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Complete your Research Project 1

Pricing strategy varies significantly across different market structures. The pricing guidelines in a monopoly market are relatively straightforward. Since the company is the only producer offering the product, it can mark-up the price as far as the customer can bear. The pricing strategies for a producer operating in a perfect competition structure are also fairly intuitive. They are price takers, and hence price is set at the marginal cost of the product. This is due to the fact that there are many firms offering nearly identical products. However, there is optimal pricing for the market structures offering differentiated products with many competitors (oligopoly) or a few producers (monopolistic competition). These are much more complex and involved. It has been stated that differentiation in products that creates differences in customer valuation is the most prevalent type of competition. In such markets pricing strategies may include the three C’s of cost, competition, and customer.

Develop a paper detailing an analysis of market structures and relating pricing strategies that are suitable for each of these structures. Furthermore, include a real world example of pricing strategy for a specific company by identifying its market structure.

Decision Sciences
Volume 49 Number 5
October 2018
© 2017 Decision Sciences Institute
Optimal Outsourcing Strategies When
Capacity Is Limited
Salar Ghamat
Lazaridis School of Business and Economics, Wilfrid Laurier University, 75 University Ave W,
Waterloo, Ontario, Canada, e-mail: sghamat@wlu.ca
Hubert Pun†
Ivey Business School, Western University, 1255 Western Road, London, Ontario, N6G 0N1,
Canada, e-mail: hpun@ivey.uwo.ca
Xinghao Yan
College of Business and Innovation, The University of Toledo, 2801 W. Bancroft, Toledo, OH
43606-3390, e-mail: xinghao.yan@utoledo.edu
ABSTRACT
Outsourcing the production of selected components to competitors is becoming more
common among original brand manufacturers (OBMs); however, OBMs’ increased
attention to outsourcing and the growing demand in many markets can result in capacity
allocation conflicts for the contract manufacturers. In this study, we consider a scenario in
which the OBM decides whether to outsource to a third-party supplier or to a competitive
contract manufacturer (CCM) who has the option of producing a competing product and
also has limited capacity. This setting consists of two levels of competition: competition
in the component market between the CCM and the spot market, and competition in
the final-product market between the OBM and the CCM. The CCM first chooses the
wholesale price and decides whether or not to sell a competing product to the customers.
Next, the OBM decides the proportion of its component demand to outsource to the
CCM, and then firms set the retail prices. We are interested in investigating the impacts
of the CCM’s capacity and the impacts of these two levels of competition. We show that
the OBM might multisource its component demand only when competition in the finalproduct market is intense. We also find that when the CCM’s capacity increases, demand
may decrease, while the retail price may increase. Moreover, the CCM can be worse
off from having more capacity, even when the CCM’s capacity is available for free. Our
results also show that demand may increase when competition in the final-product market
becomes more intense. Finally, we find that the value of having a third-party supplier to
produce the component decreases amid the intensity of competition in the final-product
market. [Submitted: June 5, 2015. Revised: July 16, 2017. Accepted: October 3, 2017.]
Subject Areas: Capacity Allocation Conflict,
Manufacturer, and Price Competition.
† Corresponding author.
958
Competitive
Contract
Ghamat, Pun, and Yan
959
INTRODUCTION
TPV Technology Limited (TPV), the largest electronic manufacturer of computer
monitors, sells monitors under its own brands—AOC and Envision—in the finalproduct market and acts as a supplier to Philips, which sells monitors under the
Philips brand. This arrangement means that Philips competes with TPV’s AOC
and Envision brands. The overall demand for monitors is beyond the capacity of
TPV, and thus, TPV has decided to reduce the production of its own brands in
order to satisfy the outsourcing orders it receives from Philips (Wang, 2008).
Outsourcing the production of certain components to competitive contract
manufacturers (CCMs) like TPV is becoming more common among original
brand manufacturers (OBMs); however, growing demand often results in capacityallocation conflicts for these CCMs. For example, Apple outsources its NAND
Flash memory requirement to Samsung (Kim, 2012), but as smartphones become
more popular, Samsung finds it increasingly difficult to fulfill the demand. Such
capacity-allocation conflict “would be bad for Apple if Samsung were forced to
choose between Apple and itself in case of a supply shortage at its factories”
(Forbes, 2013). In another example, Franz Inc. (Franz) is a contract manufacturer
that produces home décor accessories (e.g., tableware, vases, and jewellery) for
OBMs like Enesco and Lenox. In 2002, Franz started to sell products under its
own brand while continuing to supply for the OBMs. The company reached its
capacity limit due to increasing orders from OBMs, and eventually, in 2005, Franz
decided to prioritize the production of its own brand products ahead of others
(Yan, 2013). Tesla Motors was the supplier of battery packs for Mercedes B-class
Electric Drive. Despite strong demand for its own automobile, the Tesla Model S,
Tesla Motors could not increase the production amount due to its limited supply
of batteries (Herron, 2013).
These examples show that when the CCM has a limited capacity, the OBM
can influence the CCM’s output to the final-product market by using a portion of
the CCM’s capacity, thereby mitigating competition in the final-product market.
On the other hand, precisely because of this reason, the CCM may set a higher
wholesale price. However, there often exist other firms (e.g., spot market) that
can supply the component, so in order to remain competitive in the component
market, the CCM cannot set an unreasonable wholesale price. To illustrate, in
the Apple/Samsung example, even though Samsung holds a 30% market share in
the NAND Flash memory wholesale market, there are many other suppliers (e.g.,
Toshiba, SanDisk, and Intel) from which Apple can outsource to (DRAMeXchange, 2014). In conclusion, the introduction of a capacity constraint introduces
some nontrivial trade-offs to the firms. As both supply chain partnership between
competitors and capacity shortages are becoming more common, studies of the
interaction between these phenomena and the resulting impacts become more
crucial.
In this study, we analyze an OBM’s outsourcing strategies when the CCM
has limited capacity. In particular, the OBM does not produce a critical component
of its product in-house (e.g., the computer monitor in TPV’s example, the NAND
Flash memory in Samsung’s example, the home accessories in Franz’s example
and the battery pack in Tesla’s example) and must therefore decide the proportion
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Optimal Outsourcing Strategies when Capacity is Limited
of the production of the component to be outsourced to the CCM, while the
remaining production can be outsourced to a third-party supplier. The CCM has
limited capacity in the production of the critical component, so it must decide
whether or not to sell products to customers under its own brand. Moreover, the
CCM must decide the wholesale price of the component in order to compete with
other third-party suppliers. Our study considers the following research questions:
(1) What are the impacts of the CCM’s capacity on the outsourcing strategy
and on the firms’ profitability?
(2) How does the competition in the final-product market (between the OBM
and the CCM) and the competition in the component market (between
the CCM and the third-party supplier) affect the outsourcing strategy
and the firms’ profitability?
In response to these questions, we present several interesting findings. First,
despite the fact that CCM has the option of not selling final products to customers,
but rather using its capacity to act as the OBM’s sole supplier, we find that the
firms may forgo this opportunity. In particular, regardless of the capacity limit,
the CCM always sells in the final-product market when the competition between
the OBM and the CCM is low. However, when the competition in the final-product
market is very intense, the CCM might hold a monopoly in the component market,
while the OBM holds a monopoly in the final-product market. In order to be
the monopoly in the final-product market, the OBM would buy all the CCM’s
capacity for relatively high wholesale price and supply the rest of its component
demand from the cheaper third-party suppliers. We also show that the OBM only
multisources its component when the CCM does not sell in the final-product
market.
Second, when capacity increases, one might expect that demand would increase while retail price would decrease. Surprisingly, we find that this intuition
does not hold true when there is a shift in outsourcing strategy. Moreover, even
when capacity is available for free, the CCM can be worse off from having more
capacity. The impact of “profit decreases in capacity” is always larger when both
firms are coopetitors than when they are competitors. Third, our results illustrate
that the demand for the CCM’s product may increase when the competing products
become more substitutable. Furthermore, even though the CCM has less incentive
to allocate its capacity to produce components for the OBM when the intensity of
competition in the final-product market increases, the value of having a third-party
supplier to produce the component decreases as competition intensifies.
This article is organized as follows. In the next section, we review the related
literature. We then present the mathematical model and the analytical results in
Sections 3 and 4. In Section 5, we analyze the value of competition in the component
market through a comparison of the basic model using a benchmark model without
the third-party supplier. In Section 6, we consider a scenario where OBM can order
excess quantity (buy-and-hold) to impact CCM’s output to the final-product market.
Finally, we provide concluding remarks and managerial insights. We present the
details of the derivation of the equilibriums and the proofs of the results in the
Appendix.
Ghamat, Pun, and Yan
961
LITERATURE REVIEW
Our article relates to two areas of research. The first stream of literature examines
the scenario of competition between supply-chain partners. Venkatesh, Chintagunta, and Mahajan (2006) and Xu, Gurnani, and Desiraju (2010) study the optimal
strategies of a manufacturer who owns the proprietary component brand. The manufacturer decides whether to use the components exclusively, whether to become
a supplier of an OBM, or whether to become a hybrid of both. These two studies
show that the proprietary component manufacturer should hold a monopoly in the
final-product market only when the two products are almost perfect substitutes. In
our study, the component is not of a proprietary nature, so the manufacturer cannot
hold a monopoly in the final-product market.
Wang, Niu, and Guo (2013) examine the advantage of being the first mover
when the component is not of a proprietary nature. These authors assume that the
CCM’s wholesale price should be smaller than the third-party supplier’s wholesale
price. However, we show that in a setting with capacity, the OBM would be willing
to pay a higher wholesale price in order to reduce competition in the final-product
market. Pun (2014) studies how an OBM should outsource its nonproprietary components when firms can exert effort to improve their production process. He finds
that the OBM might be better off outsourcing both the production and the processimprovement effort to the competitor, even when the competitor has a higher cost.
Pun (2015) considers the optimal degree of cooperation between two competing
manufacturers when the components are not proprietary and finds that competitors can be worse off from more cooperation, even when these competitors have
better production capabilities. We extend this stream of literature by considering
the impacts of the CCM’s capacity on the outsourcing strategy and on the firms’
profitability.
Another related body of work examines the ways that capacity constraint
affects firms. Osborne and Pitchik (1986) characterize the Nash equilibria in a
duopoly that has limited capacity, showing that limited capacity could be beneficial because capacity constraint can be used to mitigate competition. Gupta and
Wang (2007) study the capacity-allocation problem of a contract manufacturer
that can accept two types of orders: high-volume contractual orders and one-time
transactional orders. They find that the threshold acceptance policy is optimal, and
a contract manufacturer can be better off serving only transactional orders when
capacity is tight. Ülkü, Toktay, and Yücesan (2007) consider the capacity constraint of a contract manufacturer and consider how the risk should be distributed
to different OBMs when the OBMs’ demand levels are uncertain. Ozkan and
Wu (2009) consider make-to-stock and make-to-order mechanisms for a supplier,
seeking the point at which the fixed-capacity allocation level between two different
orders becomes optimal. Martı́nez-de-Albéniz and Talluri (2011) study dynamic
