Strategic Second Sourcing by Multinationals. Jay Pil Choi and Carl Davidson Michigan State University March 2002

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1 trategic econd ourcing by Multinationals Jay Pil Choi and Carl Davidson Michigan tate University March 2002 Abstract: Multinationals often serve foreign arkets by producing doestically and exporting as well as by investing directly in foreign production facilities. We argue that if the ultinational copetes in an oligopolistic arket characterized by strategic copleents then there are strategic reasons to use two production facilities -- precoitting to a second source allows the fir to keep average cost low while at the sae tie increasing its arginal cost. The increase in arginal cost softens product arket copetition resulting in higher profits. In our odel, firs can sink capacity doestically, where the constant arginal cost is known, sink capacity in the foreign country, where the constant arginal cost is uncertain, or do both. In the absence of strategic considerations, the fir usually chooses to either export or use foreign direct investent -- it rarely uses both sources of production. In contrast, price copetition in the product arket akes it uch ore likely that the fir will choose to use a second source. In fact, there are cases in which the fir sinks capacity in both locations even in the absence of cost uncertainty. We argue that this theory also has iplications for the ake or buy literature in production anageent and the literature on second sourcing in industrial organization. Finally, we show that the practice of second sourcing has iplications for the degree of exchange rate pass through when the uncertainty about foreign costs is driven by fluctuations in the exchange rate. JEL Codes: F1, L1 Keywords: Multinationals, econd ourcing, Foreign Direct Investent.

2 I. Introduction Multinational enterprises doinate any international arkets and account for a significant portion of the international trade between developed countries. 1 As a result, large literatures, both epirical and analytical, have developed aied at explaining the behavior of such firs. While there are any stylized facts that have been uncovered, two are particularly relevant for what follows. First, there is evidence that exports and foreign direct investent () are copleentary any ultinationals do both. econd, there are any industries in which two-way between developed countries is prevalent. 2 While any of the analytic odels of ultinationals are consistent with ost of the other stylized facts, they cannot provide explanations for these two phenoena. In any odels, firs choose between exporting and. is attractive because it allows the fir to avoid transportation costs and tariffs, but it is costly because it requires the fir to build a new production facility. Thus, involves a trade-off between high fixed costs and low variable costs. In such odels, if the fir chooses to build a foreign production facility, it stops exporting and exports are substitutes. 3 Kogut and Kulatilaka (1994) and Rob and Vettas (2001) have provided odels in which ultinationals use both exporting and to serve foreign arkets. In Kogut and Kulatilaka s odel, the fir faces cost uncertainty and therefore setting up a foreign production facility provides it with an option value if costs turn out to be unexpectedly 1 In 1990 ultinationals accounted for over 75% of the total U.. trade in erchandise. Data fro 1999 reveals that over 60% of ultinational trade can be traced to a sall set of developed countries and that 70% of their foreign direct investent is hosted by industrial countries (Caves, Frankel, and Jones 2002, p ) 2 ee Caves (1982) or Markusen (1995) for a survey of the stylized facts concerning ultinationals. Evidence on the copleentary nature of exporting and can be founding Blostro, Lipsey and Kulchycky (1988), Blonigen (2001), and Denekap and Farrantino (1992), and Head and Ries (2001). Evidence on two-way can be found in Julius (1990) and Brainard (1997b). 3 ee, for exaple, Caves (1971), Buckley and Casson (1981), ith (1987), and Horstan and Markusen (1987, 1996). 2

3 high in one plant the fir can shift production to its low cost alternative. In Rob and Vettas odel there is uncertainty about deand growth in the foreign arket. The ultinational begins by exporting when deand is low. Eventually deand becoes large enough to justify. However, the cobination of deand uncertainty and the irreversibility of investent akes it optial to continue exporting even after building a foreign production facility. The reason is siple if the fir builds a foreign facility large enough to handle all of its expected foreign deand it runs the risk of winding up with excess capacity if deand turns out to be unexpectedly low. Producing soe of its output at hoe and exporting it to the foreign arket allows the fir to circuvent such risk. This arguent, while copelling, does not provide an explanation of why ultinationals would eploy such a strategy in a ature arket nor does it explain why we observe two-way in so any industries. In this paper we provide a new explanation for the practice of producing output both at hoe and abroad. We argue that this practice, which we refer to as second sourcing, and two-way both arise naturally in oligopolistic arkets characterized by strategic copleents. In particular, we show that if the ultinationals are engaged in this type of copetition there are strategic reasons to use two production facilities -- precoitting to a second source allows each fir to keep average cost low while at the sae tie increasing arginal cost. The increase in arginal cost softens product arket copetition resulting in higher profits. In our odel, the fir can sink capacity doestically, where the constant arginal cost is known, sink capacity in the foreign country, where the constant arginal cost is uncertain, or do both. Then, after the capacity decision has been ade and the 3

