Strategic Outsourcing Decisions for Manufacturers That Produce Partially Substitutable Products in a Quantity-Setting ∗ Duopoly Situation

Decision Sciences C 2007, The Author Volume 38 Number 1 Journal compilation C 2007, Decision Sciences Institute February 2007

Strategic Outsourcing Decisions for Manufacturers that Produce Partially Substitutable Products in a Quantity-Setting ∗ Duopoly Situation

Tiaojun Xiao School of Management Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, P. R. China, e-mail: [email protected]

Yusen Xia† Robinson College of Business, Georgia State University, Atlanta, GA 30303, e-mail: [email protected]

G. Peter Zhang Robinson College of Business, Georgia State University, Atlanta, GA 30303, e-mail: [email protected]

ABSTRACT This article examines production and outsourcing decisions for two manufacturers that produce partially substitutable products and play a strategic game with quantity competition. When both manufacturers outsource key components to the same upstream supplier, their products become more substitutable due to the increased commonality of the products. In addition, outsourcing may create better consumer perception about the product if the manufacturers choose reputable suppliers with better brand or quality. We explicitly model the substitutability change and the brand/quality effect and provide conditions under which the manufacturers should outsource the components to a supplier. We present the subgame perfect Nash equilibriums for the situation in which there is only one supplier and the case in which two suppliers compete with each other in the upstream supply chain. Numerical examples are presented to illustrate the ﬁndings. Subject Areas: Common Components, Game Theory, Outsourcing Strategy, Product Substitutability, and Supply Chain Management.

INTRODUCTION With globalization and competitive pressure on specialization, outsourcing has become prevalent in many industries. As one Business Week editorial commented,

∗We would like to thank the referees, the associate editor, and the editor for their many helpful suggestions and insightful comments, which have signiﬁcantly improved the content and presentation of the article. The ﬁrst author’s research is supported in part by the NSFC under grant 70301014 and 70671055; and the fund for Study on the Evolution of Complex Economic System at Innovation Center of Economic Transition and Development of Nanjing University of the Ministry of Education, China. †Corresponding author.

81 82 Strategic Outsourcing Decisions for Manufacturers

“What were once considered core competencies for high tech and other companies are now becoming inexpensive global commodities. Chip design, mechanical and electrical engineering, testing, software writing, and high-tech manufacturing are heading to India, China, Eastern Europe” (Business Week, 2005, p. 124). For example, in the aerospace industry, Boeing outsources to numerous manufacturers the production of more than 34,000 components to be assembled into its 747 pas- senger aircraft (Shy & Stenbacka, 2003). In the computer industry, manufacturers such as Dell, Hewlett-Packard, Toshiba, and Lenovo purchase almost all of the components for their products from suppliers all over the world. Outsourcing al- lows these companies to focus their resources on the design and marketing of their products. A direct consequence of outsourcing is that products from different companies in the same industry share many common components, making those products less differentiated from the consumer’s perspective. For instance, the desktop computers produced by different manufacturers such as Dell and Hewlett-Packard are highly substitutable in the retail market. One of the key components in computers is the central processing unit (CPU), which is supplied predominantly by Intel and AMD. From the consumer’s point of view, computers that share the same brand CPU are more substitutable than those with CPUs made by different manufacturers. Generally speaking, common components in competing products affect their substitutability, and the larger the number of key common components there are, the more substitutable the products will become. Outsourcing also has two other notable effects. The first is double marginalization, which occurs when upstream suppliers and downstream manufacturers independently engage in noncompetitive pricing, that is, they independently mark up the product’s price above their marginal costs. As a result, manufacturers are subject to less intense price competition (Iyer, 1998), and the supply chain has a lower combined profit than it would if the firms were vertically integrated (Spengler, 1950; Tirole, 1988). Second, outsourcing may increase the consumer’s positive perception about the product if manufacturers choose reputable suppliers with better brand or quality (Ramdas, Fisher, & Ulrich, 2003). For example, when Apple Computer announced the plan to adopt Intel’s chips, the decision was viewed very positively by the market (Clark, Wingfield, & Bulkeley, 2005). In this article, we study the outsourcing decision of two manufacturers that produce partially substitutable products and play a strategic game with quantity competition. For key components, the manufacturers can either keep the production in house (insourcing) or outsource to suppliers. If they both choose to outsource to the same supplier, the substitutability of the end products increases. We explicitly model the change of the substitutability as well as the brand/quality effect when a core component is outsourced to a supplier. The main conclusion of this article is that the manufacturers should outsource the key components if the change of the substitutability due to outsourcing is relatively small and if the brand-quality effect outweighs the double marginalization effect. Otherwise, they should keep the production in house. In the sections that follow, we review the related literature, describe the basic model, and then investigate the subgame perfect equilibrium for two conditions, (i) only one supplier in the upstream supply chain and (ii) two competing suppliers. Xiao, Xia, and Zhang 83

After providing numerical examples for additional insights, we conclude with a summary and directions for future research.

LITERATURE REVIEW This research is closely related to the literature of outsourcing, product commonality, and channel structure. There are strategic as well as tactical/operational rea- sons for outsourcing. From the strategic point of view, Cachon and Harker (2002) find that firms may be better off outsourcing when the production cost exhibits economies of scale. Shy and Stenbacka (2003) believe that competition in the final product market affects a firm’s outsourcing decision. They investigate how the degree of competition changes the incentive to outsource key components. Kim (2003) shows how the investment capability of a contract manufacturer affects the outsourcing decision. Gilbert, Xia, and Yu (2006) show that strategic outsourcing can mitigate downstream manufacturers’ overinvestment in the reduction of production costs. Although both our study and Gilbert et al. (2006) consider two manufacturers and one supplier in the base model, there are several key differences. First, while Gilbert et al. (2006) focus on the role of outsourcing in dampening cost-based competition between two competing manufacturers, our focus is on the effect of product substitutability and the supplier’s brand/quality on the manufacturer’s outsourcing decision. Second, Gilbert et al. (2006) assume that the product substitutability is constant and the supplier and manufacturers have the same production cost. In our article, we explicitly consider the change of product substitutability as well as different production costs. Third, our findings complement those of Gilbert et al. (2006). For example, Gilbert et al. (2006) conjecture that the supplier would never want to induce an asymmetric equilibrium. We find, however, that under certain conditions, the supplier can either attract both manufacturers to outsource or sell only to one manufacturer, that is, induce an asymmetric equilibrium. From the tactical or operational point of view, outsourcing plays a role in cost reduction, production smoothing, and leadtime reduction. Van Mieghem (1999) studies a stochastic two-stage game with recourse between a manufacturer and its subcontractor, where both firms invest in production capacities. He characterizes the relationship between outsourcing and pricing flexibility. Kamien and Li (1990) illustrate the production smoothing effect of outsourcing. Yang, Qi, and Xia (2005) study the outsourcing quantity for a multiperiod production and inventory system with Markovian capacity and random demand. Our study is also related to research on component commonality and consumer perception. Ramdas et al. (2003) investigate how to select components to manage product portfolios. While their research assumes that sharing of components does not significantly affect consumers’ perceptions about product differentiation, our model specifically considers the impact of outsourcing on consumer perception change. Robertson and Ulrich (1998) discuss the advantage of a plat- form approach for product design and suggest that it is necessary to make a trade- off between distinctiveness and commonality. Desai, Kekre, Radhakrishnan, and Srinivasan (2001) study the consumer perception issue with common components and explore whether to use common components for two products when there are 84 Strategic Outsourcing Decisions for Manufacturers two segments of consumers with different quality perceptions. To the best of our knowledge, no research has explicitly considered the change in substitutability of the final products after key components are outsourced to the same supplier. Thus, our research complements the literature by explicitly modeling two effects of outsourcing: change in product substitutability and change in consumer perceptions. In the channel structure literature, our study is mostly related to the work of McGuire and Staelin (1983). In their seminal work, McGuire and Staelin (1983) show that two upstream firms should use independent retailers to sell their products when the products’ substitutability coefficient is high. In their setting, downstream retailers can dampen the price competition between the two manufacturers. Some extensions to McGuire and Staelin’s work have been made, and readers are referred to Choi (1991), Lee and Staelin (1997), and Gupta and Loulou (1998). Our article further extends the work of McGuire and Staelin (1983) in that, instead of exam- ining whether the upstream members in the supply chain should use downstream retailers, we investigate whether the downstream firms should outsource their key components to upstream suppliers. In our model, two manufacturers play an outsourcing game and compete for production quantities. Ingene and Parry (2004) present a modeling approach to the change of competitive substitutability with a linear demand function for three situations (i) a cross-price effect, (ii) a compensating change in slopes, and (iii) a compensating change in intercepts. They point out the weakness in the price competition model such as aggregate demand amplification (i.e., the total market demand for manufacturers increases and even becomes price-insensitive when the substitutability between their products increases), which does not occur in a quantity competition setting. Thus, we assume that manufacturers play a quantity competition game in their outsourcing decisions.