price competition under uncertain demand. They provide a characterization of
the equilibrium and show that firms may price their product at the reservation
value of their competitor. The studies discussed in this paragraph assume that the
firms are either supply-chain partners or competitors, and we extend this stream
of literature by considering the case where competitors are also supply-chain
partners.
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Optimal Outsourcing Strategies when Capacity is Limited
Yang, Hu, Gurnani, and Guan (2017) consider the distribution strategy of a
supplier of a proprietary component brand with limited capacity when this supplier
and its OBM sell two perfectly substitutable products to customers. These authors
find that the OBM may order excess inventory, and all firms and their customers can
be better off from a system with limited capacity. To demonstrate the robustness
of their results, they extend their model to a situation where there is a spot market
for the component. This robustness check is based on the case where the supplier’s
capacity is large, and dual sourcing does not arise in this capacity level. In our
study, we consider the case where the component is not of a proprietary nature, such
that there is a spot market for the component. The OBM and the CCM (supplier)
sell two imperfectly substitutable products, and we emphasize our results on the
impact of different degrees of substitution to firms’ optimal outsourcing strategies,
profitability and on the value of a spot market. Furthermore, by focusing on various
possible ranges of capacity, we explicitly study the OBM’s dual sourcing strategy,
which is never optimal when the supplier’s capacity is sufficiently large, but may
be optimal for a highly capacitated system.
To the best of our knowledge, we are the first to examine how capacity
affects the supply-chain structure in a multilevel oligopolistic competition setting,
where there is competition in the component market between the CCM and the
spot market, and competition in the final-product market between the OBM and
the CCM.
MODEL DEVELOPMENT
We consider a scenario where an OBM (Firm O) must outsource the production of
a critical component. The component can be a monitor for the TPV example, an
NAND Flash memory for the Samsung example, or a battery pack in Tesla example.
For simplicity, we follow the literature on the supply-chain relationship between
competitors (e.g., Venkatesh et al., 2006; Xu et al., 2010; Wang et al., 2013; Pun,
2014, 2015) by assuming that the final product consists of this component only.
There are two potential suppliers of this component. The first is a CCM (firm
C) that also has a competing product. The production cost is normalized to zero,
and firm C sells components to firm O at a wholesale price wC . Moreover, firm C’s
production capacity of the component is k.i Similar to Gupta and Wang (2007), we
assume that firm C produces everything in-house and does not outsource to other
third-party suppliers when facing capacity shortage.
The second component supplier is a third-party supplier (firm T) that does
not have the option of producing a competitive product under its own brand.
Firm T can also be interpreted as the spot market, where the component can be
purchased off the shelf. Similar to other related literature on contract manufacturing
(e.g., Jeannet, 2009; Wang et al., 2013), we assume that there are many identical
and independent third-party suppliers competing to become firm O’s supplier,
i Since there are many industry examples where a firm reveals its production capacity, we assume that firm C’s production capacity is public information. To illustrate, we note that Samsung and TPV Technologies present their capacity information on public web sites (www.
icinsights.com/news/bulletins/Samsung-TSMC-And-Micron-Top-List-Of-IC-Industry-Capacity-Leaders/
and www.tpv-tech.com/attachment/201504131218064_en. pdf).
Ghamat, Pun, and Yan
963
and firm T is one such supplier. This assumption is in line with many industry
practices. As an example, even though Samsung holds a 30% market share in
the NAND Flash memory market, there are many other noncompetitive suppliers
(e.g., Toshiba, SanDisk, and Intel) from which Apple can outsource this critical
component (DRAMeXchange, 2014). We incorporate the asymmetry between
the component manufacturers by assuming firm C can be more cost-efficient
than firm T (Arya, Mittendorf, & Sappington, 2008; Pun, 2015). Thus, unlike
firm C, the production cost of firm T is assumed to be nonnegative. Due to the
intense competition among these suppliers, firm T’s wholesale price wT ≥ 0 is
exogenously determined as the equilibrium market price in a competitive market,
which is simply the production cost (i.e., perfect competition). Note that when
wT = 0, the two component suppliers are symmetric. The reason that, unlike firm
T, firm C’s wholesale price is assumed to be endogenous is because firm O might
accept a higher wholesale price for the component of firm C (compared to the price
offered by other noncompetitive suppliers) only because buying from firm C can
reduce firm C’s output to the final-product market. Moreover, because firm O can
outsource to any of these noncompetitive suppliers whenever one of them meets
capacity, we do not consider a capacity limit for firm T.
Firm O decides the proportion of its component demand to be allocated to
firm C (γ ∈ [0, 1]), and the remaining component demand (1 − γ ) will be allocated
to firm T. There are three outsourcing strategies for firm O: (1) Firm O does not
outsource to firm C (i.e., γ = 0), so firms O and C are pure competitors; (2) Firm
O single-sources to firm C (i.e., γ = 1), and (3) firm O multisources to firms C
and T (i.e., 0 < γ < 1). The two firms are supply-chain partners and competitors when γ > 0 if firm C also sells products under its own brand.
We use a demand model that is extensively used in the literature; this demand
model is also commonly used when examining the scenario where a firm outsources
the production of a component to its competitor (e.g., Venkatesh et al., 2006; Xu
et al., 2010; Pun, 2014). In particular, we consider a set of heterogeneous customers
that differ in their taste preference. The taste preference captures different attributes
of a product, such as the brand image or the physical design of the product.
Customers are spread evenly on a (Hoteling) line, and the location of each customer
represents her relative taste preference between the two products. The product of
firm O is located at point zero and the product of firm C is located at point M.ii As
a result, the ideal taste preference for a customer at point zero is firm O’s product,
and similarly, the ideal preference for a customer at point M is firm C’s product.
Each customer incurs a disutility per unit distance when buying a product that
does not match her ideal preference (e.g., brand misfit). Despite the fact that all
our results can be derived for a more general form, for expositional convenience,
we assume that the disutility per unit distance is equal to 1.
The distance between the location of the two products (M) measures the
degree of differentiation between the two products; when M is small, the two
products are more substitutable, and hence competition becomes intense. The
ii The customers’ taste preference captures the customers’ brand preference, so the location of the product is
based on the brand of the product. The source of the component of a product does not affect the customers’
taste preference. Thus, we do not explicitly model the location points of the components produced by firm
C and firm T. In another words, firm O’s product is always located at point zero whether firm O sources the
component from firm C or from firm T.
964
Optimal Outsourcing Strategies when Capacity is Limited
Figure 1: Relationship between customer’s utilities and demands.
length of the Hoteling line is sufficiently larger than M such that all customers
located between the two firms would buy, but not all customers located outside
the two firms would buy. See Figure 1 for a visual illustration of the line and the
location of the two firms. In particular, the customers located between the two
products are the bargain shoppers that choose among the two products that gives
them the higher utility. The customers located outside of the two products are loyal
customers that would only consider their preferred brand, and they would buy if
their preferred brand gives them positive utility.
The customers have a unit reservation price for a product. Consequently,
when buying a product from firm i ∈ {O, C} at retail price pi , a customer that is
d away from firm i would have utility:
U = 1 − d − pi .
(1)
We follow the standard approach in calculating the demand of firm i (Di )
(e.g., Venkatesh et al., 2006; Xu et al., 2010; Pun, 2014). Specifically, we find the
customers located outside of the two firms who are indifferent between buying
a product or not, and the customer located between the two firms who is indifferent between buying either product. Then the demand of firm i can be derived
accordingly. Figure 1 illustrates the relationship between the customers’ utilities
and the demands; the triangles represent the customers’ utility from buying firms’
products (customers at zero distance will have a utility of 1 − pi ).
The profit function of firm O is as follows:
πO = (pO − wC ) γ DO + (pO − wT ) (1 − γ ) DO .
(2)
The two parts of πO are the profits from selling products containing firm C’s
component and from selling products containing firm T’s component. When firm
C sells products under its own brand, the profit and the capacity constraint are
πC = wC γ DO + pC DC ,
(3)
γ DO + DC ≤ k.
(4)
Ghamat, Pun, and Yan
965
When firm C does not sell products under its own brand, the profit and the
capacity constraint of firm C are
πC = wC γ DO and
(5)
γ DO ≤ k.
(6)
As commonly used in the related literature (e.g., Cui, Raju, & Zhang, 2008;
Wang et al., 2013) and consistent with many industry practices (e.g., Foxconn,
Asustek), we assume that firm C first sets the wholesale price wC , and then firm O
decides the proportion of its component demand to be outsourced to each supplier,
given the wholesale prices. Therefore, we consider two levels of competition:
competition in the component market between firms C and T, and competition
in the final-product market between firms O and C. The game sequence is as
follows.
1) Firm C decides wC and chooses whether or not to sell its own product.
2) Firm O decides γ .
3) Firm O decides pO . If applicable, firm C decides pC .
We use backward induction to find the equilibrium solutions.
EQUILIBRIUM SOLUTION
The competition in the final-product market, that is captured through product
substitutability M, can affect firms’ strategic choices (equilibrium solution). We
will show in Propositions 1 and 4 that firm O always single sources when the
degree of competition is low (M > MÌ„) and might multisource when competition
is intense (M ≤ M̄). This is because firm C cannot set an arbitrary high wholesale
price due to the competition with firm T in the component market. Moreover, when
the competition between firms O and C in the final-product market is small, firm
O is not willing to pay a high wholesale price to buy-out firm C’s capacity.
For clarity of expositions, we first focus the analysis to the case when the
product competition is low (M > MÌ„). Specifically, we present the equilibrium
strategy in Proposition 1. We then examine the impact of firm C’s capacity on
firms’ price, demand, and profit in Proposition 2, and the impact of the product
substitutability on firms’ demand in Proposition 3. Finally, we expand the analysis to the case when the final product competition is very intense (M ≤ M̄) in
Proposition 4.
In order to derive the equilibrium solution, we use the Karush-Kuhn-Tucker
conditions to consider firm C’s capacity constraint. We separate the optimization
problem into two cases: (1) binding capacity equilibrium, where firm C uses all
of its capacity; and (2) nonbinding capacity equilibrium, where firm C has some
unused capacity. Consequently, starting from the last stage of the game, we derive
two different sets of optimal pricing strategies for the firms, depending on the
capacity constraint (i.e., binding/nonbinding). In the second stage of the game,
firm O decides the proportion of its component demand to be allocated to firm C
(γ ∈ [0, 1]), given firms C and T’s wholesale price (wC and wT , respectively), firm
966
Optimal Outsourcing Strategies when Capacity is Limited
C’s capacity level k and product substitutability M. Finally, in the first stage of the
game, firm C chooses its wholesale price, anticipating the outsourcing strategy of
firm O.
In the equilibrium solution, firm C maximizes its profit function by choosing
the wholesale price wC for the two strategies where it acts as firm O’s supplier
(supplier only and coopetition), subject to firm O’s incentive compatibility and
participation constraints. The incentive compatibility constraint ensures that firm
O would not deviate to other strategies, given firm C’s wholesale price; the participation constraint makes sure that firm O gets at least as much as its outside option
when it outsources to firm T. Finally, knowing the best outcome of each strategy,
firm C chooses the equilibrium strategy with its wholesale price, depending on
capacity k, firm T’s wholesale price wT , and product substitutability M. Details of
the derivation of the equilibrium are presented in the Appendix.
First, we present the results for the case when the product competition is
low, and then we show the effect of high product competition on the equilibrium
solution.