4 uncertainty has been resolved, the fir selects its price. In the absence of strategic considerations (i.e., if the fir is a onopolist), the fir usually chooses to either export or use foreign direct investent -- it rarely uses both sources of production. In contrast, if the fir faces price copetition in the product arket, then it is uch ore likely to use a second source. By second sourcing, the fir can produce the bulk of its output in its low-cost facility (the doestic plant if foreign costs are high and the foreign plant if foreign costs are low) and the residual in the high-cost facility. This allows the fir to produce at low average cost while keeping its arginal cost high. The high arginal cost is desirable because it allows the fir to credibly coit to charging a high price; and, since best-reply functions are upward sloping in price gaes, this leads its copetitor to also charge a high price. As a result, the fir increases its profits above the level that it would earn using a single production facility. In fact, this strategic effect is so strong that there are cases in which the fir sinks capacity in both locations even in the absence of cost uncertainty. 4 Farrell and Gallini (1988) and hepard (1987) also provide strategic odels of second sourcing in which the role of second sourcing is to serve as a echanis to protect buyers interests against the onopolistic supplier s ex post opportunistic behavior. 5 More specifically, in their odels buyers need to ake relationship-specific investent in an ongoing relationship with a onopolistic supplier, which creates a 4 Our logic is siilar to that in Kreps and cheinkan (1983) who show that capacity precoittent can be used to soften price copetition in oligopolistic arkets. We generalize their arguent to a setting in which the fir has two potential production facilities and faces cost uncertainty. 5 There is also an extensive literature on second sourcing in the context of procureent such as Anton and Yao (1987), Desky, appington, and piller (1987), and Laffont and Tirole (1988). These odels ephasize the role of second source to discipline an incubent with private cost inforation. Riordan and appington (1989), however, argue that the benefits of second sourcing are often of liited value and in any instances sole sourcing is preferred when linkages with earlier stages of procureent (R&D activities at the developent stage) are considered. In contrast to Farrell and Gallini (1988) and hepard (1987), these odels analyze second sourcing incentives for a onopsonist. 4

5 dynaic consistency proble; the onopolist cannot coit to low future prices/higher qualities once the buyers have incurred the costs of investent. econd sourcing through licensing induces ex post copetition and allows the supplying firs to ake a low price/high quality coitent that would not be credible with single sourcing. Our odel differs fro Farrell and Gallini (1988) and hepard (1987) in two ajor respects. First, the strategic considerations in our odel are horizontal in that the otives for second sourcing ste fro oligopolistic copetition with a rival supplier whereas they consider the strategic otives for second sourcing in a vertical relationship between buyers and sellers. econd, in their odel second sourcing a coitent to a low price whereas in our odel it serves as a coitent to a high price to invite softer copetition fro the rival fir. The paper divides into four additional sections. In section II, we introduce our odel and solve for the fir s optial investent strategy in the absence of strategic considerations. We also show that the fir s choice of its production ethod has iportant iplications for the degree of exchange rate pass-through when the cost uncertainty is driven by fluctuations in the exchange rate. In section III, we show that price copetition in the product arket akes it ore likely that the fir will choose to second source. Moreover, in section IV, we show that in a duopoly it is often in the interest of both firs to sink capacity in both at hoe and abroad so that we would expect to observe two-way in such industries. Finally, we close the paper in section four where we argue that this theory has iplications for literature on voluntary export restraints, the ake or buy literature in production anageent and the second sourcing literature in industrial organization. 5