THE MODEL Consider a market in which two manufacturers (indexed as A and B) produce partially substitutable products. In addition, there are suppliers producing components that can fit into the manufacturers’ products. Denote manufacturer i’s retail price as pi and its production quantity as qi, where i = A, B. Each manufacturer determines whether to outsource the key component to a supplier so as to maximize profit. Without loss of generality, we assume that one unit of the product includes exactly one unit of the component. Denote the supplier’s wholesale price for the component as w. We make the following assumptions regarding the production of the component: (i) manufacturers own the same production technology and the unit cost of producing the component is c; (ii) the unit production cost of the component for the supplier is c0 and w ≥ c0 so that the supplier makes a nonnegative profit; and (iii) the production cost for all other components is zero, which does not change the findings qualitatively. Following Ingene and Parry (2004), we consider the following linear inverse demand function:

pi = ai − qi − dqj , 0 < d < 1, i, j = A, B, j = i, (1) Xiao, Xia, and Zhang 85

where ai represents the retail price cap (the highest feasible price) for manufacturer i and d is the substitutability coefficient of the two products. If d = 0, the two products are totally differentiated from each other, and if d = 1, they are perfect substitutes. As d increases, the two products become more substitutable. In general, the higher the commonality, the larger the substitutability coefficient will be. When both manufacturers outsource the key component to a common supplier, the substitutability coefficient increases. Thus, the new substitutability coefficient, d under outsourcing, should be greater than the original d. The linear inverse demand function is a common assumption in the literature (Tirole, 1988; Bernstein & Federgruen, 2003; Xiao & Yu, 2006). But the main results of this article do not change qualitatively if a nonlinear (exponential) inverse demand model is used. We also explicitly consider the consumer’s perception after outsourcing as in Desai et al. (2001) and Ramdas et al. (2003). Specifically, we assume that the supplier with better brand or higher quality will have greater pricing power. That is, a manufacturer will have a higher price cap if purchasing the key component from the supplier with the better reputation. Otherwise, this manufacturer’s price cap is lower or remains the same. If both manufacturers produce the component in house, the profit function for manufacturer i is π , = − − − , = , . i (qA qB ) (ai qi dq j c)qi i A B (2)

The case in which both manufacturers keep the component production in house is denoted by the superscript II. Similarly, notations OI, IO, and OO are used for situations where A outsources the component and B produces in house, A produces in house while B purchases from the supplier, and both outsource to the supplier, respectively. Because each manufacturer’s profit function (2) is quadratic and concave, by using the first-order optimality conditions, we can find the equilibrium quantities as follows: 2(a − c) − (a − c) d qII = i j , i, j = A, B, j = i. (3) i 4 − d2 II ≤ − ≤ − From (3), we have qi 0if2(ai c) (aj c) d. That is, manufacturer i has to withdraw from the market if a distinct brand or quality disadvantage exists. Man- ufacturer j will have the motivation to be a monopolist by significantly improving the company’s reputation. However, because the quality or brand improvement involves higher costs, j must make a trade-off between the benefit from being a monopolist and the cost incurred in improving reputation. To simplify the analysis throughout the article, we assume that all equilibrium quantities are positive. II The equilibrium quantity qi is an increasing function of the price cap ai and a decreasing function of the competitor’s price cap aj and unit production cost c. Differentiating (3) with respect to d, we find that the increase of commonality between the two products lowers the optimal quantities in a Cournot market if a − c a − c 4 + d2 max A , B < . (4) aB − c aA − c 4d 86 Strategic Outsourcing Decisions for Manufacturers

II That is, if the price caps aA and aB satisfy (4), the equilibrium quantity qi is a decreasing function of the substitutability coefficient d. This result reflects the fact that manufacturers prefer less substitutability in order to maintain the pricing power (Tirole, 1988). If (4) does not hold (i.e., the price caps are quite different and the substitutability coefficient d is large), then the increase of commonality will increase the equilibrium quantity of the manufacturer with a higher net price cap (the difference between price cap and production cost), but decrease that of the competitor. Clearly, the manufacturer with significant brand/quality advantage will attract more consumers. For example, in the computer industry, Apple’s quality and reliability enable the company to charge a price premium over other personal computer (PC) makers for comparable models. After its decision to adopt Intel chips and to allow its machines to run Microsoft Windows operating systems, Apple has gained significant market share since early 2005. Analysts estimated that Apple’s global PC market share will increase to 5% from just 1.9% in 2005 (Hesseldahl, 2006b). II From (1) and (3), the equilibrium price pi is 2(a + c) − d(a − c) − cd2 pII = i j , i = A, B, i 4 − d2 which is a decreasing function of the substitutability coefficient d provided that the price caps aA and aB satisfy (4). From (2) and (3), manufacturer i’s profit is π II = II 2 i ( (qi ) ), which is also a decreasing function of d under condition (4). Thus, the higher the commonality between the two products, the lower the equilibrium retail prices. In other words, when their price caps are similar, the increase of commonality or substitutability reduces the pricing power of manufacturers and intensifies competition. In addition, the increase of substitutability has a negative effect on manufacturers’ profits. On the other hand, if i outsources while j keeps the production in house, the profit function for i is π , = − − − , i (qA qB ) (aî qi dq j w)qi (5) where aî reflects the price cap after outsourcing. If both manufacturers outsource, the profit function for i becomes πi (qA, qB ) = (aî − qi − d q j − w)qi . (6) In (5), we assume that the outsourcing decision does not affect the commonality between the two products if only one manufacturer outsources. Therefore it does not affect the substitutability coefficient between the two products. However, when both manufacturers outsource, the substitutability coefficient increases from d to d, where d > d.

A MONOPOLY SUPPLIER We ﬁrst consider the situation in which there is only one supplier that produces the component in the upstream supply chain and two manufacturers also have the production capability for the component. The supplier and the manufacturers play a three-stage dynamic game with complete information as follows: Xiao, Xia, and Zhang 87

(i) The supplier decides the wholesale price w for the component, (ii) The manufacturers simultaneously determine whether to outsource the component to the supplier or to produce it internally, and

(iii) The manufacturers announce their production quantities qA and qB simultaneously. The backward induction technique is employed to ﬁnd the subgame perfect Nash equilibrium (SPE). We ﬁrst present the manufacturers’ quantity decisions and then investigate their outsourcing strategies. Finally, we explore how the supplier determines wholesale price.

Manufacturers’ Quantity Decisions Table 1 gives optimal quantities for a given supplier’s wholesale price. For com- pleteness, we include the optimal quantities when both manufacturers produce the π mn = mn 2 = component in house. In addition, it can be shown easily that i (qi ) , m, n I , O, i = A, B. That is, each manufacturer’s optimal profit is the square of the corresponding optimal order quantity. OI − II = − − − / − 2 From Table 1, we find that qA qA 2[(aˆ A aA) (w c)] (4 d ). π OI − π II This quantity difference determines the sign of ( A A ). Thus, given manufacturer B’s strategy I, A’s outsourcing decision is determined by the relative values of (aˆ A − aA) and (w − c), not by the substitutability of the two products and manufacturer B’s brand or quality. In addition, A’s outsourcing decision does not affect the equilibrium quantities if aˆ A − aA = w − c, that is, if the price cap and production cost increase synchronously, or the effect of brand or quality on the price cap (the brand effect) offsets the effect of outsourcing on the unit production cost (the outsourcing effect). However, if aˆ A − aA > w − c, then the brand effect outweighs the outsourcing effect, and A will be better off outsourcing the component. If aˆ A − aA < w − c, then the outsourcing effect outweighs the brand effect, and A will be better off producing the component in house. Note that the supplier’s production cost c0 may be less than the manufacturers’ production cost c. A manufacturer may outsource to save the production cost (c0 ≤ w < c) even when the new price cap from the supplier is not higher than the manufacturer’s own price cap (aî ≤ ai ). This explains many offshore outsourcing