48(1 − wT )2 + 97k 2 − 2(1 − wT ) − 95k
. When the
Lemma 1: Define MÌ„ = 17
48
48
competition in the final-product market is low (i.e., M > MÌ„), firm C always sells
in the final-product market.
Lemma 1 shows that firm C always sells in the final-product market when the
competition in the final-product market is low. This is because when competition
between the two products is intense, firm O would have more benefit if firm C
does not sell product to the customers. However, when the degree of competition
is not high, there is not much value for firm O to try to reduce firm C’s output to
the final-product market by buying out firm C’s capacity. Therefore, firm C would
always sell in the final-product market because of low profits in the component
market resulted from lower acceptable wholesale prices by firm O.
Proposition 1 and Figure 2 present the optimal strategies of the two firms
when M > MÌ„. We define four regions: firm O outsources to firm T in Regions
I and II, and firm O outsources to firm C in Regions III and IV. Moreover, firm
C’s capacity constraint is binding in Regions I and III, and firm C has excess
capacity in Regions II and IV. We also define capacity thresholds k12 , k23 , and
k34 (i.e., k12 < k23 < k34 ) to describe the locations of the strategy changes in the equilibrium solution. For example, k23 is located at the boundary of Regions II and III. We denote the optimal solution with superscript “*.” Firm C’s optimal wholesale price is denoted by wC ∗ , and w̄C is the maximum acceptable wholesale price by firm O such that it is better off to outsource to firm C if and only if wC ≤ w̄C . See the Appendix for analytical expressions. Proposition 1: When M > M̄, the optimal strategy is such that firm C sells
products to customers and
1) If k < k23 , firm O outsources to firm T and wC ∗ > w̄C .
2) If k ≥ k23 , firm O outsources to firm C and wC ∗ = w̄C .
The capacity constraint is binding if and only if k ≤ k12 or k23 ≤ k ≤ k34 .
Ghamat, Pun, and Yan
967
Figure 2: Optimal outsourcing strategies when M > MÌ„.
When firm C has plenty of capacity (Region IV), it has sufficient capacity to
produce for both firms. The literature that studies supply-chain partnerships with a
competitor focuses on this region (e.g., Venkatesh et al., 2006; Wang et al., 2013;
Xu et al., 2010). However, we show that even in Region IV, firm O might accept
T
a wholesale price from firm C that is higher than that of firm T (i.e., w̄C = 17w
).
16
This is because when firm O outsources to firm T, firm O and firm C have no
collaborative relationship. Thus, both firms will price their products aggressively,
so competition between these two firms is fierce. On the other hand, when firm
O outsources to its competitor (firm C), firm C has stake in firm O’s product.
Because firm C receives revenue from both selling its own product and firm O’s
product sales, it would not price its product aggressively. As a result, competition
between firms O and C is mitigated. Consequently, firm O would be better off
when cooperating with its competitor compared to the case where it outsources to
firm T.
Firm C’s capacity is intermediate at Region III. When firm O outsources
to firm C, it can reduce the supply of firm C’s product, and the competition in
the final-product market can be mitigated. Therefore, firm O would outsource to
firm C, and firm C would set a nonnegative wholesale price that is higher than
what is offered by firm T (i.e., wC ∗ = w̄C > wT ). The outsourcing strategy in this
region could explain how Philips caused TPV to reduce its own brand output by
outsourcing the production of its monitors to TPV.
We show in Lemma A1 (in the Appendix) that w̄C weakly decreases in
the capacity of firm C. Therefore, one might expect that when firm C has a low
capacity (Regions I and II, where firm C can charge a high wholesale price to firm
O), instead of using the capacity to produce for its own product, firm C is better off
using all capacity to supply to firm O so that firms O and C can hold monopolies in
the final-product market and in the component markets, respectively. Interestingly,
968
Optimal Outsourcing Strategies when Capacity is Limited
Figure 3: Firms’ demand and price as a function of k.
we find that firm O would not outsource to firm C in these two regions. This is
because, on the one hand, firm C can sell its product to the customers at a high
retail price, and hence, it would require a high wholesale price if it were to use
the capacity to produce for firm O’s product instead of for its own product. On the
other hand, competition between suppliers C and T provides a limit in terms of
how high a wholesale price firm O is willing to accept. We find that the wholesale
price that justifies firm C’s use of its capacity to produce components for firm
O’s product is higher than the wholesale price that firm O is willing to accept
(i.e., wC ∗ > w̄C ). Therefore, both firms would forgo the opportunity of holding
monopolies in the component market and in the final-product market, and both
would prefer to act as pure competitors. Moreover, when firm C sells a final product
to customers when it has small capacity, it will price its products high, which in
turn will allow firm O to price its product higher than its price in the monopoly
market. Gelman and Salop (1983) showed similar results, where they found that
when the two firms are not supply chain partners and the new entrant had limited
capacity, it was not profitable for the incumbent to hold a monopoly in the market.
We extend these authors’ results to the case where competitors are supply chain
partners.
At Region II, firm O does not outsource to firm C, even though firm C has
some unused capacity. This is because, by acting as firm O’s supplier, firm C
has to use more than its excess capacity to satisfy form O’s component demand
and thus it has to reduce the production of its own final product. However, the
gain from component sales to firm O would not compensate for the loss from the
reduction in final product sales. Therefore, firm C would set a high wholesale price
(i.e., wC ∗ > w̄C ) to discourage firm O from outsourcing to firm C. This result can
explain the market choices of some competitive CMs like Franz, who prioritize
capacity to their own brands and turn down outsourcing contracts when facing
capacity-allocation conflicts (Yan, 2013).
Proposition 2 presents the impact of capacity to demand, price and profit for
the case where M > MÌ„. Figure 3 illustrates the impact of capacity on demands
and prices (Propositions 2a and 2b) and Figure 4 illustrates the impact of capacity
on profit (Proposition 2c).
Ghamat, Pun, and Yan
969
Figure 4: Firms’ profit as a function of k.
−
T
T
Proposition 2: Define k1 ≡ 7(2+M)+3w
, k3 ≡ 56(2+M)−51w
, k23
≡ k23 − ε and
24
105
+
≡ k23 + ε, where ε is a small positive number. When M > M̄,
k23
−
+
−
−
+
+
∗
∗
(a) DC∗ (k23
) > DC∗ (k23
) and DO
(k23
) + DC∗ (k23
) > DO
(k23
) + DC∗ (k23
).
∗ −
∗ +
(b) pi (k23 ) < pi (k23 ). (c) Firm C’s profit may decrease in capacity: r ∂πC∗ < 0 ⇔ k1 < k ≤ k12 or k3 < k ≤ k34 . ∂k r | ∂πC∗ |k =k + | < | ∂πC∗ |k =k + | for all > 0.
∂k
1
∂k
3
When firm C’s capacity increases, one might expect that prices would decrease while demands would increase. We find that this intuition does not hold
when the capacity of firm C is around k23 . This is because, as k increases, the strategy changes from the two firms acting as pure competitors (Region I or Region
II) to acting as coopetitors (Region III). Therefore, firm C would shift some of its
capacity to produce components for firm O, and thus, its demand DC∗ decreases
and price pC∗ increases. Venkatesh et al. (2006) in Proposition 3 of their paper find
that firms would set higher prices under coopetition relationships. We extend this
finding to a system with limited capacity by showing that firm C sets a higher price
because, in addition to the two firms acting as coopetitors, firm C uses some of
the capacity to produce for firm O and thus produces fewer units for itself. Firm
O also sets a higher retail price pO∗ because it shifts from using a cheaper supplier
(firm T) to using a more expensive supplier (firm C), so it sets a higher retail price
in order to maintain the margin.
When firm O outsources to firm C and firm C has sufficient capacity to
produce for both firms (Region IV), or when firm O outsources to firm T and firm
C has sufficient capacity to produce for itself (Region II), the firms’ profits are not
affected by the capacity level (cf. Figure 4). However, when capacity is binding,
firm C may be worse off from having more capacity, even when that capacity can
970
Optimal Outsourcing Strategies when Capacity is Limited
be available for free. This is because, in Regions I and III, the retail prices of both
firms would decrease when firm C has more capacity, so competition becomes
more intense. We find that the impact of a decrease in retail prices is larger than
the impact of an increase in demand, so the profit of firm C decreases.
Furthermore, the second part of Proposition 2c shows that the impact of
profit-decreases-in-capacity (Region III) is larger when firms O and C cooperate
as supply-chain partners than when firms act as competitors only (Region I). This
is because firms would set higher prices under the coopetition scenario than under
the competition scenario. When capacity increases, the decrease in price under
the coopetition scenario is larger than that under the competition scenario, so the
decrease in profit is larger. This finding illustrates the importance of considering the
firm’s capacity constraint when competitors cooperate as supply-chain partners.
One key takeaway is that firms are not always better off with more capacity,
especially when they are coopetitors.
The two products are more substitutable when they are located closer to one
another (M decreases), leading to a more intense competition. Then Proposition
3 presents the impact of the degree of competition to the demand of firm C when
M > MÌ„.
Proposition 3: When M > M̄, firm C’s demand may increase in the intensity of
∂D ∗
competition in the final-product market: ∂MC < 0 ⇔ k23 ≤ k ≤ k34 (entire Region III). As expected, demand of a product decreases when competition intensifies (in Regions I, II, and IV). However, Proposition 3 shows that when the two firms are supply-chain partners and when firm C has no excess capacity (Region III), the demand for a product increases, even when the two products become more substitutable (M decreases). This is because firm O’s demand decreases when M decreases. Therefore, when capacity level is tight, firm C would allocate less capacity to produce for firm O’s product. Firm C would have more capacity to produce product under its own brand, so it would set a lower price pC∗ for its product, in turn leading to a higher demand DC∗ . In the results presented above, we assume that competition in the finalproduct market is low (i.e., M > M̄). In this case, firm O would never multisource
to both suppliers (i.e., 0 < γ < 1 is never optimal). This is because firm O will outsource as many components as possible to firm C if the wholesale price is less than w̄C . Therefore, the only possible scenario that might lead to a multisourcing is when firm C’s capacity is not enough to satisfy all of firm O’s demand and firm C sets the wholesale price such that firm O is better off to outsource to firm C. However, in Proposition 1 we show that firm C always sells in final-product market even when its capacity is low, so firm C would set a high wholesale price to deter firm O from buying out its capacity. Thus, firm O would never multisource. Next, we will illustrate in Proposition 4 that firm O may multisource when the competition between the two products is very intense (M ≤ M̄). We present the optimal strategy in Figure 5, and the analytical definitions of the six regions are presented in the Appendix. We define two new regions for the case where the competition is very intense: firm O multisources from firm C and firm T in Region Ghamat, Pun, and Yan 971 Figure 5: Optimal outsourcing strategies when M ≤ M̄. V, and firm O outsources to firm C in Region VI. Moreover, in both Regions V and VI firm O holds a monopoly in the final-product market. Proposition 4: When competition between the two products is very intense (M ≤ M̄), (a) Firm C does not sell in the final-product market in Regions V and VI. (b) Firm O multisources in Region V. Recall from Proposition 1 that when the competition between the two final products is low (M > M̄), firm C would always sell to customers in the finalproduct market. However, when the two products are very substitutable (M ≤ M̄),
Proposition 4a shows that firm C might be better off serving as firm O’s supplier
and opting not to sell in the final-product market (cf. Regions V and VI in Figure
5). There are two different reasons behind this strategy.
First, intuitively when firm T’s wholesale price is high (due to higher production cost), firm C can set higher wholesale prices compared to the cases where
firm T has low wholesale price. Then, coupled with the fact that firm C cannot set
a high retail price because of the strong degree of substitutability between the two
products, firm C can earn more profit from selling components to firm O than from
selling products in the final-product market. In these scenarios (Region VI), firm
O holds the monopoly in the final-product market, and firm C holds the monopoly
in the component market. In this case firm C has enough capacity to fulfill firm
O’s component demand. Second, when firm C’s capacity is low (Region V), firm
O would benefit from pushing firm C out of the final-product market to avoid high
competition and lower retail prices. This is because when the competition in the
final-product market is very intense, firm O can increase its retail price significantly
if firm C does not sell in the final-product market, compared to the case where
firms compete in the final-product market.
972
Optimal Outsourcing Strategies when Capacity is Limited
Proposition 4b shows that when competition among final products is very
intense, there is a region (Region V) where firm O multisources its component
from firms C and T. The reason for multisourcing is that in Region V, firm C does
not have enough capacity to fulfill firm O’s component demand.iii Therefore, in this
case, firm O, as the monopoly in the final-product market, can expand its demand
by supplying the rest of its component demand from firm T. The size of the region
where firm C does not sell in the final-product market (Regions V and VI) depends
on the degree of competition between the final products. As competition of the two
products intensifies (M decreases), the sizes of Regions V and VI increase. This
is because firms O and C can avoid this intense competition by being monopolies
in the final-product market and in the component markets, respectively.
VALUE OF COMPETITION IN COMPONENT MARKET
Contract manufacturers sometimes have the proprietary rights to produce the component, but after the patent has expired, other suppliers can also produce it. For
instance, Qualcomm served as the proprietary supplier of the CDMA chips for
cell phone producers, and the expiration of its CDMA patents ended Qualcomm’s
control over CDMA (Mock, 2005), resulting in an increase of competition in the
cell-phone-chip manufacturing market.
The purpose of this section is to evaluate the impact of competition in the
component market. In particular, in the main model, we assume that the component
is not proprietary, such that firm O has the option of multisourcing from multiple
potential suppliers (firms C and T). In this section, we consider a benchmark
scenario in which the component is of a proprietary nature, and firm C is the only
supplier that can produce the component. Firm C deploys one of the following
strategies: (1) monopoly—does not supply the component to firm O (e.g., sets a
very high wholesale price) such that firm C holds the monopoly in selling the final
product, (2) supplier only—acts as a supplier for firm O but does not enter the
final-product market, and (3) coopetitor—supplies components to firm O and sells
final products to customers.
When firm C does not supply components to firm O (monopoly), firm O
earns zero profit, and firm C’s optimization problem is:
Ï€C = pC DC
(7)
s.t. DC ≤ k.
(8)
When firm C supplies components to firm O and does not sell a final product
in the final-product market (supplier only), firm C’s optimization problem is:
Ï€C = wC DO
(9)
iii The focus of our paper is on examining how capacity shortage and two levels of competition are the main
drivers for a firm’s dual sourcing decision. Note that there are other strategic reasons for a firm to dual
source. For example, dual sourcing is a crucial supply chain risk management strategy, because suppliers
may experience disruption so relying on one supplier is a risky strategy. Another possible reason for dual
sourcing is demand uncertainty which makes flexibility of dual-sourcing invaluable for having higher service
and fulfillment rates. However, these reasons are beyond the scope of our paper and are left as future research
possibilities.
Ghamat, Pun, and Yan
973
s.t. DO ≤ k.
(10)
When firm C sells components to firm O and also sells final products in
final-product market (coopetitor), firm C’s profit is:
Ï€C = wC DO + pC DC
(11)
s.t. DO + DC ≤ k.
(12)
While under the monopoly strategy, firm O’s profit is zero, under the
component-supplier and coopetitor scenarios, firm O’s profit is:
πO = (pO − wC ) DO .
(13)
The game sequence under the benchmark is as follows:
1) Firm C decides on its strategy (monopoly, component supplier, coopetitor).
2) If applicable, firm C decides wC .