6 II. The Monopoly Model of econd ourcing Consider a onopolistic supplier of a good that serves a foreign arket with the deand curve of D(p). We develop the onopoly odel as a benchark to highlight the iportance of strategic otives of second sourcing. There are three alternative ways of serving the foreign arket for the onopolist. It can choose to export, use foreign direct investent, or adopt both odes of operation which we call second sourcing. If the fir is engaged in doestic production and exports to the foreign country, the arginal production cost is assued to be constant at c. If the fir is engaged in foreign direct investent, there is cost uncertainty. The constant arginal production cost can be either at c or c, with Pr ( c ) = α, where c < c < c. 6 Let p ( denote the onopoly price when arginal cost is c, that is, p ( = arg ax (p D(p) and let q ( and π ( represent the corresponding output and profit levels. More iportantly, we assue that the fir needs to sink capacity in advance for production wherever it chooses to produce. To avoid the coplex proble of optial capacity choice and the possibility of ixed strategy equilibria with rationing, we further assue that there is soe lupiness in capacity; investent in capacity is indivisible. 7 More specifically, there are two levels of capacity to choose, large and sall. The costs for installing the large capacity and sall capacity are given by F and F, respectively, 6 The uncertainty associated with foreign production can be linked to a variety of factors. For exaple, in the anageent literature it has been stressed that the anageent of foreign operations is ade difficult by differences in culture and labor relations (see, for exaple, Hyer 1960). As a result, the cost of anaging foreign operations ay be uncertain and higher than the cost of anaging doestic operations. If foreign labor is cheaper, this gives rise to a setting in which the uncertain foreign arginal cost ay be either higher or lower than the certain doestic arginal cost. Other factors that ay influence the uncertainty associated with foreign production include fluctuations in the exchange rate, uncertainty about governent policies towards and the rate at which technologies are introduced in soe parts of the world. 7 J.. Bain s (1954, 1956) pioneering study of the structure of U.. industry identified scale econoies at the plant level that are substantial in any industries. For recent epirical evidence of the relevance of lupy investent see Dos and Dunne (1998). 6

7 with F 2F. With the large capacity, the fir can produce up to the arket deand regardless of its cost realizations. With the sall capacity, the fir can supply up to k, where D(p ()/2 < k < D(p ( c )). This iplies that the sall capacity (k) alone is not sufficient to eet the deand even at the price of p ( c ) whereas the capacity with two sall plants (2k) is sufficiently large to eet any relevant deand. Now we can copare the fir s optial sourcing decision. If the fir serves the arket with only exports, its profit is given by: 8 EX (1) Π = π ( F The fir s expected payoff fro serving the arket with foreign direct investent is given by: (2) Π (α) = [απ ( c ) + (1 α)π ( c )] F Notice that Π (α) is linear in α with a slope of π ( π ( > 0 (see Figure 1). EX EX Taken together with the fact that Π (0) < Π and Π (1) > Π, we can establish EX that there is a critical value α* such that Π (α) Π if and only if α α*, where α* = π π ( π ( π (. ( Finally, the fir can use second sourcing by sinking sall capacity in both doestic and foreign countries. In this case, the division of total production between the 8 With the assuption of F 2F, the choice of the large capacity is always optial when the fir exports or uses foreign direct investent. 7

8 two plants depends on the cost realization in the foreign country. If arginal cost in the foreign country is low, the whole capacity in the foreign country will be exhausted first, and the rest of the deand will be et with production in the doestic country. If arginal cost in the foreign country is high, the pattern of production is reversed; that is, the capacity in the doestic country will be exhausted and the residual deand will be et with production in the foreign country. This iplies that if arginal cost in the foreign country is low, the last unit is produced doestically, the relevant arginal cost is c and the profit-axiizing price is p (. In contrast, if arginal cost in the foreign country is high, the last unit is produced in the plant located in the foreign country, the relevant arginal cost is c and the profit-axiizing price is p ( c ). The expected payoffs fro second sourcing thus can be written as: (3) Π (α) = α[π ( + (c c )k] + (1 α)[π ( c ) + ( c k] 2 F Lea 1. π ( + (c c )k < π ( c ) and π ( c )+ ( c k < π (. Proof. π ( c ) = [p ( c ) c ]D(p ( c )) [p ( c ]D(p () = [p ( c]d(p () + (c c )D(p () > π ( + (c c )k The last inequality follows due to our assuption that k < D(p ( c ) )< D(p (). iilarly, π ( = [p ( c]d(p () [p ( c ) c]d(p ( c )) = [p ( c ) c ]D(p ( c )) + ( c D(p ( c )) > π ( c ) + ( c k # 8