Table 1: Manufacturers’ optimal quantities under one supplier. A B IO 2(a − c) − (a − c) d 2(a − c) − (aˆ − w) d IqII = A B , qIO = A B , A 4 − d2 A 4 − d2 2(a − c) − (a − c) d 2(aˆ − w) − (a − c) d qII = B A qIO = B A B 4 − d2 B 4 − d2 2(aˆ − w) − (a − c) d 2(aˆ − w) − (aˆ − w) d OqOI = A B , qOO = A B , A 4 − d2 A 4 − d2 2(a − c) − (aˆ − w) d 2(aˆ − w) − (aˆ − w) d qOI = B A qOO = B A B 4 − d2 B 4 − d2 88 Strategic Outsourcing Decisions for Manufacturers decisions in which suppliers do not necessarily have better brand or quality than domestic manufacturers. In such cases, the main driver of outsourcing is the production cost savings, which can be as high as 40% (Conkey, 2006). Table 1 also suggests that, if only one manufacturer outsources, then the equilibrium quantity will decrease for the outsourcing manufacturer but will increase for the internal producing manufacturer when the wholesale price increases. A portion of demand will be transferred from the outsourcing manufacturer to the OO insourcing one. When both manufacturers outsource, in order to ensure that qi is 2(aˆ A − w) 2(aˆ B − w) positive, we assume that 2(aî − w) > (aˆ j − w) d ,ord < min{ , }. aˆ B − w aˆ A − w The implication of this assumption is that manufacturers should not outsource to the same supplier if the substitutability change is significant. This condition always holds if aˆ A = aˆ B . For simplicity, we first analyze the case in which aˆ A = aˆ B = aˆ and then study the effect of the difference between aˆ A and aˆ B through numerical examples.

Manufacturers’ Outsourcing Decisions Under Exogenous Wholesale Price π mn = mn 2 = = Because ( i (qi ) , i A, B, and m, n I , O), the normal form of the outsourcing game is equivalent to the one in Table 1. ∗ = − − 2 / − − − For convenience, we deﬁne d1 (w) (aˆ w)(4 d ) [2(aA c) (aˆ − ∗ = − − 2 / − − − − w) d] 2 and d2 (w) (aˆ w)(4 d ) [2(aB c) (aˆ w) d] 2. The ex- ∗ ∗ pression d1 (w)(d2 (w)) is the substitutability threshold for manufacturer A(B)at which the manufacturer is indifferent between strategies I and O, given that the competitor B (A) outsources. It is easy to verify that the higher the wholesale price ∗ = w, the lower the threshold di (w), i 1, 2. Proposition 1 characterizes the SPE.

Proposition 1. Assume that aˆ A = aˆ B = aˆ. Given a wholesale price w,wehave

(i) (I, I) is an SPE if and only if aˆ − w ≤ min{aA − c, aB − c}; < ≤ { ∗ ∗ } (ii) (O, O) is an SPE if and only if d d min d1 (w), d2 (w) ; − ≥ − ≥ ∗ (iii) (I, O) is an SPE if and only if aˆ w aB c and d d1 (w); − ≥ − ≥ ∗ (iv) (O, I) is an SPE if and only if aˆ w aA c and d d2 (w). The proof of Proposition 1 and all other results is given in the Appendix. Proposition 1 suggests that, given one manufacturer’s (j) outsourcing decision, the other manufacturer, (i), will also outsource only if the change of substitutability is relatively small. When the substitutability of the products is higher, the competition will become more intense, and manufacturer i will be better off producing the components in house so as to avoid fierce competition with j. Manufacturer i will choose outsourcing only if the brand effect outweighs the outsourcing effect (i.e., aˆ − ai ≥ w − c). In addition, the higher the production cost of manufacturer i and the supplier’s quality are, the more likely the above result will hold. Proposition 1 also indicates that the manufacturers are better off producing the component in house when the supplier’s price is high or the quality is low. Both manufacturers will outsource if the substitutability change is not dramatic. In addition, at the equilibrium, it is possible that one manufacturer produces the Xiao, Xia, and Zhang 89 component in house and the other outsources to the supplier, that is, there exist asymmetric equilibriums (I, O) and (O, I). ≥ ∗ ≤ Without loss of generality, we assume aA aB, which leads to d1 (w) ∗ d2 (w). That is, when the price cap for manufacturer A is higher than that for B, A has a lower threshold of substitutability coefficient given B’s strategy O. In other words, the higher the price cap is, the lower the outsourcing incentive will be. Proposition 1 can help to explain the decision made by Apple Computer to switch its chips from IBM to Intel. Although this switch increases the substitutability between an Apple computer and a PC made by other computer makers, the change is not dramatic because Apple designs its own operating system (Mac OS X) and its computers have many unique features. On the other hand, by adopting Intel’s processors, Apple increases the brand effect for its computers (Clark et al., 2005). Therefore, it is not surprising to see a significant increase in market share by Apple’s outsourcing decision as reported by Hesseldahl (2006a), in the first quarter of 2006: “50% of people buying Macs in Apple retail stores are classified as new to Mac.” Next, we relate the SPE of the game to the supplier’s wholesale price. By = ∗ solving the equation of d d1 (w) for w, we have a threshold for the wholesale ∗ − + ∗ = − 2(aA c)(2 d ) = price w1 aˆ 4 − d2 + d(2 + d) . Similarly, by solving equation d d2 (w) for w,we ∗ − + = − 2(aB c)(2 d ) ≥ obtain another threshold w2 aˆ 4 − d2 + d(2 + d) . Because aA aB, it follows that ∗ ≤ ∗ + − ≤ + − ∗ ∗ w 1 w 2 and aˆ c aA aˆ c aB . Note that w 1(w 2) is the largest wholesale price for A (B) to outsource given that B (A) outsources and aˆ + c − aA (aˆ + c − aB ) is the largest wholesale price that A (B) will outsource given that B (A) insources. > ∗ < + − From d d, we find that w1 aˆ c aA. Figure 1 gives the manufacturer’s outsourcing equilibriums as a function of supplier’s wholesale price. Figure 1 shows that outsourcing is the best choice for both manufacturers < ∗ if the supplier’s price is low (w w 1). Insourcing is the best if the price is high (w > aˆ + c − aB ). In between, the Nash equilibriums are the asymmetric strategy ∗ < profiles (O, I ) and (I , O). Only manufacturer B will prefer outsourcing if w 1 < ∗ + − < < + − w w 2 or aˆ c aA w aˆ c aB . Either one will choose outsourcing if ∗ < < + − w2 w aˆ c aA. That is, both asymmetric strategy profiles (O, I ) and (I , O) are Nash equilibriums. Consequently, there exists a mixed-strategy equilibrium ≥ ∗ > + − within this price range. Because aA aB, when w2 aˆ c aA, there does not exist a wholesale price w such that (O, I ) is a Nash equilibrium. To illustrate the effect of the supplier’s price cap and product substitutability on outsourcing decisions, we plot the manufacturer’s outsourcing decisions against aˆ and d in Figure 2 with the following parameters: aA = 16, aB = 14 < aA, w = 4, c = 2, and d = .1. Several observations can be made from Figure 2. First, if the

Figure 1: The equilibrium intervals of the wholesale price when aA ≥ aB.

(O, O)(I, O) (I, O) or (O, I) (I, O)(I, I) w c w∗ ∗ ˆ acaˆ +− 0 1 w2 aca+−A B 90 Strategic Outsourcing Decisions for Manufacturers

Figure 2: Outsourcing decisions versus aˆ and d.

d′ a − c + w a − c + w d '* (w) '* B A 2 d1 (w) 1 (I, O) or (O, I) 0.8 (I, O) (I, O) 0.6 (I, I)

0.4 (O, O)

0.2 aˆ 16 18 20 22

supplier’s brand or quality (aˆ) is low, regardless of the substitutability change, both manufacturers will be better off producing in house. Second, when the supplier’s brand effect increases and/or the product substitutability decreases, the outsourcing region for the manufacturers increases. Therefore, with better brand or quality from the supplier and less product substitutability change, the manufacturers are more likely to outsource. Third, the size of the (I, O) region depends on the values of d and aˆ. It increases with d but decreases with aˆ. That is, when the product substitutability increases or the supplier’s brand effect decreases, the (I, O) region expands. Finally, the (O, I) region (shaded area in Figure 2) may or may not exist depending on the conditions given in Corollary 1 in the following. For example, when aB = 10, we do not have the equilibrium of (O, I) and the shaded area disappears.