3) If applicable, firm C decides pC and firm O decides pO .
We use backward induction to find the equilibrium solutions; the derivation
of equilibrium is presented in the Appendix. We denote the optimal profit of firm
O under the benchmark to be πOB , and we define the value of competition to firm
O as VO ≡ πO∗ − πOB . Recall that πO∗ denotes the equilibrium profit of firm O in the
main model. Then, Proposition 5 examines how the capacity and competition in
the final-product market affect the value of competition in the component market.
(The value of competition from the perspective of firm C is the reverse of that from
the perspective of firm O.)
Proposition 5:
(a) The value of competition in the component market decreases in capacity:
∂VO
≤ 0.
∂k
(b) The value of competition in the component market decreases in the
O
≥ 0.
intensity of competition in the final-product market: ∂V
∂M
(c) Firm O is always better off if there is more than one supplier: VO > 0.
Under the benchmark scenario, when the CCM’s capacity decreases, the
wholesale price increases significantly because the CCM holds the monopoly in
the component market. On the other hand, the wholesale price would be relatively
insensitive to the capacity under the main model because of competition in the
component market. Therefore, the value of competition in the component market
is large when capacity decreases.
When the competing products are highly substitutable (i.e., small M), firm C
has less incentive to allocate its capacity to firm O, so one might expect the value
of competition in the component market to be large. However, we find that the
opposite impact holds.
Consider the case where firm C supplies components to firm O under the
benchmark. (Otherwise, firm O has zero profit, so the comparison is trivial.)
974
Optimal Outsourcing Strategies when Capacity is Limited
Firm O’s profit is relatively insensitive to the product substitutability under the
benchmark because, when it serves as the proprietary component supplier, firm
C would set a wholesale price to extract as much profit from firm O as possible.
On the other hand, under the main model, the wholesale price would be relatively
insensitive to product substitutability because of competition in the component
market. As firm O stands to gain more when the product becomes less substitutable
under the main model, the value of competition in the component market increases
in M.
Despite the fact that the value of competition might decrease for firm O depending on firm C’s capacity or product substitutability, Proposition 5c shows that
firm O always prefers to have more than one outsourcing option. This preference
relates to the fact that the availability of alternative outsourcers would provide firm
O with more bargaining power when designing a contract with the supplier.
BUY-AND-HOLD OPTION
In the main model, we have assumed that firm O cannot order excess quantity.
However, because firm O can manipulate firm C’s output to the final-product
market by using a portion of the capacity, thereby mitigating competition in the
final-product market, firm O might have the incentive to order more than its
demand. Specifically, in the second step of the game, firm O decides how much to
order from firm C and how much to order from firm T.
The analysis of this game is similar to the main model, though much more
complex due to firm O’s order-quantity constraint. The proofs are available from
authors upon request. In summary, it can be shown that the general structure of the
equilibrium stays the same. Similar to the findings presented in Proposition 4a, firm
C is better off not selling in the final-product market because product substitution
increases in the presence of the buy-and-hold option. However, when there is a
buy-and-hold option, the degree of product substitutability that is required for firm
C to prefer to drop out of the final-product market is lower compared to the main
model, where firm O does not have the buy-and-hold option. This is because firm
O does not need to price its products low when it can have excess order quantity, so
it may be better off selling its products for a monopoly price and keeping the extra
components at no cost. Consequently, firm O would be willing to pay higher prices
for firm C’s component in order to gain a monopoly in the final-product market.
In turn, firm C has a larger wholesale price so it would not sell in the final-product
market even when the products are less substitutable.
When firm C sells its own product to the end customer, firm O would never
utilize the buy-and-hold option. This is because firm C would set a sufficiently high
wholesale price when selling to end customers, so firm O would outsource to firm T
instead. Moreover, firm O would exercise the buy-and-hold option only when firm
C has a relatively large capacity (Region VI) because, otherwise, firm O’s demand
would always be enough to exhaust firm C’s capacity (Region V). Therefore, the
existence of the buy-and-hold option for firm O would largely affect the area under
which firm C is the supplier only and firm O is single-sourcing from firm C, thus
making this strategy optimal for a larger set of parameters. We show that all of our
results in the main model hold in the presence of the buy-and-hold option.
Ghamat, Pun, and Yan
975
CONCLUDING REMARKS AND MANAGERIAL INSIGHTS
In this article, we examine the impact of capacity on the optimal channel structure
when the contract manufacturer may have a competing product. Using a game
theoretical approach to study the dynamics of firms’ strategic decisions allows us
to better understand the effect of various factors on firms’ decisions—factors that
might not be present in single-case or multiple-case study.
We show that capacity limitation, which is a commonly experienced conflict
among contract manufacturers, can have nontrivial impacts. In particular, when
firms act as supply chain partners, the CCM might reduce its own product output
in order to fulfill the OBM’s outsourcing orders. Thus, we present an explanation
for both prioritizing capacity to a firm’s own product (such as the strategy used by
Franz in the motivating example) and reducing the firm’s own product output to
shift profits to component sales to a competitor (such as the motivating example of
TPV technologies). However, the former strategic move (by Franz) can be justified
whenever a firm has limited capacity that can satisfy its own demand only, and the
latter strategy (by TPV technology) becomes more plausible whenever a firm has
a lot of excess capacity to accommodate OBM orders as well as most of its own
demand. Furthermore, we characterize the conditions under which the OBM might
benefit from multisourcing its component. We show that when the competition in
the final-product market is very intense, the OBM might benefit from buying out
the CCM’s capacity while outsourcing the rest of the component demand to a
third-party supplier.
We also show that firms’ prices might increase and demand might decrease as
capacity increases. Interestingly, we find that the CCM’s profit may decrease in its
capacity, and this deterioration becomes more severe when firms are supply-chain
partners. For example, since 2014, LG Display produces the OLED screens used
by OBMs like Apple and also by its own firm, LG Electronics. Due to increasing
demand in electronic markets, LG Display is planning to expand its production
capacity to accommodate both OBMs (e.g., Apple) and its own brand’s increasing
supply needs (Fingas, 2015). However, our results show that it might be better
for a contract manufacturer—in this example, LG Electronics—to limit the output
of its own product in order to maintain higher market prices and thus reduce
market competition. Therefore, in terms of managerial insights and implications,
our results suggest that increasing capacity level may be harmful to the industry.
Finally, we show that, in the component market, the value of competition to the
OBM is small when the two products are highly substitutable.
Moreover, the results of our study provide strategic insights for practicing
managers when their firms compete with a supplier that has limited capacity. In
particular, when there is a need for capacity expansion to reach economies of
scale, the disruption in the industry’s supply/demand balance “often leads to long
and recurring periods of overcapacity and price cutting” (Porter, 2008). However,
our results show that if the competitors can share the capacity, the increase in
capacity levels may result in a more profitable industry rather than a price war.
Such insight would increase the desirability of cooperating with competitors when
there is a potential to achieve economies of scale through increased capacity
levels.
976
Optimal Outsourcing Strategies when Capacity is Limited
In the main model, to understand the implications of different capacity levels
on the firms’ strategic decisions, we assume an exogenous capacity for firm C.
Consider the possibility where firm C’s capacity choice is a decision variable.
Because changing capacity is a long-term decision, it would be determined much
earlier in the timeline of the events—before firm C designs a wholesale price contract to accept orders from firm O. Therefore, in the case of endogenous capacity,
firm C’s capacity decision would be the first event of the game sequence. Thus,
the resulting equilibrium solution with firm C’s endogenous capacity would be a
subset of the current model’s equilibrium solution. Firm C’s profit is highest at k3
(cf., Region III). Therefore, assuming that the capacity is free or has a simple linear
cost function, if at the first stage of the game firm C were to choose its capacity k, it
would have limited its capacity such that all of it was going to be used (binding capacity) by both firm O and firm C. The reason behind this strategy is that in Region
III, firm C can reduce the competition in the final product market by having lower
output. The lower output of firm C will allow firms to increase their market prices.
As a result, firm C can also increase its wholesale price, which will compensate for
its lower output to the final-product market. Therefore, in terms of optimal strategy,
firm C would prefer to choose a capacity such that the equilibrium solution is in
Region III, where firms O and C are supply chain partners and both firms sell in
the final-product market. In this region, firm C uses all of its capacity (binding)
and firm O enjoys the limited output of firm C into the final-product market.
We used a stylized model to study the dynamics of the firms’ optimal decisions, but this model had some limitations. We used a deterministic demand model,
so a possible avenue of future research would be to analytically study the impact
of demand uncertainty on the capacity-allocation problem of a CCM. Moreover, in
our model, we considered only one CCM that can produce a competitive product.
It would be interesting to consider multiple strategic contract manufacturers, each
with the option of producing their own brand products.
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APPENDIX
In this section we derive the equilibrium solution for the 3-stage game
defined in “Model Development” section. From Equation (1): DO =
1
(2 + M − 3pO + pC ); DC = 12 (2 + M − 3pC + pO ). We only consider the
2
region where 0 < M < 2 − pO − pC such that the two products are competing. 1—Stage 3 of the game 2 Both firms’ profit function is concave in its price (i.e., dd pπi 2i < 0), so FOC gives: pO ∗ (pC ) = 16 (2 + M + pC + 3wC γ + 3wT (1 − γ )). For firm C, using KKT conditions to consider the capacity constraint, we have two optimal pricing strategy: (1) Nonbinding capacity constraint: pC ∗ (pO ) = 16 (2 + M + pO + wC γ ); +(2+M−3pO )γ . We solve (2) Binding capacity constraint: pC ∗ (pO ) = 2−2k+M+pO3−γ for the optimal prices under each capacity condition: (Case 1) Nonbinding 1 capacity constraint: pO ∗ = 35 (14 + 7M + 19wC γ + 18wT (1 − γ )), pC ∗ = 1 (14 + 7M + 9wC γ + 3wT (1 − γ )); For case 1, we need γ DO + DC < 35 1 (9wT + 42(1 + γ ) + 21 M(1 + γ ) + γ (51wT γ − 60wT − 8wC (1 + 6γ ))) k ⇔ 70 < k. (Case 2) Binding capacity constraint: pO ∗ = 2 8−2k+4M+3(3−γ )(wC γ +wT (1−γ )) 7(2+M)+3(2+M+w −4w )γ −12k−9(w −w )γ +3wT C T C T , pC ∗ = . 17−3γ 17−3γ 2—Stage 2 of the game 2 Case 1) Firm O’s profit function is strictly convex (i.e., dd γπ2O > 0) which implies
that optimal allocation ratio γ ∗ is an extreme point. Because in case 1 firm C’s
capacity is nonbinding the extreme point is either zero or one (i.e., γ ∗ = {0, 1}).
For firm O to set a nonzero ratio (i.e., γ ∗ = 1), the resulting profit should be higher
2
2
T)
C)
≤ 3(14+7M−16w
⇔ (0 < wT ≤ than its profit when γ = 0 (i.e., 3(14+7M−17w 2450 2450 7(2+M) 7(2+M) 14(2+M) 17wT 1 and 0 ≤ w ≤ ) or ( < w < and 0 ≤ w C T C ≤ 16 (28 + 17 16 17 17 14M − 17wT ))), such that firm O will outsource all its component demand to firm C. Ghamat, Pun, and Yan 979 Case 2) Firm O’s profit function is neither convex nor concave. Nevertheless, there T is only one root to the FOC condition ( ddπγO = 0 → γ = 4−k+2M−4w ), which 4(wC −wT ) 2 is a minimizer ( dd γπ2O | γ = 4−k+2M−4wT > 0). However, depending on the values of
4(wC −wT )
the parameters, this critical point may not be in the feasible region (0 ≤ γ ≤ 1).
Although, because there is only one stationary point, we can claim that the profit
function is maximized at an extreme point: (1) if the stationary point is in the feasible region, or (2) if the stationary point is not in the feasible region and the profit
function is a decreasing/increasing function of γ in the feasible region. Therefore,
for firm O to set a nonzero ratio the resulting profit should be higher than the profit
2
6
T +4γ (wC −wT ))
(k − 4 − 2M + 4wT )2 ≤ 6(k−4−2M+4w
⇔
when γ = 0 (i.e., 289
(17−3γ )2
+3kγ −6Mγ −68wC γ
1
(0 ≤ wC ≤ 68
(12 − 3k + 6M) and 0 ≤ wT ≤ 136−34k+68M−12γ
)
136−80γ
1
1
1
or ( 68 (12 − 3k + 6M) < wC < 4 (4 − k + 2M) and 56 (3k − 12 − 6M + 68wC ) +3kγ −6Mγ −68wC γ ). ≤ wT ≤ 136−34k+68M−12γ 136−80γ In the binding capacity case, in order to have nonnegative prices and profits, firm C’s capacity has to be between 0 ≤ k ≤ 4 + 2M. Because γ ∗ is always and extreme point multisourcing can only happen when firm C does not have enough capacity to fulfill firm O’s component demand in which case firm O is the monopoly in the final-product market and firm C acts as the supplier only. Consequently, we separate the game into three competing strategies: 1) γ ∗ = 1, Coopetition (Superscript C); 2) γ ∗ = 0, Competition (Superscript T); and 3) 0 < γ ∗ ≤ 1, Supplier only (Superscript S). We can express the optimal prices and capacity conditions for each strategy as follows. The optimal prices for the coopetition strat1 1 C∗ egy (C) are: (Case 1) pO = 35 (14 + 7M + 19wC ), pCC∗ = 35 (14 + 7M + 9wC ) 1 1 C∗ iff k > 5 (6 + 3M − 4wC ); (Case 2) p O = 7 (4 − k + 2M + 3wC ), p C∗
C =
1
1
(10
−
6k
+
5M
−
3w
)
iff
k
≤
(6
+
3M
−
4w
).
The
optimal
prices
for
the
C
C
7
5
1
T∗
T∗
competition strategy (T) are: (Case 1) pO = 35 (18wT + 7M + 14), pC =
1
3
(3wT + 7M + 14) iff k > 70
(14 + 3wT + 7M) and 0 ≤ wT ≤ 7(2+M)
; (Case
35
17
1
1
T∗
T∗
2) pO = 17 (9wT − 2k + 4M + 8), pC = 17 (3wT − 12k + 7M + 14) iff
3
k ≤ 70
(14 + 3wT + 7M) and 0 ≤ wT ≤ 14 (4 − k + 2M). The limits on wT ensures that firm T’s component is competitive in the component market—that
is firm O would get a nonnegative profit if it uses firm T’s component.
When firm O buys out firm C’s component capacity, firm C will have the
supplier only role. In this case, firm O is the monopoly in the final product market that is only feasible when 0 ≤ k ≤ 1 and 0 ≤ wT ≤ 1 − k with
S
S
S∗
DO
= 2 − 2pO
, pO
= 12 (1 + wC γ + wT (1 − γ )). Firm O’s allocation ratio
in the supplier only strategy√is such that firm O buys all firm C’s capacity
1−w +
(1−w )2 −4k(w −w )
T
T
C
T
) and if necessary firm O mul(γ DO = k ⇔ γ ∗ =
2(wC −wT )
tisources the rest of its component demand from firm T.
3—Stage 1 of the game
In the equilibrium, firm C maximizes its profit function by choosing its wholesale
price for each strategy that it acts as the supplier (i.e., S and C) subject to firm O’s
980
Optimal Outsourcing Strategies when Capacity is Limited
incentive compatibility and participation constraints. The incentive compatibility
constraint ensures that firm O would not deviate to other strategies given firm C’s
wholesale price. The participation constraint makes sure that firm O gets at least
as much as its outside option strategy T. Finally, knowing the best outcome of each
strategy, firm C chooses the equilibrium strategy with its wholesale price for each
capacity k, competition level M, and firm T’s wholesale price wT .
Knowing the optimal set of prices in each strategy, firm C’s optimization
problem for the coopetition scenario with binding capacity constraint pricing strategy (case 2, represented by superscript B) is:
max πCCB
wC
s.t.
πOCB ≥ πOT B if k ≤
3
(14 + 3wT + 7M) and
70
1
(4 − k + 2M) (IR)
4
3
(14 + 3wT + 7M) and
πOCB ≥ πOT N if k >
70
7 (2 + M)
0 ≤ wT ≤
(IR)
17
0 ≤ wT ≤
πOCB ≥ πOS if 0 ≤ k ≤ 1 and 0 ≤ wT ≤ 1 − k
0≤k≤
(IC)
1
(6 + 3M − 4wC ) .
5
Superscript N is used to represent nonbinding capacity case (case 1). We
solve the problem using KKT conditions. Note that, the two IR constraints are
exclusive and thus we solve two similar optimization problems for each. Firm
C’s optimal wholesale prices are such that firm O’s participation constraint binds.
Therefore, these wholesale prices represent the maximum wholesale price before
firm O outsources to firm T (w̄C ). The optimal wholesale price for collectively
exhaustive and individually exclusive regions in case 2 of coopetition scenario
are:

1
7 (2 + M)
49 (2 + M)
(10 − 6k + 5M) iff
w̄ C =
< wT ≤ and 10 179 17 20 1 (2 + M − 2wT ) ≤ k ≤ (21M + 9wT + 42) or 27 70 2+M 7 (2 + M) < wT ≤ and 17 2 20 (2 + M − 2wT ) ≤ k ≤ 2M + 4 (1 − wT ) or 27 49 (2 + M) 56 (2 + M) ≤ wT ≤ and 221 179 1 1 (7M − 17wT + 14) ≤ k ≤ (10 + 5M) or 7 13 Ghamat, Pun, and Yan 981 7 (2 + M) 49 (2 + M) < wT ≤ and 179 17 1 1 (21M + 9wT + 42) ≤ k ≤ (10 + 5M) 70 13 w̄ C = ; 1 (12 − 3k + 6M + 56w T ) iff 68 1 49 (2 + M) (21M + 9wT + 42) 0 ≤ wT ≤ and 0 ≤ k ≤ 179 70 49 (2 + M) 2+M 20 (2 + M − 2wT ) or < wT ≤ and 0 ≤ k ≤ ; 179 2 27 w̄ C = 1 (6 − 5k + 3M + 17w T ) iff 20 1 56 (2 + M) (21M + 9wT + 42) ≤ k and 0 ≤ wT < 221 70 49 (2 + M) 1 56 (2 + M) (24 + 12M − 17wT ) or ≤ wT ≤ < 20 221 179 1 1 (21M + 9wT + 42) ≤ k < (7M − 17wT + 14) ; and 70 7 w̄ C = 1 (6 − 5k + 3M) iff 4 56 (2 + M) 1 (24 + 12M − 17wT ) ≤ k and 0 ≤ wT ≤ 221 20 56 (2 + M) 7 (2 + M) 1 < wT ≤ < (24 + 12M − 17wT ) or 6 221 17 1 1 (10 + 5M) ≤ k < (17wT − 4 − 2M) ; and 13 6 Firm C’s optimization problem for nonbinding case (case 1) of coopetition scenario is: max πCCN s.t. πOCN ≥ πOT B if k ≤ wC 3 (14 + 3wT + 7M) and 70 1 (4 − k + 2M) (IR) 4 3 (14 + 3wT + 7M) and πOCN ≥ πOT N if k >
70
0 ≤ wT ≤
982
Optimal Outsourcing Strategies when Capacity is Limited
0 ≤ wT ≤
7 (2 + M)
17
(IR)
πOCN ≥ πOS if 0 ≤ k ≤ 1 and 0 ≤ wT ≤ 1 − k
k>
(IC)
1
(6 + 3M − 4wC ) .
5
KKT conditions would result in collectively exhaustive and individually
exclusive regions with optimal wholesale prices as follows.