9 EX Lea 1 iplies that Π (0) < Π and Π (1) < Π (1); without cost uncertainty, second sourcing is always doinated by one of the two alternative ode of operation. By continuity, second sourcing is also doinated by exporting for sall values of α and doinated by foreign direct investent for values of α close to 1. We now investigate whether second sourcing can be the preferred ethod of operation for interediate values of α. Intuitively, we would expect this to be the case. As we have just shown, for low values of α the fir is effectively choosing between exporting and second sourcing. econd sourcing involves risk, but ay result in a lower average cost. ince the fir s profit function is convex in costs, it generally prefers the ore risky production ethod. However, for very low values of α second sourcing entails a higher expected average cost than exporting. Thus, the fir chooses to export. As α increases, the expected average cost associated with second sourcing falls and it should eventually doinate exporting. Now, consider the case in which α is high, where the fir chooses between and second sourcing. In this case, is the riskier production ethod and will be preferred if the expected average cost fro and second sourcing are siilar. However, as α falls, the expected average cost associated with rises faster than the expected average cost fro second sourcing so that second sourcing should eventually becoe the superior alternative. To check our intuition, we first siplify our analysis by placing a restriction on F and F. ince the relative size of 2 F and F affects the relative erit of second sourcing in a predictable way, we assue F = 2 F. This iplies that there is no 9

10 intrinsic advantage of having one plant of the large capacity vis-à-vis two plants of the sall capacity if the arginal costs are the sae regardless of the capacity choice. We first copare the option of second sourcing vis-à-vis the option of exporting. As in the coparison of foreign direct investent and exporting, once again we can EX define a unique value αˆ such that such that Π (α) Π if and only if α αˆ because Π EX EX (α) is a strictly increasing function of α and Π (0) < Π and Π (1) > Π. The critical value αˆ can be expressed as (4) α ˆ = π π ( π ( π ( ( c k ( + (2c c k Let Σ be the set of α in which second sourcing is the preferred ode of operation. Proposition 1 tells us that the existence of such a set depends on the relative agnitude of αˆ and α*. Proposition 1 is illustrated in Figure 1. Proposition 1. If α ˆ < α*, we can find a range of α such that second sourcing is the preferred ode of operation. In this case, let Ε, Σ, and Φ be the sets of α in which exporting, second sourcing and foreign direct investent are optial, respectively. Then, the optial sourcing decision can be characterized by two critical cut-off points α and α such that 0 <α < α <1 and Ε = [0, α ], Σ = [α,α ], Φ = [α, 1]. If α ˆ > α*, second sourcing is always doinated by one of the other two, i.e., Σ =φ. 10

11 Proof. Let us define αˆ (0,1) as the unique value of α such that Π (α) Π (α) if and only if α αˆ. We can find such a value because d Π (α)/dα = π ( π ( > [π ( + (c c )k] [π ( c ) + ( c k] =d Π (α)/dα (where the inequality follows fro Lea 1) and Π (0) > Π (0) and Π (1) < Π (1). The critical value α can be expressed as ˆ α ˆ = π ( π ( c k ( (2c c k By coparing α ˆ, α ˆ, and α*, it can be easily verified that α ˆ < α* if and only if α ˆ > α*. EX EX Now, since d Π (α)/dα > dπ (α)/dα > d Π /dα = 0, Π > Π (0) > Π (0) and Π EX (1) < Π (1) < Π, the sets Ε, Σ, and Φ can be characterized by two critical cutoff points α and α where α = in [α ˆ, α*] and α = ax [α*, α ˆ ]. such that 0 < α < α <1 and Ε = [0, α ], Σ = [α,α ], Φ = [α, 1]. If αˆ < α*, α = αˆ and α =α ˆ. ince α < α* < α, we have Ε = [0, α ], Σ = [α,α ], Φ = [α, 1]. If α ˆ > α*, we have α =α = α*. This iplies that Ε = [0, α*], Σ = φ, Φ = [α*, 1]. # The relative agnitude of αˆ and α* is in general abiguous. The following lea, however, helps us understand the likelihood of second sourcing. Lea 2. α < 0. k 11