Corollary 1. Assume aˆ A = aˆ B = aˆ and aA ≥ aB. There exists w such that (O, I ) − 2 − is an SPE if and only if d ≥ (4 d )(aA c) − 2. 2(aB − c) − d(aA − c) Corollary 1 suggests that, as the two manufacturers become more similar (i.e., the difference between their price caps becomes smaller), (O, I) is more likely to be an equilibrium. Therefore, two equilibriums exist as shown in the shaded area of Figure 2. This result is consistent with that of Gilbert et al. (2006) in which there exist two asymmetric equilibriums for two symmetric manufacturers that have the same cost structure and brand effect. If the difference between two price caps becomes more signiﬁcant, outsourcing becomes a less attractive choice for manufacturer A because manufacturer A has a larger price cap or brand effect. On the other hand, if the new substitutability is small, B will be more likely to outsource if A chooses to do so. If the new substitutability is sufﬁciently large, then B is better off insourcing so as to differentiate its products from A’s to avoid intense competition. Xiao, Xia, and Zhang 91

Supplier’s Endogenous Prices (the Optimal Wholesale Price) Now, let us examine the supplier’s optimal wholesale price. When both manufacturers purchase the component from the supplier, the supplier’s profit function is aˆ − w π OO(w) = (w − c ) qOO(w) + qOO(w) = 2(w − c ) . (7) S 0 A B 0 2 + d Applying the first-order condition of (7) with respect to w, we derive the optimal OO = 1 + > OI ≥ IO solution as w 2 (aˆ c0) w w . At the manufacturer’s strategy profile (I , O), the supplier’s profit function is 2(aˆ − w) − (a − c) d π IO(w) = (w − c )qIO(w) = (w − c ) A . (8) S 0 B 0 4 − d2 IO = 1 + − 1 − The optimal solution for (8) is w 2 (aˆ c0) 4 (aA c) d, which is a decreasing function of the substitutability and an increasing function of the new price cap and the production cost. Similarly, at the strategy profile (O, I ), we have OI = 1 + − 1 − w 2 (aˆ c0) 4 (aB c) d. As Figure 1 indicates, the manufacturer’s decisions are dependent on the supplier’s wholesale price. Therefore, it is necessary to consider the price constraint under which each strategy profile is valid. Proposition 2 completely characterizes the supplier’s optimal wholesale price. = = ≥ OO ≤ ∗ Proposition 2. Assume that aˆ A aˆ B aˆ and aA aB.Ifw w 1, the optimal wholesale price of the supplier is w OO. Otherwise, the optimal wholesale price is ⎧ ⎪ ∗, ≤ ∗ IO ≤ ∗ ⎨⎪w1 if d d3 or w w1 ∗∗ = IO, > ∗ ∗ < IO < + − w ⎪w if d d3 and w1 w aˆ c aB ⎩⎪ + − , > ∗ IO ≥ + − , aˆ c aB if d d3 and w aˆ c aB √ − + 2− 2 − 2 π IO − 2 π IO− − − ∗ = B B 4d (4 d ) [(4 d ) 4(aˆ c0)(aA c)] − π IO = π IO IO where d3 2d2π IO 2, S (w ), and 2 IO B = 2{d(4 − d )π + 2(aA − c)[2(aA − c) − (aˆ − c0) d]}≥0. OO ≤ ∗ Proposition 2 shows that, when w w 1, the supplier can induce both OO > ∗ ∗ manufacturers to outsource. If w w 1, there exists a threshold d3 such that the supplier is indifferent between selling to both manufacturers and selling to B only. Note that the supplier never wants to sell only to manufacturer A because of our assumption that A has a higher brand effect (aA > aB). That is, in order to attract A, the supplier must offer a lower price, which is less profitable than inducing either B or both A and B to outsource. When deciding whether to sell to B or both manufacturers, the supplier faces a trade-off between the demand volume and the price. If the supplier can sell to both manufacturers, the supplier’s volume may be high, but the price may be low. On the other hand, if the supplier sells only to B, the supplier can charge a higher price though with a lower volume. Therefore, when the supplier foresees that the > ∗ new product substitutability is high (d d3 ), the supplier may sell only to B in order to avoid a lower price necessary to induce both manufacturers to outsource. Otherwise, when the new product substitutability is relatively low, the supplier should sell to both manufacturers. 92 Strategic Outsourcing Decisions for Manufacturers

Figure 3: Supplier’s optimal proﬁt versus d.

Supplier’s optimal profit π OO S 35

IO 25 π S

20 OI π S 15

10 ′ d 0.4 0.5 0.6 0.7 0.8 0.9

Figure 4: Supplier’s optimal selling strategy.

c aˆ =18 0 (I, O) 2 1

′ d 0.4 0.5 0.6 0.7 0.80.9 -1 aˆ =16 -2

(O, O) -3 -4 -5

Proposition 2 provides an interesting contrast to Gilbert et al. (2006), who find that the supplier does not benefit from selling only to one manufacturer. In our model, we allow the change of product substitutability and market caps of the two manufacturers, and this is the key driver of the difference. Figures 3 and 4 are used to illustrate Proposition 2. Figure 3 gives the supplier’s optimal profit against the new substitutability coefficient (d) with the following parameters: aA = 16, aB = 14, aˆ = 18, c = 2, c0 = 1, and d = .35. Using IO∗ = OI∗ = OO∗ = ∗ Figure 1, we find that w 6, w 4, and w w 1, with the specific value depending on d. Figure 3 shows that selling only to A is a dominated strategy for the supplier. When d is relatively small (d < .537), the supplier can earn a larger profit by selling to both manufacturers; however, when d is large (d > .537), it is Xiao, Xia, and Zhang 93 better off to sell only to B. To illustrate our early discussion that the supplier has to offer a fairly low price in order to attract both manufacturers to outsource, let d = .6, a relatively large value. Then we can derive the optimal price w OO∗ = ∗ = IO∗ = w 1(.6) 2.794. Recall that w 6. Thus, when d is relatively large, the benefit of higher demand volume from both manufacturers may not offset the lower price the supplier has to offer as demonstrated by the profit difference at d = .6 in Figure 3. In Figure 4, we show the effect of c0, d , aˆ on the supplier’s selling strategy, with the same values of aA, aB, c, and d as in Figure 3 but varying c0 and d . From Figure 1, the optimal supplier’s prices are w IO∗ = 4 for aˆ = 16, w IO∗ = 6 for = OO∗ = ∗ aˆ 18, and w w 1. The two curves in Figure 4 represent the supplier’s indifference curves between selling to two manufacturers and selling only to B when aˆ = 16 and 18, respectively. For the region below each curve, the supplier benefits from selling to two manufacturers (i.e., (O, O)). Above the curve, the supplier is better off selling to B only (i.e., (I, O)). This suggests that, given the new substitutability coefficient, the supplier will prefer two outsourcing manufacturers if the supplier’s unit production cost is relatively small and will favor selling to B only if the supplier’s unit cost is relatively high. On the other hand, given the supplier’s unit production cost, the supplier will prefer selling to both manufacturers when the new substitutability is low and selling to B only when the substitutability becomes higher. Moreover, because the curve for aˆ = 16 is below the one for aˆ = 18, the supplier with better brand is more likely to sell to both manufacturers.

DUOPOLY SUPPLIERS In the previous section, we assume that a single supplier monopolizes the market of the key component. In reality, there are often multiple suppliers that produce substitutable components and compete in price. When there are several competing suppliers, several questions are of interest. Which supplier is most beneficial to the manufacturer that desires outsourcing? How do the wholesale price and the increased commonality affect the manufacturers’ outsourcing decisions? What are the optimal wholesale prices for suppliers? To answer these questions, we extend the monopoly-supplier model to the setting with two competing suppliers and focus on the effect of the wholesale price competition and the asymmetry of the net price cap on manufacturers’ outsourcing decisions. Because of the competition, there is a price-undercutting process between the two suppliers, which is beneficial to the manufacturers. As stated in the economic literature, when two suppliers that produce a homogeneous component with the same unit-production cost engage in a Bertrand pricing competition, the equilibrium prices are equal to the marginal cost. Conse- quently, each supplier earns zero profit. Here, we consider the case in which the two suppliers produce partially differentiated components. When one manufacturer outsources the component to supplier l, the price cap is al,(l = 1, 2). In general, a1 = a2 due to the differentiation of the key component. If a1 > a2, the final product with the component from supplier 1 has better quality or brand. Therefore, the pricing power of the manufacturer purchasing the component from supplier 1 is greater. 94 Strategic Outsourcing Decisions for Manufacturers

Let the unit wholesale price and the unit production cost of the component of supplier l be w l and cl,(l = 1, 2), respectively. The expression (al − cl) represents the total net price cap for supplier l and (al − w l) represents the net price cap for the manufacturer that purchases from supplier l. In this section, we consider two situations by differentiating whether or not the two manufacturers have the capability to produce the key component.