868 (2 + M)
217 (2 + M)
7 (2 + M)
iff
≤ wT ≤
and k
w̄ C =
876
3723
17

1
(176 + 88M) ;
>
219
17wT
iff
w̄ C =
16

0 ≤ wT

1
868 (2 + M)
(24 + 12M − 17wT ) .
and k
3723
20
Lemma A1: The maximum acceptable wholesale price by firm O such that it
is better off to outsource to firm C weakly decreases in capacity of firm C (i.e.,
d w̄C
≤ 0).
d k
Proof of Lemma 1, Propositions 1, and Proposition 4: The Equilibrium
Solution
Despite the fact that each case (binding and nonbinding) has wholesale prices
for exclusive regions there are overlaps between two scenarios’ feasible regions.
Firm C chooses the scenario with higher profits considering firm O’s incentive
compatibility constraint. For example, if firm C prefers binding capacity case
it has to make sure that {πOCB ≥ π CN
O |wC }). Moreover, firm C can choose to set
wholesale price high enough so to deter firm O from outsourcing to firm C (violating
IR constraints). Firm C would set high wholesale prices when firm Cs profit
from competition strategy is more than its profit from coopetition strategy (i.e.,
πCT ≥ πCC ). Replacing the optimal pricing and wholesale price of each region
we can show that without considering the supplier only strategy, firms’ optimal
outsourcing strategies is as follows.
Competition Strategy: (outsource to firm T).
I. Binding Capacity Case

1
2+M
(42 + 21M + 9wT )
0 ≤ wT < and 0 ≤ k < 11 70 2+M 8 2+M (2 + M − 2wT ) . < wT < and 0 ≤ k < or 11 2 21 Ghamat, Pun, and Yan 983 II. Nonbinding Capacity Case 1 2+M 1 (42 + 21M + 9wT ) ≤ k < (56 (2 + M) and 11 70 105 2 2 −51wT − 49(2 + M) − 10566wT + 4242wT (2 + M) . 0 ≤ wT < Coopetition Strategy: (outsource to firm C). III. Binding Capacity Case 7 (2 + M) 49 (2 + M) < wT ≤ and 179 17 20 1 (2 + M − 2wT ) ≤ k ≤ (42 + 21M + 9wT ) 27 70 20 2+M 7 (2 + M) (2 + M − 2wT ) < wT ≤ and or 17 2 27 ≤ k ≤ 2M + 4 (1 − wT )) 56 (2 + M) 1 49 (2 + M) or ≤ wT ≤ and (7M − 17wT + 14) 221 179 7 1 (10 + 5M) ≤k≤ 13 49 (2 + M) 1 7 (2 + M) (42 + 21M + 9wT ) or < wT ≤ and 179 17 70 1 1 (10 + 5M) ⇒ wC = (10 − 6k + 5M) . ≤k≤ 13 10 1 2+M (56 (2 + M) − 51wT and 0 ≤ wT < 11 105 2 2 − 49(2 + M) − 10566wT + 4242wT (2 + M) ≤ k 56 (2 + M) 1 2+M (24 + 12M − 17wT ) or ≤ wT < ≤ 20 11 221 1 1 (42 + 21M + 9wT ) ≤ k < (24 + 12M − 17wT ) and 70 20 1 49 (2 + M) 56 (2 + M) (42 + 21M + 9wT ) ≤ k ≤ wT ≤ and or 221 179 70 1 1 (6 − 5k + 3M + 17wT ) . < (7M − 17wT + 14) ⇒ wC = 7 20 56 (2 + M) 1 868 (2 + M) (24 + 12M − 17wT ) ≤ < wT ≤ and 3723 221 20 984 Optimal Outsourcing Strategies when Capacity is Limited 1 7 (2 + M) 56 (2 + M) (176 + 88M) OR < wT ≤ 219 221 17 1 1 (10 + 5M) ≤ k ≤ (176 + 88M) and 13 219 k≤ 1 (6 − 5k + 3M) 4 8 49 (2 + M) 1 2+M (2 + M − 2wT ) ≤ k ≤ ≤ wT ≤ and 11 179 21 70 2+M 8 49 (2 + M) (42 + 21M + 9wT )) or < wT ≤ and 179 2 21 20 (2 + M − 2wT ) ≤ k ≤ (2 + M − 2wT ) 27 ⇒ wC = ⇒ wC = 1 (12 − 3k + 6M + 56wT ) . 68 IV. Nonbinding Capacity Case 7 (2 + M) 868 (2 + M) ≤ wT ≤ 3723 17 217 (2 + M) 1 (176 + 88M) ⇒ wC = and k >
219
876