12 Proof. α [ π ( π ( ]( c k = < 0. 2 k [ π ( π ( + (2c c k] This coparative statics result indicates that second sourcing is ore likely to occur as the lupy capacity level of the sall plant, k, becoes larger since a larger proportion of the total output can be produced in a lower cost plant. 9 This result is also consistent with the fact Π (α) is an increasing function of k whereas the capacity size of the sall plant is irrelevant for the other two alternative odes of production. To suarize, if there is a high probability that foreign costs will be low (i.e., if α is high), it is in the interest of the onopolist to produce all of its output using. If there is a high probability that foreign costs will be low (i.e., if α is low), then it is in the interest of the onopolist to produce all of its output doestically and export it. Finally, there are soe cases in which for interediate values of α the fir finds it optial to second source, producing the bulk of its output in its low cost plant and the residual in its high cost plant. The rationale for second sourcing is provided by Kogut and Kulatilaka (1994) it provides the fir with an option that allows the to produce the bulk of their output in their low cost facility in the presence of cost uncertainty. In the next section we extend our odel to allow for strategic interaction with a rival and show that strategic considerations ake second sourcing ore likely. However, before we do so, we can use our odel to investigate the iplications of second sourcing for an iportant issue related to exchange rate uncertainty. A nuber of authors have exained the iplications of arket structure and other factors on the extent of exchange 9 It should be, however, noted that it is ore likely that the capacity cost of a sall plant F will increase with the level of k. Then, this increase in F should be taken into account in the calculation of the relative erit of alternative sourcing decisions. 12

13 rate pass through. 10 If we assue that the cost uncertainty associated with foreign production is the result of exchange rate uncertainty, then our odel provides the ideal setting in which to exaine the link between the fir s production ethod and exchange rate pass-through. To analyze this, we assue that each unit of foreign currency is worth e units of the ultinational s doestic currency units and we choose units such that the fir s arginal production cost is the sae in both countries if e = 1. Then, we can write the fir s foreign arginal cost as ec in its doestic currency. The exchange rate is assued to fluctuate between two values e and e with e > 1 > e. This iplies that arginal cost is lower in the doestic plant when e = e while it is lower in the foreign plant when e = e. For each realization of the exchange rate e, the fir s axiization proble with exports only (in doestic currency units) can be written as: EX Π = ax epd(p) cd(p) = e[(p c )D(p)], e where p is the price in foreign currency and c is the arginal cost of production in doestic currency. Thus, the effects of an appreciation of the foreign currency (i.e., an increase in e) on the export price are equivalent to those of a decrease in the fir s arginal cost. This iplies that the iport price for the foreign country would fall with an appreciation of the foreign currency. In a siilar way, in ters of its price effects, a depreciation of the foreign currency is equivalent to an increase in the fir s arginal cost with the iport price for the foreign country increasing with a depreciation of the foreign currency. 10 ee, for exaple, Mann (1986), Dornbusch (1987), Froot and Kleperer (1989), Fisher (1989) and Krupp and Davidson (1996). 13

14 Next we investigate the behavior of exchange rate pass-through to iport prices with second sourcing. uppose that the fir is second sourcing and that the exchange rate appreciates. Then, the ultinational will fully utilize its capacity in the doestic country and then produce the residual in its foreign facility. This iplies that its relevant arginal cost is e c. In this case, the ultinational s profit function can be written as: e pd( p) [ ck + ec( D( p) k)] = e( p D( p) + ( e 1) k, where p is the price in the foreign currency. It follows that the ultinational s profit axiizing price is the sae regardless of the realization of e, when e > 1. This iplies that once the capacity of the doestic plant has been exhausted, there will be no further exchange rate pass-through when there is an appreciation of the foreign currency. Now consider the case where the exchange rate depreciates with second sourcing. Then, the ultinational first fully utilizes its capacity in the foreign country and produces the residual in its doestic plant. This iplies that the fir s relevant arginal cost is c. In this case, the ultinational s profit function can be written as: c epd( p) [ eck + c( D( p) k)] = e p D( p) + (1 e) ck, e c where > 1, e so that the price is sensitive to changes in e. Our conclusion is that prices are sensitive to changes in the e when the exchanges rate depreciates but prices invariant to changes in e when the exchange rate appreciates. As a result, exchange rate passthrough is sensitive not only to the production ethod but also to the direction of fluctuations with second sourcing characterized by asyetric exchange rate passthrough. We suarize the result above in the following proposition. 14