Manufacturers Without Production Capability We ﬁrst consider the situation in which neither manufacturer owns the production capability and must purchase the component from one of the two competing suppliers. The notation Ol is used to represent the strategy to outsource the component to supplier l, where l = 1, 2. The game has the following three stages:

(i) The duopoly suppliers simultaneously decide their component prices w 1 and w 2. (ii) The two manufacturers simultaneously announce the outsourcing strategy O1 or O2.

(iii) The manufacturers decide their production quantities qA and qB simultaneously. As in Table 1, we summarize manufacturers’ optimal quantities under different strategy proﬁles in Table 2. Table 2 shows that the equilibrium quantity for one manufacturer, A, is a decreasing function of manufacturer A’s supplier’s price w 1, but an increasing function of competitor B’s purchase price w 2. The latter suggests that an increase of w 2 causes a portion of demand to be transferred from B to A. Because the equilibrium proﬁt for each manufacturer is equal to the square of the corresponding equilibrium quantity, the normal form of the outsourcing game is equivalent to Table 2. Proposition 3 characterizes the SPEs for the manufacturers.

Table 2: Manufacturers’ optimal quantities under two suppliers.

A B O1 O2 a − w 2(a − w ) − (a − w ) d O q O1 O1 = 1 1 , q O1 O2 = 1 1 2 2 , 1 A 2 + d A 4 − d2 a − w 2(a − w ) − (a − w ) d q O1 O1 = 1 1 q O1 O2 = 2 2 1 1 B 2 + d B 4 − d2 2(a − w ) − (a − w ) d a − w O q O2 O1 = 2 2 1 1 , q O2 O2 = 2 2 , 2 A 4 − d2 A 2 + d 2(a − w ) − (a − w ) d a − w q O2 O1 = 1 1 2 2 q O2 O2 = 2 2 B 4 − d2 B 2 + d

Proposition 3. Given cl ≤ w l < al, l = 1, 2, we have < ≤ ∗ (i) (O1, O1) is an SPE of the outsourcing subgame if d d d4 (w 1, w 2), where − − 2 ∗ , = (a1 w1)(4 d ) − d4 (w1 w2) 2; 2(a2 − w2) − (a1 − w1) d Xiao, Xia, and Zhang 95

< ≤ ∗ (ii) (O2, O2) is an SPE of the outsourcing subgame if d d d5 (w 1, w 2), where − − 2 ∗ , = (a2 w2)(4 d ) − d5 (w1 w2) 2; 2(a1 − w1) − (a2 − w2) d ≥ { ∗ ∗ } (iii) If d max d4 (w 1, w 2), d5 (w 1, w 2) , both (O2, O1) and (O1, O2) are SPEs of the outsourcing subgame. ∗ ∗ In Proposition 3, d4 (w 1, w 2)(d5 (w 1, w 2)) is a substitutability coefficient threshold at which manufacturer A is indifferent between strategies O1 and O2, ∗ given that B selects O1 (O2). It can be shown that d4 (w 1, w 2) is a decreasing ∗ function of the wholesale price w 1 but an increasing function of w 2, while d5 (w 1, w 2) is a decreasing function of w 2 but an increasing function of w 1. Proposition 3 suggests that given B’s strategy O1, A will outsource to supplier 1 only if the substitutability increase is small. When the substitutability increase is significant, A will experience intense competition with B if they both outsource to supplier 1. Anticipating this consequence, A would outsource to supplier 2 to avoid the detrimental competition. A case in point: In the mobile phone industry, High Tech Computer (HTC), a Taiwanese company specializing in designing and manufacturing mobile com- puting and communication products for Cingular, T-Mobile, and Vodafone, com- petes directly with Nokia in the Smartphone market. In the upstream supply chain, Microsoft and Symbian are two main suppliers of software for these devices. Cur- rently, HTC uses only Microsoft’s windows system while Nokia adopts Symbian’s software. HTC’s close relationship with Microsoft limits its ability to develop phones based on the other supplier’s software. However, this limitation actually benefits HTC greatly in that it dramatically differentiates HTC’s products from Nokia’s and there is “little competition for HTC on Microsoft smart devices” (Einhorn, 2006, p. 43). As a result, the company has achieved outstanding profit and stock performance. We also find that the manufacturers will purchase the components from different suppliers to keep the products differentiable so as to maintain their pricing power when the substitutability coefficient d is sufficiently high. Otherwise, they will outsource to the same supplier. In addition, Proposition 3(iii) suggests that besides two pure-strategy SPEs, there is a mixed-strategy SPE, depending on the wholesale prices. Now, we turn our attention to the optimal wholesale prices offered by the suppliers. Suppose the equilibrium is that both manufacturers outsource to a single supplier, for example, supplier 1. Let w 21(w 1) be the solution to equation d = ∗ = − 1 − − d4 (w 1, w 2) with respect to w 2. We can show that w21(w1) a2 2 (a1 w1) d 2 (a1 − w1)(4 − d ) 2(2 + d) , which is an increasing function of w 1 and d . Based on Proposition 3, supplier 2 will offer a lower price to induce one manufacturer to buy from supplier 2. At the equilibrium (Oi, Oj), the optimal wholesale price reaction of supplier 1 is 1 1 w (w ) = (a + c ) − (a − w ) d, (9) 11 2 2 1 1 4 2 2 which is an increasing function of w 2, that is, supplier 1 will undercut if supplier 2 undercuts. 96 Strategic Outsourcing Decisions for Manufacturers

Proposition 4 characterizes the optimal wholesale prices for the two suppliers.

Proposition 4. Assume a1 − c1 > a2 − c2. We have the following results: (i) When supplier 1 can only attract one manufacturer, supplier 1’s optimal ∗ wholesale price is w 11, and the optimal wholesale price for supplier 2 is ∗ > ∗ w 22 if d d4 (w 11(c2), c2), where 2 ∗ 8(a + c ) − 2(a − c ) d − a d w = 1 1 2 2 1 , 11 16 − d2 2 ∗ 8(a + c ) − 2(a − c ) d − a d w = 2 2 1 1 2 . 22 16 − d2 ≤ ∗ Supplier 2 will withdraw from the component market if d d4 (w 11(c2), c2); { ∗ } (ii) In order to attract two manufacturers, supplier 1 will offer max w 12, c1 ∗ ∗ − 2 + + − + − > = a1[4 d d(2 d )] 2(2 d )(a2 c2) if d d4 (w 11(c2), c2), where w12 4 − d2 + d(2 + d) . Supplier 1 can decide its optimal wholesale price by comparing the proﬁts between inducing two manufacturers buying from it and selling to one manufacturer ∗ ∗ π O1 O1 = π O1 O1 ∗ π O2 O1 = π O2 O1 ∗ , ∗ only; that is, comparing ( S1 S1 (w12)) with ( S1 S1 (w11 w22)). Proposition 4 suggests that there exists an undercutting process similar to the Bertrand pricing competition for homogeneous products, even if the upstream ﬁrms produce differentiated products. However, the supplier whose total net price cap (ai − ci) is lower may not cut price to its marginal cost ci due to the change of the product substitutability, which differs from the Bertrand pricing competition for homogeneous products. We illustrate the optimal wholesale prices using a numerical example in = = = ∗∗ Table 3, in which we assume that a2 8, c2 2, and d .5. wl is the optimal wholesale price of supplier l, where l = 1, 2. ((Oi, Oj), i, j = 1, 2, j = i) represents two asymmetric SPEs. Table 3 shows that the commonality between the products has a negative effect that prevents the manufacturers from outsourcing to

Table 3: The optimal wholesale prices and the equilibrium proﬁts of suppliers.

Optimal Wholesale Parameters Thresholds Proﬁts Price Equilibrium

∗ ∗ ∗ π O1 O1 π O2 O1 ∗∗ ∗∗ No. a1 c1 d d4 (w 11(c2), c2) S1 S1 w 1 w 2 SPE

1102.6 −.149 8.658 6.742 3.822 2.000 (O1, O1) 2102.9 −.149 6.036 6.742 5.556 4.444 (Oi, Oj) 3103.6 −.386 3.906 5.005 6.063 4.508 (Oi, Oj) 4103.9 −.386 1.420 5.005 6.063 4.508 (Oi, Oj) 5 14 2 .6 .935 27.668 16.273 7.822 2.000 (O1, O1) 6 14 2 .9 .935 24.497 16.273 7.308 2.000 (O1, O1) 7 14 3 .6 .641 22.915 13.503 7.822 2.000 (O1, O1) 8 14 3 .9 .641 19.882 13.503 7.308 2.000 (O1, O1) Xiao, Xia, and Zhang 97 the same supplier. If the difference in brand or quality between the two suppliers is sufﬁciently large, then the supplier with better brand or quality can monopolize the market. Otherwise, the two suppliers share the market.