1
868 (2 + M)
(24 + 12M − 17wT ) ⇒ wC
and k
0 ≤ wT
3723
20
=
17wT
16
Figure 2 in the article illustrates the four-region strategies that are outlined
above at M = 1 where ŵT = 2+M
is the maximum wholesale price of firm T in
11
Region II. For expositional convenience define capacity thresholds that separate
the four regions:
3
(14 + 3wT + 7M)
70
⎧
⎪ 1
⎪
(56 (2 + M) − 51wT
⎪
⎪
⎪
105
⎪

⎪
⎨
2
2
− 49(2+M) −10566wT +4242wT (2 + M) if 0 ≤ wT < 2+M k23 ≡ 11 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2+M 8 2+M ⎪ ⎩ (2 + M − 2wT ) if ≤ wT < 21 11 2 ⎧ 1 868 (2 + M) ⎪ (24 + 12M − 17wT ) if 0 ≤ wT < ⎨ 20 3723 k34 ≡ (2 1 868 + M) 7 (2 + M) ⎪ ⎩ (176 + 88M) if ≤ wT ≤ 219 3723 17 k12 ≡ Ghamat, Pun, and Yan 985 Next, we analyze supplier only option of firm C. Firm C’s profit function in supplier only strategy is an increasing function in wholesale price (i.e., πC = wC DO ); therefore, firm C would choose a wholesale price that is incentive compatible with firm O. max πCS = wC DO wC s.t. πOS ≥ πOT B if k ≤ 3 (14 + 3wT + 7M) and 70 1 (4−k+2M) (IR) 4 3 (14 + 3wT + 7M) and πOS ≥ πOT N if k >
70
7 (2 + M)
0 ≤ wT ≤
(IR)
17
1
πOS ≥ πOCB if k ≤ (6 + 3M − 4wC ) (IC)
5
1
πOS ≥ πOCN if k > (6 + 3M − 4wC ) (IC)
5
0 ≤ k ≤ 1 and 0 ≤ wT ≤ 1 − k.
0 ≤ wT ≤
In the above maximization problem the two IC (IR) constraints are exclusive
and do not appear together. First, we find the minimum wholesale price that is
required for firm C to be better off being supplier only compared to its profit in
the four-region strategies outlined above. Then, we find the wholesale price range,
for which IR and IC constraints are satisfied while keeping wholesale price higher
than the minimum required for firm C to prefer supplier only strategy. Because firm
O’s profit in the supplier only strategy is a decreasing function in wholesale price,
the wholesale price that maximizes firm C’s profit in the supplier only strategy
will force either the IC or IR constraint to bind. Therefore, we find the wholesale
price that binds each constraint. Then, whichever wholesale price that is smaller
would be the maximum wholesale price that firm C can charge in the supplier only
strategy for its corresponding region depending on k, wT and M. If this maximum
acceptable wholesale price is larger than the minimum required wholesale price
for firm C to prefer the supplier only strategy, firm C would apply the maximum
acceptable wholesale price and thus incentivize firm O to buyout firm C’s capacity
(supplier only strategy). For illustration purposes, we show the analysis only for
the Region IV where wC = 217(2+M)
. In this region the optimal strategy, without
876
consideration of supplier only strategy, is coopetition strategy with nonbinding
capacity constraint. Therefore, firm C, in order to prefer the supplier only strategy,
91
should have πCS ≥ πCCN |wC = 217(2+M) ⇔ wC DO ≥ 876
(2 + M)2 ; this would result
876
2
for firm C to
in a minimum required wholesale price of wC ≥ 364+364M+91M
876k
prefer the supplier only strategy to coopetition strategy. Because in this region
1
(i.e., 868(2+M)
≤ wT ≤ 7(2+M)
and k > 219
(176 + 88M)) capacity is always
3723
17
1
larger than k > 70 (42 + 21M + 9wT ) we only need to consider πOS ≥ πOT N
986
Optimal Outsourcing Strategies when Capacity is Limited
2
(IR). Moreover, with a minimum wholesale price of w ≥ 364+364M+91M
the
876k
1
capacity in this region is always larger than k > 5 (6 + 3M − 4wC ) which
leads us to only consider πOS ≥ πOCN (IC). As mentioned, we only need to
consider the wholesale prices that make the IC and IR constraint binding. πOS =
1
(49(25(2 − k)k − 3(2 + M)2 ) + 714(2 + M)wT − 867wT2 );
πOT N → wC = 2450k
√
7
πOS = πOCN
→
(96 − 175k + 48M + 5 192k + 457k 2 − 672kM)
768
(we only consider the positive root).
In the sequential equilibrium the supplier only strategy is optimal if and only if
1
7
Min{ 2450k
(49(25(2 − k)k − 3(2 + M)2 ) + 714(2 + M)wT − 867wT2 ), 768
(96−
√
2
364+364M+91M
2
;
175k + 48M + 5 192k + 457k − 672kM)} ≥
876k
That is
868(2 + M)
1922
and
≤ wT
0 w̄C
I) Competition, γ ∗ = 0, binding
Equilibrium Region
T)
DC = 3(14+7M+3w
70
1
Ï€C = 980
(784k(2 + M) − 3(14 + 7M − 17wT )2 − 714kwT − 735k 2 )
91(2+M)−51wT −105k
pC =
140
T
DC = 70k−21(2+M)+51w
70
2
2
T −63291wT
Ï€C = 4704(2+M) +29512(2+M)w
78400
T
pC = 112(2+M)+153w
560
T
DC = 84+42M−17w
140
T
pC = 14+7M+3w
35
T)
Ï€C = 3(14+7M+3w
2450
2
2
2
T +14)
DO = 3(7M−17w
70
T
pO = 224+112M+323w
560
−7M−14)
Ï€O = 3(17wT2450
T +14)
DO = 3(7M−17w
70
T
pO = 98−35k+49M+51w
140
−7M−14)
Ï€O = 3(17wT2450
T +14)
DO = 3(7M−17w
70
T +14
pO = 7M+18w
35
−7M−14)
Ï€O = 3(17wT2450
T)
DO = 3(4−k+2M−4w
17
DC = k
2
T
pO = 8−2k+4M+9w
17
T
pC = 14−12k+7M+3w
17
2
T −4)
πO = 6(k−2M+4w
289
Firm O
T)
πC = k(14−12k+7M+3w
17
Firm C
Table A1: Equilibrium profits, prices, and demands of the firms when wT ≤ ŵT .
988
Optimal Outsourcing Strategies when Capacity is Limited
Ghamat, Pun, and Yan
989
Knowing the best response optimal prices firm C will choose the wholesale
2
price: Case 1) Firm C’s profit function is strictly concave ( dd wπCC2 > 0) and has
) at dd πwCC = 0; Case 2) Firm C’s profit function is
a maximum (wC = 217(2+M)
876
2
1
(10 − 6k + 5M)) at
strictly concave ( dd wπCC2 > 0) and has a maximum (wC = 10
d πC
= 0. Note that, in binding case firm C’s capacity has to be small enough so
d wC
that firm C can use all of its capacity while maintaining positive prices and profits
(i.e., 0 ≤ k ≤ 16 (10 + 5M)).
Similar to the main model, there is an overlap between the capacity conditions. Because firm C is the first mover, considering the incentive compatibility conditions of firm O, it decides which of the optimal wholesale prices
to choose when capacity is in the overlapping region. Consequently, firm C’s
optimal action in each region is: A) Binding Capacity Case : k ≤ 56 + 5M
+
12

1
5
1
(2 + M) ⇒ wC = 10
(10 − 6k + 5M); B) Non − Binding Capacity Case :
12
73

1
5
+ 12
(2 + M) ⇒ wC = 217(2+M)
.
k > 56 + 5M
12
73
876
Before claiming the above regions to be the equilibrium of the game we also
consider a case where firm C chooses to be a monopoly. In this scenario, firm C faces
a capacity constraint (i.e., DC < k) and only decides on its market price. Solving for the optimal price considering the price and demand nonnegativity, we have: if k ≥ √ 1 ⇒ pC = 12 ⇒ πC = 12 OR if k < 1 ⇒ pC = 12 + 12 1 − 2k + k 2 ⇒ πC = 1 (2k − k 2 ). 2 Comparing with the cooperation scenario, we show that there are some cases that firm C prefers to be monopoly in the final product market and thus results in four different regions of equilibrium depending on firm C’s capacity and product substitutability M: A. Binding Capacity Case √ 1 1. Coopetition : if k ≤ 876 (365 + 365)(2 + M) and M ≥ k5 2. Monopoly : √ √ 1 ( 39858 (2 − k)k − 182) if 0.9612 < k ≤ 1 and M < 91 { if k ≤ 0.9612 and M < k5 B. Nonbinding Capacity Case 3. Coopetition : if k ≥ 1 and √ M > 0.1939
1
(365
+
365)(2 + M) < k < 1 and M {if 876 √ √ 1 ( 39858 (2 − k)k − 182) ≥ 91 4. Monopoly : if k ≥ 1 and M ≤ 0.1939 Finally, we consider a case where firm C chooses to be supplier only. In this case, firm C chooses the wholesale price wC and only after that firm O will decide on 2 the market price of its product. Firm O’s profit function is strictly concave ( dd pπOO2 >
C
0). So, FOC gives: pO ∗ = 1+w
. Then, firm C chooses its optimal wholesale
2
d2 π
price. Having a strictly concave profit function ( d wCp2 > 0): if k ≥ 12 ⇒ wC =