15 Proposition 2: With second sourcing, the behavior of exchange rate pass-through to iport prices is asyetric. When the iporting country s currency appreciates vis-àvis the ultinational s doestic currency (i.e., increase in e), there is no exchange rate pass through with second sourcing. In contrast, when the forer depreciates against the latter, the iport price is sensitive to the exchange rate with the rate of pass-through being the sae as the one observed without second sourcing. III. trategic econd ourcing Now, suppose that there are two firs that produce differentiated products copeting in prices in this arket. We begin by assuing that the second fir has a constant arginal cost of c with unliited capacity. In the first part of this section we show that the presence of this rival akes it ore likely that the fir will choose to use second sourcing as its production ode. At the end of the section we extend the odel so that both firs ay use second sourcing and show that two-way second sourcing can be supported as a sub-gae perfect Nash equilibriu. In our initial strategic odel, fir 1 akes its investent decision in the first stage of the gae, before the uncertainty about arginal cost in its foreign facility has been resolved. In stage 2, after the uncertainty is resolved, the firs copete in prices. Thus, when fir 2 sets its price, it has coplete inforation about fir 1 s investent decision and fir 1 s arginal cost. We use p ( c, c 1 2 ) to denote the vector of Nash equilibriu prices when fir j s arginal cost is cj and π ( c, c 1 2 ) represents the vector of corresponding profit levels for 15

16 the two firs. Then, if fir 1 produces doestically and exports, the equilibriu price vector is p(c, and fir 1 s profits are (5) Π EX = π ( c, ) - F 1 c where the sub-script refers to the fact that these profits are earned in a strategic setting. If fir 1 chooses to use instead, the equilibriu prices vector is p(c, if fir 1 s foreign arginal cost is c; otherwise the equilibriu price vector is p( c,. It follows that fir 1 s expected profit fro using in this strategic setting are (6) Π α ) = απ ( c, + (1 α) π ( c,. ( 1 1 F The profit functions in (5) and (6) have the sae properties as their corresponding functions for the onopolist exained in section II. In particular, for values of α close to EX zero, exporting doinates (since Π = π ( c, - F> π 1 ( c, F = 1 Π (0)), while doinates exporting for values of α close to one (since Π = π 1( c, -F< EX π c, F = Π (1)). In addition, (α) is linear in α with slope 1 ( Π * π 1( c, π 1( c, > 0, so that there exists a unique value of α, call it α, such that Π * * π (α) Π if and only if α α, where α = EX ( c, π ( c, 1 1. π 1( c, π 1( c, Now, suppose that fir 1 decides to second-source by sinking capacity in both locations. Then its arginal cost depends on the realization of its foreign arginal cost and on the size of its capacity. As in the case of onopoly, we want to assue that the 16

17 sall plant is not large enough to allow fir 1 to eet all of its deand even when the equilibriu price vector is p ( c,, but that with two sall plants the fir has enough capacity to eet any relevant deand for its product. This will be the case if D p( c, ) / 2 < k < D ( p( c, )) where D ( p 1 ) denotes fir 1 s deand curve. The fact 1( 1 c that k < D1 ( p( c, ) iplies that regardless of the realization of the foreign arginal cost, fir 1 will have to use both plants to eet deand. This eans that if fir 1 s foreign arginal cost is low, it will produce at capacity in its foreign plant, produce the residual in its doestic plant, and the Nash equilibriu price vector will be p( c,. In contrast, if fir 1 s foreign arginal cost is high, it will produce at capacity in its doestic plant, produce the residual in its foreign plant, and the Nash equilibriu price vector will be p ( c,. It follows that fir 1 s expected profit fro second sourcing is given by (7) Π (α) = α[ π ( c, ) + (c c )k] + (1 α)[ π ( c, ) + ( c k] 2 F 1 c 1 c o far our analysis in this section has closely paralleled the onopoly case exained in section II. Here is where the analysis begins to diverge. In the onopoly case, Lea 1 allowed us to show that exporting doinates second sourcing for low values of α while doinates second sourcing for high values of α. There is no counter-part to Lea 1 when fir 1 operates in a strategic setting. To see this, suppose that α = 0. Then fir 1 earns π ( c, ) - F by exporting while its profit fro second 1 c sourcing is π ( c, ) + ( c k 2F. It is not clear which of these values is larger. 1 c Exporting allows fir 1 to produce at lower average cost. However, by second sourcing fir 1 is able to produce the bulk of its output doestically (so that average cost ay be 17