Manufacturers with Production Capability Here we consider the situation in which both manufacturers own the production capability, and there are two suppliers in the upstream supply chain. Components from the suppliers are partially substitutable. Now each manufacturer has three strategies: producing in house (I), outsourcing to supplier 1 (O1), and outsourcing to supplier 2 (O2). The stages of the game are the same as those in the above except that in stage 2, a manufacturer can also select strategy I. For simplicity, we assume that the price cap for each manufacturer is a if the manufacturer produces the component in house and al if it outsources the input to supplier l, l = 1, 2. Without loss of generality, we assume a1 − c1 > a2 − c2.Given π II π II that B produces the component internally, the profit for A (B)isøA (øB )ifA also π Ol I π Ol I insources the component. The profit for A (B)isøA (øB )ifA outsources the component to supplier l, l = 1, 2. Similarly, we can define notations for situations where A produces the input internally. Similar to the development of the first two models, we can derive ordering quantities for the two manufacturers (for the sake of brevity, these equations are not provided here). Proposition 5 characterizes the SPEs of the two manufacturers and the suppliers’ optimal wholesale prices.

Proposition 5. Assume that a1 − c1 > a2 − c2 and aA = aB = a. When the two manufacturers own the production capability for the component, we have

(i) (I , I ) is a unique SPE of the outsourcing subgame if a − c ≥ a1 − c1;

(ii) If a1 − c1 > a − c ≥ a2 − c2, supplier 2 will withdraw from the component market, and supplier 1 will become a monopoly supplier. The SPEs are then given by Proposition 1;

(iii) If a − c < a2 − c2, the optimal wholesale price for supplier l satisﬁes ≤ ∗ < − + cl wl al a c such that two manufacturers have an incentive to outsource, and the SPEs are given by Proposition 3.

Proposition 5 shows that the manufacturers will produce the component in house if their net price caps are higher than those under outsourcing. When Sup- plier 2’s brand effect is not higher than its outsourcing effect (i.e., c2 − c ≥ a2 − a), supplier 2 would withdraw from the component market because neither manufacturer purchases its input. Thus, the model becomes the one with the monopoly supplier. Otherwise, the model becomes the duopoly-supplier model in which the two manufacturers do not own the production capability and the two suppliers have a price undercutting process. When the two suppliers have the same effect of brand and outsourcing (i.e., c2 − c1 = a2 − a1), they would cut their wholesale prices to their marginal costs, which is consistent with the result in the Bertrand pricing competition for homogeneous products. 98 Strategic Outsourcing Decisions for Manufacturers

NUMERICAL EXAMPLES In the theoretical analysis above, we assume that the manufacturers have the same new price caps when they outsource the key component to the supplier (aˆ A = aˆ B ). If aˆ A = aˆ B , it is intuitive that when the price cap of a supplier increases, the manufacturer(s) will be more likely to outsource, and the supplier can charge a higher wholesale price. Although we can develop analytical results, the mathematics will become complex. Therefore, for the sake of brevity, we use numerical examples for illustration. Example 1 illustrates the case of one supplier while example 2 considers two suppliers. Note that, given the values of aˆi (i = A, B) and the other parameters, Table 1 becomes a matrix with speciﬁc numbers. Thus, given a wholesale price, we can easily obtain the Nash equilibrium for the outsourcing game in Table 1. Example 1. Consider the monopoly supplier model in which two manufacturers own the production capability of the input. The parameters are given as follows:

aA = 10, aB = 8, aˆ B = 12, c0 = 4, c = 5, and d = .5. The profits of manufacturers A, B, and the supplier at the SPE are denoted by π ∗ π ∗ π ∗ A(w), B (w), and S(w), respectively. Table 4 lists the SPE of the outsourcing subgame and the profits of the members of the supply chain given the wholesale prices. Table 4 also shows the effect of the price on the outsourcing decisions of the manufacturers. We observe from Table 4 that the wholesale price and the difference between aˆ A and aˆ B affect the outsourcing decisions for the manufacturers and their profits. When the wholesale price is low, both manufacturers are likely to outsource. When they outsource, the larger the increased substitutability coefficient is, the lower the profit will be for the members in the supply chain. On the other hand, when the wholesale price is sufficiently large, insourcing is a better choice. In addition, when

Table 4: Numerical results for monopoly supplier given wholesale prices.

Given Values Equilibrium Proﬁts at the Equilibrium π ∗ π ∗ π ∗ No. aˆ A wd SPE A(w) B (w) S(w) 1 12 6.5 .6 (O, O) 4.475 4.475 10.577 2 12 6.5 .9 (I , O) 3.738 5.138 5.667 3 12 8.5 .6 (I , O) 4.840 1.440 5.400 4 12 8.5 .9 (I , O) 4.840 1.440 5.400 5 13 6.5 .6 (O, O) 7.101 3.805 11.539 6 13 6.5 .9 (O, O) 6.368 2.606 10.345 7 13 9.5 .6 (I , I ) 5.138 .871 .000 8 13 9.5 .9 (I , I ) 5.138 .871 .000 9 16 8.5 .6 (O, O) 12.803 .715 19.039 10 16 8.5 .9 (O, I ) 12.960 .360 16.200 11 16 9.5 .6 (O, I ) 9.404 .538 16.867 12 16 9.5 .9 (O, I ) 9.404 .538 16.867 Xiao, Xia, and Zhang 99

Table 5: Numerical results for duopoly suppliers given wholesale prices.

Given Values Equilibrium Proﬁts at the Equilibrium π ∗ π ∗ π ∗ No. d w 1 w 2 SPE A S1(w 1, w 2) S2(w 1, w 2)

1 .6 5 3.5 (O1, O1) 3.698 7.692 .000 2 .6 5 5.5 (O1, O1) 3.698 7.692 .000 3 .6 7 3.5 (O2, O2) 2.996 .000 5.192 4 .6 7 5.5 (O1, O1) 1.331 9.231 .000 ∗ 5 .9 5 3.5 (Oi, O j ) 3.638 4.133 2.600 6 .9 5 5.5 (O1, O1) 2.973 6.897 .000 7 .9 7 3.5 (O2, O2) 2.408 .000 4.655 8 .9 7 5.5 (O1, O1) 1.070 8.276 .000

Note: (Oi, Oj), i, j = 1, 2, j = i;“∗” represents the mean at two equilibriums.

the increase of substitutability coefficient is significant, the two manufacturers are more inclined to produce the components in house. Comparing rows 3 and 4 with rows 7 and 8, we find that when the net price cap of manufacturer A is fixed, the supplier can induce B to outsource by lowering price. Example 2. Consider the duopoly-supplier model where the manufacturers do not own the production capability for the key component. We use the following values of the parameters: a1 = 10, a2 = 8, c1 = 3, c2 = 2, and d = .5. Given the value of d, the magnitude of d reflects the increased substitutability when the key component is produced by the same supplier. Table 5 illustrates the effect of the substitutability coefficient and the wholesale prices on the outsourcing strategies of the manufacturers as well as the suppliers’ profits. For the optimal π ∗ wholesale prices, one can refer to Table 3. Table 5 only gives the SPE profit A of manufacturer A because the two manufacturers are symmetric. The expression π ∗ Sl(w 1, w 2) represents the profit of supplier l at the SPE. From Table 5, we observe that, as the substitutability coefficient increases, the two manufacturers are likely to outsource to different suppliers to avoid direct competition. Table 5 also shows the price-cutting process of the two manufacturers. For example, in rows 7 and 8, when the equilibrium is (O1, O1), supplier 2 can reduce price to induce both manufacturers to purchase its component. Similarly, we can explain the undercutting process from the results in rows 3 and 4.

