 . 5 3 3 . 5

Qua

lity

leve

ls


( f ) Eq u i l i b r i u m Q u a l i t y L e v e l s i n R S V

xn(RSV) xs(RSV)

Figure 5 Comparison between quality levels of NB and SB under di↵erent scenarios (µ= 1000, cn = 6, cs = 6,

↵n = 0.8, ↵s = 0.2, ⌘n = 8, ⌘s = 8, ✓= 0.3, � = 10.5, � = 8 for quality competition and � = 7.5, �= 5 for

price competition)

Stackelberg leader (RSV), SB would be of lower quality than NB if the quality competition level is

relatively low. In fact, we can analytically prove such for MSV under some special scenarios (e.g.,

symmetric cost structure).

Proposition 6. In the MSV game with cn = cs, ↵n = ↵s, store brand is of higher quality than

18

national brand, i.e., xMSV ⇤s � x

MSV ⇤n .

These observations and result challenge the notion that NB product is of higher quality than its

competing SB product, an assumption commonly held in private-label literature (e.g., Choi and

Coughlan, 2006; Chen et al., 2011; Fang et al., 2013). On the empirical end, Aplebaum et al (2003)

had suggested that NB does not always imply higher quality. Our result basically finds that, in

absence of any cost or market advantage, the manufacturer should actually choose to provide a

product of lower quality level in anticipating that the retailer will serve the market with its own

brand in the near future. To the best of our knowledge, our paper is the first work that provides

analytical evidence against this common assumption.

5.3. Impact of Cost Parameters

One distinction of our model is to allow a more general quality-dependent cost structure. This is

achieved by inviting the quality-incremental parameter ✓ to characterize the marginal production

cost ci+ ✓xi, where i2 {n, s}, and the quality investment parameter ⌘i for the lump-sum cost ⌘ix2i .

We are thus interested in the impact of these parameters, ✓ and ⌘i, on the equilibrium solutions

and profitability.

• As the quality-incremental parameter ✓ increases,

(a) the quality level of the SB product decreases;

(b) the quality level of the NB product decrease under MSV and VDN but increases under RSV;

(c) both the retailer’s and the supply chain’s profits decrease;

(d) the manufacturer’s profit increases under MSV and VDN but concave under RSV.

It is intuitive that as the marginal cost becomes more quality sensitive (larger ✓), the stakeholders

would be hesitant to set a higher quality level for their own products (Figure 6-a and 6-c). However,

as shown in Figure 6-a, such does not hold for the NB product when the retailer is the Stackelberg

leader (RSV). According to observations in §5.2, the manufacturer will set a higher quality as well

as higher wholesale price in RSV than MSV or VDN. Numerical evidence also suggests that the

wholesale price increases with the quality-incremental parameter ✓. Therefore, a strong motive

to o↵er upscale product, together with a pressured cost structure, pushes the manufacturer to

compete more aggressively on quality under RSV.

The impact of the quality-incremental parameter ✓ is more prominent on profit — only the

manufacturer can possibly benefit from an increase, and both the retailer and the supply chain

will su↵er from the same (Figure 7-a, 7-c and 7-e). Particularly in the MSV and VDN games, the

manufacturer opts to o↵er lower quality than the retailer. A higher ✓ basically puts more burden on

19

0

5

10

15

20

25

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

Qua

lity

leve

l

Quality incremental parameter (θ)

( a ) Q u a l i t y L e v e l o f N a t i o n a l B r a n d

xn(Cent) xn(VDN)

xn(RSV) xn(MSV)

0

2

4

6

8

10

12

8 1 0 1 2 1 4 1 6 1 8

Qua

lity

leve

l

Quality investment parameter (η)

( d ) Q u a l i t y L e v e l o f S t o r e B r a n d

xs(Cent) xs(VDN)

xs(RSV) xs(MSV)

0

5

10

15

20

25

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

Qua

lity

leve

l


( c ) Q u a l i t y L e v e l o f S t o r e B r a n d

xs(Cent) xs(VDN)

xs(RSV) xs(MSV)

0

5

10

15

20

8 1 0 1 2 1 4 1 6 1 8

Qua

lity

leve

l


( b ) Q u a l i t y l e v e l o f N a t i o n a l B r a n d

xn(Cent) xn(VDN)

xn(RSV) xn(MSV)

Figure 6 Variation of equilibrium quality levels of NB and SB under di↵erent scenarios (µ= 1000, cn = 6, cs = 6,

↵n = 0.8, ↵s = 0.2, � = 10.5, � = 8, �= 7.5, �= 5, ✓= 0.3 when ⌘ varies and ⌘= 8 when ✓ varies)

the retailer and subsequently gives the manufacturer advantage in this competition. For the RSV

game, as can be observed from Figure 6-a, the manufacturer keeps o↵ering the low-end product

when ✓ is small but a higher quality product when ✓ is large. Therefore, the quality-incremental

cost burden is transferred from the retailer to the manufacturer at the threshold ✓. Such explains

why the profit for the manufacturer is concave in the RSV game.

Di↵erent from the quality-incremental parameter ✓, the quality investment parameters ⌘i have

a monotone impact on the quality levels. Specifically when manufacturer is the Stackelberg leader,

Proposition 7 shows that the equilibrium quality levels decrease with the investment parameter ⌘i.

The same observations consistently hold in other two games (RSV and VDN) as well.

Proposition 7. In MSV game, the quality investment parameter ⌘i has negative impact on the

quality level xi, where i2�n, s

.

Since the lump-sum quality investment cost is sunken, its impact on the pricing is minimum.

Then naturally neither member would increase its quality level in front of a rising investment cost.

However, the quality investment parameter ⌘i shares similar impact with the quality-incremental

20

parameter ✓ on profitability.