18 very close to its average cost fro exporting) and produce the residual in its foreign plant where arginal cost is high. This high arginal cost allows fir 1 to credibly coit to charging a higher price than it would if it exported; and, since the goods are strategic copleents, this leads its rival to charge a higher price as well. 11 The increase in fir2 s price that is triggered by second-sourcing ay increase fir 1 s profits enough to offset the higher average cost. As a result, second sourcing ay doinate exporting even in the case in which α = 0. A siilar arguent allows us to conclude that second sourcing ay also doinate even when α = 1 and that second sourcing ay be the optial ode of production for all α! Our goal is to show that strategic considerations ake second sourcing ore likely. To do so, we need to copare fir 1 s investent decision in this strategic setting with the investent decision that it would ake in the absence of strategic considerations. This can be accoplished solving fir 1 s proble under the assuption that fir 2 s price is fixed at p ( c, ). We refer to this as the non-strategic case. With 2 c fir 2 s price held fixed at this value, fir 1 earns the sae profit fro exporting in the strategic and non-strategic cases. Moreover, the value of α which equates the profit * earned by exporting with the expected payoff fro (α ) is the sae in both settings. In the non-strategic case, fir 1 behaves in the sae anner as the onopolist exained in section II. Its profit functions have the sae properties as those introduced in (1)-(3) and its investent decision is copletely characterized by Proposition 1. There 11 In order to ensure that the firs prices are strategic copleents we ust place a restriction on our i profit functions. Following Bulow, Geanakoplos, and Kleperer (1985), if we use π p, p ) to denote ( i j the profits earned by fir i in the price gae, then the actions of the two firs will be strategic copleents if the cross-partials of π i and π j are both positive. 18

19 are cases in which second sourcing is never optial (when α ˆ > α*) and there are cases in which it is the preferred production ethod. In the latter case, Proposition 1 infors us that second sourcing is optial if α [ α, α ]. If we use Σ (Σ N ) denote the set of α in which second sourcing is the preferred ode of operation in the strategic (non-strategi setting, then Proposition 2 tells us that strategic considerations widen the set of α under which second sourcing is optial. Proposition 3: econd sourcing is ore likely in the presence of a rival that is, Σ N Σ. Proof: It is sufficient to show that the presence of a rival reduces α and increases α. Define α to be the value of α such that Π (α) = Π (α ) and define α N to be the value of α such that Π (α) = (α where the sub-script N refers to the non-strategic case. Then, fro (6) and (7), N Π N ) α solves (8) k f ( α) = π 1( c, π 1( c, α where f ( α ). Fro (2) and (3), α N solves α( c + (1 α)( c (9) k f ( α) =. π ( π ( ince fir 2 s price is held fixed at p2( c, in the non-strategic case, it follows that π ( =π 1( c,. In addition, since the goods are strategic copleents, π ( > π 1( c, (since in the strategic case fir 2 charges a price lower than 19

20 p ( c, ) when fir 1 s foreign arginal cost is. This iplies that the right-hand-side 2 c (9) is lower than the right-hand-side of (8). ince f '( α) > 0, it follows iediately that α > α N. Now, define α to be the value of α such that Π = Π (α )and define α EX N to be EX the value of α such that Π = Π (α. Then, fro (5) and (7), N N ) (10) α π ( c, + ( c k] + (1 α)[ π ( c, + ( c k] = π ( c, ). Fro (1) and (3), α (11) α [ π ( + ( c k] + (1 α)[ π ( + ( c k] = π (. By construction, the right-hand-sides of (10) and (11) are equal. In addition, the left- hand-sides of (10) and (11) are increasing in α and π (, > π ( (since in the 1 c α solves [ c N solves strategic case fir 2 charges a price higher than p2( c, when fir 1 s foreign arginal cost is c ). It follows that α < α. # N An exaple with syetric linear deand and syetric cost uncertainty can be used to illustrate our basic results. uppose that the deand for fir i s product is given by Q = 1 P + δp with 0 <δ < 1and that c = c and c = c +. Then, if we define i i j x 2 1 c(1 δ ) 2 δ 1 π ( c, = and z <, it is straightforward to show that δ 4 δ 2 (12) α = k z[ 2x + z] 1 α = k z[2x z] and 12 A general forula that gives the Nash equilibriu profit for fir 1 in each possible case is provided in footnote