CONCLUSIONS When different manufacturers with partially substitutable products use the same supplier for the key components, the final products become more substitutable. In this article, we have explicitly modeled this change of substitutability when the manufacturers make their outsourcing decisions. We also considered the brand/quality effect resulting from outsourcing to a reputable supplier to reflect consumer’s perception about final products made by different firms. While we focused on two competing manufacturers in the downstream channel, we have 100 Strategic Outsourcing Decisions for Manufacturers examined the situation in which there is one supplier in the upstream industry as well as the one in which two suppliers compete with each other. Our analysis provides several managerial insights for both manufacturers and suppliers. From the manufacturer’s point of view, to decide whether to outsource, a manufacturer must consider not only the supplier’s production cost and brand effect, but also the increased product substitutability if a competitor outsources to the same supplier. In general, the manufacturers are better off outsourcing to the outside supplier(s) when the increased substitutability is relatively small and/or the brand/quality effect is relatively high. Otherwise, they should keep the production in house. In some circumstances, even if outsourcing can benefit the manufacturer because of the supplier’s better quality and lower cost, the benefit might not offset the intense competition that results from outsourcing. Thus, it might still be better to keep the component production in house. From the supplier’s perspective, suppliers can use the price as a mechanism to affect manufacturers’ outsourcing decisions. If a supplier is in a monopoly position in the industry, its best strategy is to sell its products to either one or both manufacturers. In order to induce both manufacturers to outsource, the supplier must offer a lower price. Therefore, the supplier faces a trade-off between the demand volume and the price it charges in searching for its best strategy. When facing competition, the supplier has to lower its wholesale price to attract the manufacturer(s) to outsource even if the supplier’s products are differentiated from its competitor’s. If one supplier has a significant cost advantage, it is possible to drive its competitor out of the market by undercutting the price. This article addresses the question of when manufacturers should outsource their key components. Questions remain, however, regarding how to measure the change in product substitutability and consumer perception about the final products after outsourcing. One approach is to seek consumers’ opinions through survey- based research. Our work can also be extended in several other ways. In reality, one manufacturer might invest to improve the brand and quality of its product as a strategy to monopolize the market. Thus, the manufacturer would be interested in iden- tifying the conditions that would drive other manufacturers out of the market. In this article, we have assumed that the supplier(s) has the pricing power for the component. One may use an auction mechanism to acquire the component. In addition, we have considered the situation in which the required information is complete and available to all parties. It would be valuable to examine the effect of incomplete information between the two manufacturers or between the manufacturers and the supplier(s) on the outsourcing decision. Finally, we can extend our model that considers the substitutability change and the brand/quality effect by incorporating the cost reduction opportunity as discussed in Gilbert et al. (2006). [Received: January 2006. Accepted: November 2006.]

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APPENDIX Proof of Proposition 1. Part (i) When manufacturer A chooses strategy I, π II ≥ π IO − ≥ − B B (w) if and only if aB c aˆ w. Thus, B chooses I if its brand effect does not outweigh its outsourcing effect. Similarly, A chooses I if and only if aA − c ≥ aˆ − w. Hence, the strategy proﬁle (I, I) is an SPE of the outsourcing subgame if the brand effect does not outweigh the outsourcing effect for each manufacturer; that is, aˆ − w ≤ min{aA − c, aB − c}. π IO − π OO IO − Part (ii) The sign of ( A (w) A (w)) is the same as that of (qA (w) OO IO OO π mn = mn 2 qA (w)) because both qA (w) and qA (w) are positive and i (qi ) . Let

2(a − c) − (aˆ − w) d aˆ − w f (d ) = qIO(w) − qOO(w) = A − . 1 A A 4 − d2 2 + d From aˆ > w, it follows that f 1(d ) is an increasing function of the substitutability coefficient d . The solution of equation ( f 1(d ) = 0) is ∗ = − − 2 / − − − − . d1 (w) (aˆ w)(4 d ) [2(aA c) (aˆ w) d] 2 (A1) Furthermore, when B outsources the key component, A will outsource if d < d < ∗ > ∗ d1 (w) and produce in house if d d1 (w). With A choosing strategy O, we can similarly derive a substitutability coefficient threshold for B, ∗ = − − 2 / − − − − , d2 (w) (aˆ w)(4 d ) [2(aB c) (aˆ w) d] 2 (A2) at which B is indifferent between strategies O and I. Manufacturer B can make a < < ∗ larger profit by outsourcing if d d d2 (w). Otherwise, B earns more profit by < ≤ { ∗ producing in house. Thus, (O, O) is an SPE if and only if d d min d1 (w), ∗ } d2 (w) . Parts (iii) and (iv) can be proved similarly as Parts (i) and (ii). Xiao, Xia, and Zhang 103

OO > OI ≥ IO OO ≤ ∗ Proof of Proposition 2. From w w w and w w 1, it follows that the optimal wholesale price of the supplier is w OO because the supplier can sell more products to two manufacturers than to only one manufacturer. OI ≤ ∗ < OO If w w 1 w , it is obvious that the supplier prefers selling to two ∗ manufacturers by offering a wholesale price w 1 to selling only to manufacturer A, from which the supplier can obtain a higher demand. Thus, we only need to consider OI > ∗ OO > OI > ∗ ∗ the case with w w 1. From (w w w 1(d )), (w 1(d ) is a decreasing function of d and the concavity of the π OO(w), it follows that S ∗ ∗ ∗ dπ OO w (d ), d ∂πOO w , d dw ∗(d) ∂πOO w , d S 1 = S 1 1 + S 1 < 0. (A3) dd ∂w dd ∂d π OO ∗ ≥ π OO ∗ Thus, we have S (w 1(d ), d ) S (w 1(1), 1). OI From w ≤ aˆ + c − aA, it follows that (aB − c) d ≥ 4(aA − c) − 2(aˆ − c0). Furthermore, the proﬁts of the supplier at equilibriums (O, O) and (O, I ) are

6(a − c) − ˆ − − A 4(aA c) a c0 2 ∗ 4 + 3d − d π OO w (1), 1 = , S 1 4 + 3d − d2 and

[2(aˆ − c ) − (a − c) d]2 π OI(w OI) = 0 B , S 8(4 − d2) respectively. π OO ∗ >πOI OI OI ≤ + − We show S (w 1(1), 1) S (w ) when w aˆ c aA in two cases: Case (i) with aˆ − c0 ≤ 2(aA − c) and Case (ii) with aˆ − c0 > 2(aA − c). Case (i) From (aB − c) d ≥ 4(aA − c) − 2(aˆ − c0) ≥ 0, it follows that 2[(aˆ − c ) − (a − c)]2 π OI(w OI) ≤ 0 A . S 4 − d2 Let 2 2 Dπ1(aˆ − c0) = 2(4 − d )(aA − c)[(aˆ − c0)(4 + 3d − d ) − 6(aA − c)] 2 2 2 − (4 + 3d − d ) [(aˆ − c0) − (aA − c)] .

π OO ∗ >πOI OI π > From the above, we know that S (w 1(1), 1) S (w ) is equivalent to D 1 0. Differentiating Dπ 1 with respect to (aˆ − c0), we have

dDπ1

d(aˆ − c0) 2 2 2 =−2(4 + 3d − d )[(aˆ − c0)(4 + 3d − d ) − (aA − c)(8 + 3d − 2d )].

From ((aB − c) d ≥ 4(aA − c) − 2(aˆ − c0) ≥ 0), (aA ≥ aB) and (0 < d < 1), it follows that 2 (aˆ − c0)(4 + 3d − d ) 1 ≥ (4 − d)(4 + 3d − d2)(a − c) ≥ (8 + 3d − 2d2)(a − c), 2 A A 104 Strategic Outsourcing Decisions for Manufacturers

which implies that Dπ1(aˆ − c0) is a decreasing function of (aˆ − c0). Furthermore, it follows from (aˆ − c0 ≤ 2(aA − c)) that 2 2 Dπ1(aˆ − c0) ≥ Dπ1(2(aA − c)) = 3d(1 − d)(8 + d − d )(aA − c) > 0. ∗ − − > − > − 3(aˆ c0) Case (ii) From (aˆ c0 2(aA c)), it follows that w1 (1) aˆ 4 + 3d − d2 . OO ≥ ∗ π OO Furthermore, from (w w 1(1)) and the concavity of S (w), we have 2 2 ∗ 2(aˆ − c ) (1 + 3d − d ) π OO(w (1), 1) > 0 . 1 (4 + 3d − d2)2 2 2 2 2 2 Let Dπ2(aˆ − c0) = 16(aˆ − c0) (4 − d )(1 + 3d − d ) − (4 + 3d − d ) [2(aˆ − 2 c0) − (aB − c) d] . Differentiating Dπ 2 with respect to (aˆ − c0), we have π dD 2 2 2 2 = 4d[(aB − c)(4 + 3d − d ) + 6(aˆ − c0)(1 − d)(8 + d − d )] > 0. d(aˆ − c0)

Furthermore, from (aˆ − c0 > 2(aA − c)) and (aA ≥ aB), we have

Dπ2(aˆ − c0) > Dπ2(2(aB − c)) 2 2 3 4 5 = (aB − c) d(512 − 160d − 112d − d + 14d − d ) > 0. π OI OI >πOI ∗ ∗ < OI < ∗ Note that S (w ) S (w 2) when w 1 w w 2. Thus, summarizing the above, π OO ∗ >πOI OI∗ OI ≤ + − OI∗ we know that S (w 1(d ), d ) S (w ) when w aˆ c aA, where w is the optimal wholesale price of the supplier at equilibrium (O, I ). In other words, only selling to A is not an optimal choice for the supplier because the supplier can gain a higher proﬁt from selling to two manufacturers. According to the above, the supplier sells either to two manufacturers or only to manufacturer B. Now, we seek for a threshold of the substitutability coefﬁcient at which the supplier is indifferent between selling to two manufacturers and only ∗ π OO ∗ = π IO IO IO ≤ to B. Let d3 be the root of equation S (w 1(d ), d ) S (w ) when w aˆ + c − aB .Wehave

2 2 2 IO 2 IO ∗ −B + B − 4d (4 − d )π [(4 − d )π − 4(aˆ − c )(a − c)] d = 0 A − 2, 3 2d2π IO = { − 2 π IO IO + − − − − }≥ where B 2 d(4 d ) S (w ) 2(aA c)[2(aA c) (aˆ c0) d] 0 and the negative root is removed. Thus, the proposition follows from (A3) and Figure 1.