4500

5000

5500

6000

6500

7000

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

Man

ufac

ture

r's p

rofit


( a ) M a n u f a c t u r e r ' s P r o f i t

NB manuf-VDN NB Manuf-RSV

NB-manuf-MSV

58005900600061006200630064006500

8 1 0 1 2 1 4 1 6 1 8

Man

ufac

ture

r's p

rofit


( b ) M a n u f a c t u r e r ' s P r o f i t

NB manuf-VDN NB manuf-RSV

NB manuf-MSV

41000

42000

43000

44000

45000

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

Reta

iler's

pro

fit


( c ) R e t a i l e r ' s P r o f i t


Retailer-MSV

4700048000490005000051000520005300054000

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6

Supp

ly c

hain

pro

fit


( e ) S u p p l y C h a i n P r o f i t



480004850049000495005000050500510005150052000

8 1 0 1 2 1 4 1 6 1 8

Supp

ly c

hain

pro

fit


( f ) S u p p l y C h a i n P r o f i t



4100041500420004250043000435004400044500

8 1 0 1 2 1 4 1 6 1 8

Reta

iler's

pro

fit


( d ) R e t a i l e r ' s P r o f i tRetailer-VDN Retailer-RSV Retailer-MSV

Figure 7 Variation of profits with quality parameters under di↵erent scenarios (µ= 1000, cn = 6, cs = 6, ↵n = 0.8,

↵s = 0.2, � = 10.5, � = 8, �= 7.5, �= 5, ✓= 0.3 when ⌘ varies and ⌘= 8 when ✓ varies)

• As quality investment parameter ⌘i increases,

(a) both the retailer’s and the supply chain’s profits decrease;

(b) the manufacturer’s profit increases.

21

The reason is similar to that of the quality-incremental parameter. As can be observed from Fig-

ure 6-b and 6-d, the manufacturer constantly o↵ers the low-end product compared to the retailers.

Thus the retailer takes the greater burden of quality cost, whether in lump-sum or during produc-

tion, than the manufacturer does. Therefore, the manufacturer benefits while the rest experience

the opposite from the rising quality investment cost. This e↵ect is illustrated in Figure 7-b,7-d and

7-f.

6. Concluding Remarks

Motivated by the lack of consideration of quality decisions in private label literature, and in con-

testing the commonly held assumption that national brand is superior to store brand, we study

the competition between a national-brand manufacturer and a store-brand retailer. Under this

framework, we explicitly characterize equilibrium quality levels and study how competition, chan-

nel power and cost parameters may a↵ect the quality decision as well as profitability of each

stakeholder.

Our model distinguishes from literature in three aspects. First, the national brand and the store

brand are allowed to compete on both quality and price levels. This allots su�cient room to analyze

the rationale behind quality di↵erence, and to understand the interaction between the quality and

pricing competitions. Second, stakeholders make decisions based upon a general quality-dependent

cost structure, which involves both lump-sum quality investment cost as well as marginal quality-

incremental cost. Thus any quality di↵erence can be rather strategic than purely cost driven. Lastly,

it accommodates a wide set of power structures between the manufacturer and the retailer. Either

party can be the Stackelberg leader in quality setting, or makes decision simultaneously. The paper

explores how the channel power may impact quality and pricing decisions.

Our findings suggest that quality decisions are paramount to the competition between the

national and store brands. As long as both parties are allowed to determine the quality levels at

their own choice, it is possible for the retailer to set a higher quality level for its store brand than

the manufacturer would for the national brand. Further, even though the store brand could be of

higher quality than the national brand, the retailer will always set a lower retail price for the former

than the latter, to ensure the competitiveness of its home brand. This is consistent with numerous

practical evidences such as those documented in Dunne and Narasimhan (1999). Therefore, any

assumption on the quality inferiority of store brand should be carefully posed with respect to its

own context.

The study also o↵ers fruitful managerial insights to stakeholders in the private label industry

through investigating the impact of various market and production factors on the profitability

22

levels. From the retailer’s point of view, it should be more concerned with quality competition

than price competition, especially when the quality-dependent costs are evident. As throughout our

observation, quality competition a↵ects the retailer’s profit adversely while the price competition

bears positive implication to all parties. Further, only the manufacturer may benefit from ferocious

quality competition or costly production and quality investment. That is, even though quality

competition may allow the retailer to o↵er upscale store brand at a competitive price, such does

not necessarily lead to a loss to the manufacturer. Thus the manufacturer will share an opposite

view with the retailer on the value of intense quality competition. Nevertheless, both the retailer

and the manufacturer should be mindful to their channel power, since one is always better-o↵ as a

Stackelberg leader than follower. Interestingly, the Stackelberg leader may set a lower quality for

its own brand and let the competitor take the higher quality position.

The analysis also shed light on the welfare of the consumers. The same numerical study implies

that consumers are better-o↵ when the national brand manufacturer, rather than the store brand

retailer, is the Stackelberg leader. And from a pure quality perspective, retailer’s strong channel

power stipulates the quality in national brand product, and vice versa.

The present paper can be extended in many ways. One potential extension would be to consider

two or more retailers who sell national brand and their own store brands at the same market.

In this case, each store-brand product competes not only with the national-brand product but

also with other store-brand products at the same market. On the other hand, the national-brand

manufacturer may own its own distribution and operate under a dual-channel setting. In either

case, it would be interesting to see how the channel power structures may a↵ect the pricing and

quality decisions of the supply chain.

Acknowledgments

This work is done when the first author visited Concordia University as Research Associate. The authors

are grateful for the generous support provided to this research by the Natural Sciences and Engineering

Research Council of Canada [NSERC RGPIN-2011-402324, RGPIN-2014-04626] and the Fonds Quebecois

de Recherche sur la Societe et la Culture [FQRSC NP-174166].

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