1 ⇒
πC = 14 or if k < 12 ⇒ wC = 12 + 12 1 + 4(k 2 − k) ⇒ πC = k − k 2 . 2 Firm C’s profit when only a supplier is always dominated by its profit in the 990 Optimal Outsourcing Strategies when Capacity is Limited Table A2: Equilibrium profits, prices, and demands of the firms when there is no competition in the component market. Equilibrium Region I) Coopetition, binding II) Monopoly, binding III) Coopetition, nonbinding IV) Monopoly, nonbinding Firm C Firm O 2 1 πC = 10 (10k − 6k 2 + 5kM) πO = 3k 50 1 pC = 10 (10 − 6k + 5M) 1 pO = 10 (10 − 4k + 5M) DC = 7k 10 DO = 3k 10 πC = 12 (2k − k 2 ) √ pC = 12 + 12 1 − 2k + k 2 DC = k πO = 0 91 πC = 876 (2 + M)2 361 πO = 31974 (2 + M)2 77 pC = 292 (2 + M) pO = 293 (2 + M) 876 (2 + M) DC = 119 438 19 DO = 146 (2 + M) πC = 12 πO = 0 pC = 12 DC = 1 – – – – monopoly or coopetition scenarios presented in the four-region equilibrium above. Consequently, we claim that the four-region equilibrium is the unique equilibrium of this sequential game. Table A2 presents the optimal prices, demands and profits of the firms in each region of the equilibrium. Proof of Proposition 5: Value of competition In this proposition we evaluate the effect of capacity and product substitutability on value of competition. From Table A1 and A2 we can find VO for any given capacity k, product substitutability M and firm T’s wholesale price wT (e.g., Non − 2 361 T) ] − [ 31974 (2 + M)2 ]). There are in binding cooperation : VO = [ 3(14+7M−17w 2450 total 11 different values of competition outcomes for firm O depending on capacity level and product substitutability when wT ≤ ŵT . Knowing the VO (k, M, wT ) functions we can derive the results in Proposition 4. The results for firm C can be driven in the same way. Salar Ghamat is an assistant professor of operations and decision sciences at Lazaridis School of Business and Economics, Wilfrid Laurier University. He received his PhD in management science from Ivey Business School (Western University) in 2017. His areas of research include strategic supply chain management, and healthcare operations management. He has published papers in Production and Operations Management (POM), Decision Sciences (DS), and International Journal of Production Economics (IJPE). Hubert Pun is an assistant professor of the management science area group at the Ivey Business School (Western University). He graduated from the Kelley School of Business (Indiana University) in 2010, where he completed his PhD in operations management and decision sciences. His research interests include, Ghamat, Pun, and Yan 991 marketing/operations interface, co-opetitive supply chain management, and healthcare operations management. He has published in Manufacturing & Service Operations Management (M&SOM), Production and Operations Management (POM), European Journal of Operational Research (EJOR), Naval Research Logistics (NRL), Decision Sciences (DS), etc. Xinghao Yan is an assistant professor in the Management Science Department at the College of Business and Innovation, University of Toledo. His research encompasses and integrates several disciplines including operations management, supply chain management, marketing, and healthcare management through the modelingbased and evidence-based research methods. His research interests range from information asymmetry and uncertainty in supply chains and their impact on supply chain performance, quality contracting, supply chain coordination, healthcare supply chains/operations, as well as behavioral operations in supply chain management. This document is a scanned copy of a printed document. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material. Optimal pricing of new subscription services: Analysis of a market experiment Danaher, Peter J Marketing Science; Spring 2002; 21, 2; ProQuest Central pg. 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Quant Mark Econ (2011) 9:129–154 DOI 10.1007/s11129-011-9097-0 Local competition, entry, and agglomeration Ting Zhu & Vishal Singh & Anthony Dukes Received: 16 October 2008 / Accepted: 24 February 2011 / Published online: 19 April 2011 # Springer Science+Business Media, LLC 2011 Abstract This paper analyzes competition between two spatially differentiated multiproduct retailers who encounter entry from a low-cost discounter. We assess how entry affects the pricing of the incumbent stores and the role played by the location of the entrant. Our primary objective is to identify how traditional retailers respond to new forms of low-cost retailing. Results show that post entry, the prices for some products are higher than the pre entry. However, which product prices increase depends on the incumbent’s location. Contrary to conventional wisdom, we find that the store closer to the entrant is better off compared to the incumbent located further away. We empirically demonstrate the main workings of our theory using sales data from several grocery stores that saw entry by discount stores in their trading areas. Keywords Entry . Retail Competition . Agglomeration JEL Classification L13 . L81 “They didn’t do what some people thought they would do, which is kill the little guys…On the contrary, their sales actually increased” General manager of Grossmont Center in San Diego on Wal-Mart’s entry in the shopping mall quoted in “In a Turnabout, Malls Get a Lift From Wal-Mart”, Wall Street Journal, Nov 22, 2006, page B1 The authors are grateful to Thomas Gehrig, Sridhar Moorthy, Nikolaos Vettas, Bo Zhou and several participants at the workshop on Competition Strategies and Customer Relations, Swedish School of Economics and Business Administration, Helsinki, Finland. The authors are listed in reverse alphabetical order and contributed equally. Electronic supplementary material The online version of this article (doi:10.1007/s11129-011-9097-0) contains supplementary material, which is available to authorized users. T. Zhu (*) University of Chicago, Chicago, IL, USA e-mail: tzhu@chicagogsb.edu V. Singh New York University, New York, NY, USA A. Dukes University of Southern California, Los Angeles, CA, USA 130 T. Zhu et al. 1 Introduction The past decade or so has seen a tremendous growth in the mega retailers such as Wal-Mart, Home Depot, Staples, Costco, IKEA, and others, which has fundamentally changed the buying and spending patterns of consumers. The dramatic growth and success of these stores have garnered debates over the economic and social consequences of “big box” retailers. Commentators have argued about the pros and cons of the entry by these stores into the local markets. One issue that has received a lot of attention in the business press is the impact of these “big box” stores on the locally owned/operated small retailers. A number of anecdotal accounts suggest that entry by such mega stores has negative effects on incumbent retail establishments (Stone 1995; Shils and Taylor 1997). These accounts cite as the crucial factor that makes the large-scale discounter so formidable is its severe cost advantage.1 If traditional retailers are unable able to match these costs, at least in the short to medium term, they will be unable to compete directly with the discounter on price. This means that, in order to survive, these retailers must find alternative ways to structure their pricing. This research is aimed at understanding the response strategies for traditional retailers in the presence of a low-cost entrant. Fundamental to determining an incumbent’s optimal response is an understanding of the shift in consumer shopping patterns, as implied by a discounter’s entry. If consumers differ with respect to their shopping and transportation costs, then the entrant’s location will have an impact on who switches from an incumbent store to the discount retailer and who remains in an incumbent’s residual clientele. Moreover, shopping and transportation costs are likely to interact with consumers’ shopping objectives, which may change as a result of entry by a large, multiproduct retailer. For example, a consumer in need of groceries and durables on the same shopping trip may bypass the nearby grocery store for a distant supermarket located near a new discount store. Therefore, in this research, we analyze the relationship between the discounter’s entry location and an incumbent’s response to entry, bearing in mind differences in consumers’ shopping objectives and costs. There has been a growing body of empirical research evaluating the impact of alternate retail formats in the sales of traditional supermarkets. A general finding in this literature is that entry of a discount store leads traditional food retailers to lower their prices (Basker and Noel (2007); Hausman and Leibtag (2007), although the price response is not consistent across product categories (Singh et al. (2006). Our theory offers an explanation for differential price response by incumbents by suggesting that, while prices change due to entry, prices on some products may in fact increase. Furthermore, consumer heterogeneity and the location of the new entrant play a critical role in the relative changes in incumbent’s profits. For a stable market size, one expects entry to reduce profits at incumbent stores. While that is the case in our model, we ask how location affects the relative losses at each incumbent. Counter-intuitively, our model predicts that a distant incumbent may suffer to a greater extent than an incumbent nearby the entrant. This result stands in contrast to 1 According to industry reports, for example, operating costs at Wal-Mart are about 17% of sales, as compared to 22% at the average grocery store (Coggins and Sanauer 2000). Local competition, entry, and agglomeration 131 common notions that a low-cost entrant, such as a Wal-Mart, is hardest on the stores in its immediate vicinity. Our findings are based on a spatial model of competition between two multiproduct stores that encounter entry by a discount store into the market. Precompetitor entry, our modeling approach parallels that used previously in the literature, most notably, Lal and Matutes (1989). The incumbent retailers are located at the end points of a Hotelling line and are assumed to carry two products. Consumers are heterogeneous in terms of their location along the line as well as their shopping preferences. In particular, we consider two types of consumers – value buyers and convenience shoppers – that differ in terms of their transportation and shopping cost as well as their reservation price for the products. Equilibrium prices and profits from this game serve as a before entry benchmark. We then analyze an after entry setting by considering entry by a discount store that locates at one of the end points, i.e. in the immediate location of one of the incumbents. The model incorporates many aspects of the retailing world such as differentiation in the product assortments and cost advantages for the discounter. In particular, we assume that the new entrant carries one of the products offered by the incumbent stores and also offers a unique product. Thus, there is a partial overlap in the product offering of the incumbents and the new entrant. For instance, we can think of the incumbents as two grocery stores offering fresh produce and general merchandise, and the entrant as a Wal-Mart discount store offering general merchandise and durable electronics. Wal-Mart is assumed to have cost advantages in that it can procure the general merchandise items at a lower cost than the supermarkets. Following competitor entry, we consider another dimension of consumer heterogeneity based on the difference of the purchase basket or the types of products consumers need. Since some products (such as durables) are bought less frequently than others, we assume some of the consumers need all three products, while other consumers only buy a subset of the available products (Kumar and Rao 2006). Using the structure described above, our primary objective in this paper is to determine how entry by this differentiated competitor affects the pricing and profits of the incumbent stores. In particular, we analyze the multi-product pricing strategies employed by the incumbents and the role played by the location of the entering discounter. In general, one would expect the prices for the products to fall due to increased competition in the market and the impact of entry on profits to be higher for the store closer to the new competitor. However, once we incorporate differentiation of product offerings by the entrant and consumer heterogeneity, we may get different results. In particular, our analysis shows that in the post-entry equilibrium, the prices for the products not offered by the discounter are higher than the pre-entry prices. More interestingly, contrary to the conventional wisdom we find that the store that is closer to the new entrant is better off compared to the incumbent located further away. The intuition for these results is as follows: In the before entry equilibrium, the two incumbent retailers earn equal profits and segment the market symmetrically, serving both value buyers and convenience shoppers. After entry by the discounter, however, its low price draws the value buyers – the price sensitive segment – out of the market for the items it carries. This in turn fosters market segmentation and 132 T. Zhu et al. softens price competition between the incumbents for these items. Furthermore, the new entrant’s unique product offering and lower prices attract more convenience shoppers to visit the location it occupies, which introduces positive demand externalities to the neighboring retailer. This encourages the nearby incumbent to abandon the value buyer segment altogether and focus exclusively on the priceinsensitive segment. The distant retailer, on the other hand, is unable to attract this segment because of their hi... Purchase answer to see full attachment

  
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