Proof of Proposition 3. Because the proof of parts (i) and (ii) is similar to the proof of Proposition 1, we only prove Part (iii) here. Similar to the proof of Part (ii) of Proposition 1, we can show that if B selects O1, there exists a substitutability ∗ coefﬁcient threshold d4 (w 1, w 2) such that A is indifferent between strategies O1 ∗ − − 2 , = (a1 w1)(4 d ) − and O2, where d4 (w1 w2) 2(a − w ) − (a − w ) d 2. < 2 <2 ∗ 1 1 > ∗ A will select O1 if d d d4 (w 1, w 2) and O2 if d d4 (w 1, w 2). Given B’s strategy O2, there exists a threshold for the substitutability coefﬁcient ∗ − − 2 , = (a2 w2)(4 d ) − d5 (w1 w2) 2(a − w ) − (a − w ) d 2 such that A is indifferent between strategies 1 1 2 2 < < ∗ > ∗ O1 and O2. A will select O2 if d d d5 (w 1, w 2) and O1 if d d5 (w 1, w 2). Xiao, Xia, and Zhang 105

> ∗ Thus, given B’s strategy O1, A prefers strategy O2 if d d4 (w 1, w 2); given B’s > ∗ strategy O2, A prefers strategy O1 if d d5 (w 1, w 2). From the symmetry of the game, Part (iii) follows.

Proof of Proposition 4. Because a1 − c1 > a2 − c2, there exists w 1 such that − > − ∗ < < ∗ a1 w 1 a2 c2 which implies d5 (w 1, c2) d d4 (w 1, c2). Supplier 1 gets zero profit when the equilibrium (O2, O2) is selected by the manufacturers. In order to gain a positive profit, supplier 1 can always cut its price to attract manufacturer(s) because a1 − c1 > a2 − c2. Thus, the strategy profile (O2, O2) is not an equilibrium. Part (i) Without loss of generality, we assume that the equilibrium (O1, O1) is selected by both manufacturers. Thus, supplier 2 will gain zero profit because neither manufacturer purchases supplier 2’s input. In order to gain a positive profit, supplier 2 will undercut until at least one manufacturer buys supplier 2’s input. ∗ According to the proof of Proposition 3, we know that d4 (w 1, w 2) will decrease ∗ and d5 (w 1, w 2) will increase as supplier 2 undercuts. When supplier 2 fiercely cuts price such that both manufacturers buy the key component from supplier 2, supplier 1 will have a similar undercutting process. Hence, we only need to consider the case in which supplier 2 cuts a proper price such that one manufacturer prefers outsourcing the key component to supplier 2; that is, (Oi, Oj) is an SPE of the outsourcing subgame. ∗ According to the proof of Proposition 3, we know that d4 (w 1, w 2)isa decreasing function of the wholesale price w 1 but an increasing function of w 2. Furthermore, it follows from equation (9) that dd (w (w ), w ) ∂d∗(w (w ), w ) dw (w ) ∂d∗(w (w ), w ) 4 11 2 2 = 4 11 2 2 11 2 + 4 11 2 2 > 0, dw2 ∂w1 dw2 ∂w2 that is, the lower the wholesale price w 2, the lower the substitutability coefficient ∗ threshold d4 (w 11(w 2), w 2). Thus, neither manufacturer prefers buying the key < ∗ component from supplier 2 if d d4 (w 11(c2), c2). Supplier 2 will withdraw from ≤ ∗ the component market if d d4 (w 11(c2), c2). Supplier 2 will determine an optimal > > ∗ wholesale price w 2 c2 to attract the manufacturer(s) if d d4 (w 11(c2), c2). At the equilibrium (Oi, Oj), the profit function of supplier 2 is 2(a − w ) − (a − w ) d π Oi O j (w , w ) = (w − c ) 2 2 1 1 . (A4) S2 1 2 2 2 4 − d2 π Oi O j , The optimal solution of S2 (w1 w2) with respect to w 2 is 1 1 w (w ) = (a + c ) − (a − w ) d > c , (A5) 22 1 2 2 2 4 1 1 2 which is an increasing function of w 1, that is, supplier 2 will undercut if supplier 1 undercuts. From (9) and (A5), the equilibrium wholesale prices of suppliers are 2 ∗ 8(a + c ) − 2(a − c ) d − a d w = 1 1 2 2 1 , 11 16 − d2

2 ∗ 8(a + c ) − 2(a − c ) d − a d w = 2 2 1 1 2 . 22 16 − d2 106 Strategic Outsourcing Decisions for Manufacturers

At this equilibrium, only one manufacturer buys the key component from supplier 1. Thus, it may further lower supplier 1’s wholesale price to attract two manufacturers. Part (ii) Now we see whether supplier 1 would like to further lower the price to induce the equilibrium (O1, O1). At this equilibrium, the proﬁt function of supplier 1 is 2(w − c )(a − w ) π O1 O1 (w ) = 1 1 1 1 , (A6) S1 1 2 + d

O1 O1 = + / and the optimal wholesale price of supplier 1 is w1 (a1 c1) 2. Because O1 O1 > ∗ w1 w11, supplier 2 can offer a wholesale price to induce one manufacturer to O1 O1 buy supplier 2’s input if supplier 1 offers w1 . Thus, supplier 2 will cut the price ∗ < < ∗ until its unit cost is c2. Note that d5 (w 1, c2) d d4 (w 1, c2). The root of equation ∗ ∗ − 2 + + − + − = = a1[4 d d(2 d )] 2(2 d )(a2 c2) (d d4 (w 1, c2)) is w12 4 − d2 + d(2 + d) , at which A is indifferent between strategies O1 and O2, given supplier 2 offering c2 and B’s strategy being { ∗ } O1. From Proposition 3, supplier 1 will offer max w 12, c1 to induce the two manufacturers to buy supplier 1’s input.

Tiaojun Xiao is an associate professor in the School of Management Science and Engineering, Nanjing University, China. He received his Master’s degree from Central South University of Technology and his PhD from Southeast University, China. He is an elected member of the International Statistical Institute, a member of the International Society for Business and Industrial Statistics, and secretary of Sino-German Center for Research into Evolutionary Economics and Chinese Economic Development. His research interests include applied game theory, evolutionary management theory, supply chain disruption and risk management, and supply chain coordination. He has published numerous journal articles and two books.

Yusen Xia is an assistant professor in the Department of Managerial Sciences of the Robinson College of Business, Georgia State University. He received his PhD from the McCombs School of Business at the University of Texas at Austin. His publications have appeared in Operations Research, IIE Transactions, Naval Re- search Logistics, Annals of Operations Research, European Journal of Operational Research, and others. Currently, his research interests lie in the interfaces between operations and marketing and managing uncertainties and risks in supply chains.

G. Peter Zhang is an associate professor in the Department of Managerial Sciences at Georgia State University. His research interests include neural networks, forecasting, and supply chain management. He currently serves as an associate editor of Neurocomputing and Forecasting Letters and is on the editorial review board of Production and Operations Management and International Journal of E-Business Research. He is the editor of the book, Neural Networks in Business Forecasting (Hershey, PA: IRM Press, 2004). His research has appeared in European Journal of Operational Research, IIE Transactions, IEEE Transactions on Neural Networks, IEEE Transactions on SMC, International Journal of Forecasting, Journal of the Operational Research Society, Neurocomputing, and others.