21 (13) α N = 4 k 4 x + 4k 1 α N =. 4x If we copare these values we find that, as expected, ( α ) = sign[ 4x + (1 + 2z)] > 0 sign α and sign( α N α ) = sign[4x (1 + 2z) ] > 0, N where the last inequality follows fro the fact that z < ½ and 2x >. This confirs that rivalry akes second sourcing ore likely. Moreover, fro (12), if k z( 2x + z), then in the presence of a rival second sourcing is the preferred ode of operation for all α. 13 Lea 1 guarantees that this cannot be the case when the fir is a onopolist. Thus, there are cases in which the strategic advantages fro second sourcing are so great that it is the optial production ethod even in the absence of cost uncertainty! We can also use this exaple to exaine how an increase in the spread of the distribution governing the foreign arginal cost affects the likelihood of second sourcing. Fro above, it is clear that an increase in reduces both α and α. Thus, an increase in akes it ore likely that we will observe second sourcing for low levels of α and less likely that we will observe second sourcing for high levels of α. There are two reasons for this. First, if α is low the fir is effectively choosing between exporting and second sourcing while if α is high, the choice is between and second sourcing. In the forer case, second sourcing is the riskier alternative while in the latter case it is the safer alternative. Due to the fact that the profit function is convex, an increase in the spread of the distribution causes leads the fir to rely ore heavily on the riskier x 13 Our analysis holds for k [, x z]. Thus, for k [ z(2x + z), x z] second sourcing is 2 optial for all α. This region is non-epty if x(1 2z ) > z(1 + z). 21

22 production ethod. econd, if α < ½ then an increase in causes the expected foreign arginal cost to fall. In this case, second sourcing becoes relatively ore attractive than exporting since under second sourcing part of the fir s output is produced in the foreign country. On the other hand, if α > ½, then an increase in causes the expected foreign arginal cost to rise. This akes relatively ore attractive than second sourcing, since all of the output is produced in the foreign country under. To derive the net affect on the likelihood of second sourcing note that with this deand curve α α = k z 1 1 z +. It follows that 2x + z 2x z k ( α ) 1 sign α = sign (2x z ) 1 (2x + z ) > 2 2 so that the set of α for which second sourcing is optial widens as increases. 0, IV. Two-Way Direct Foreign Investent We noted in the introduction that any industries are characterized by two-way. We can provide a strategy-based explanation for this phenoenon by expanding our odel to allow both firs to ake an initial investent decision. To do so, we assue that the two firs are based in different countries. Each fir can produce at hoe at a known arginal cost of c. Alternatively, they can build a foreign facility where the unknown arginal cost will be either c = c - (with probability α) or c = c + (with probability 1-α). As in our previous odels, the cost of building a doestic or foreign plant with unliited capacity is given by F while the cost of building a sall plant in either location is given by F with 2F = F. To be consistent 22

23 with our previous odels, we assue that one sall plant is always too sall to eet arket deand, but that two sall plants are sufficient to eet any deand. In this Di ( p( c, ) setting, this will be the case if < k < Di ( p( c, ) 2 for i = 1,2. Under this assuption, a fir that second sources always has to use both plants to eet deand but it is never fully capacity constrained. For siplicity, we illustrate our point using linear deand. We assue that the product arkets in the two countries are not segented and that the aggregate deand for fir i s product is given by Q = 1 P + δp with 0 <δ < 1. It is straightforward to i i j show that with this deand curve and cost structure our restriction on k is equivalent to x + y 2 δ < k < x y, where x π ( c, and y. 2 4 δ Our goal is to show that there exists a sub-gae prefect Nash equilibriu in which both firs use second sourcing to produce their output. ince the odel is syetric, all that we need to show is that it is in fir 1 s interest to second source given that its rival is doing so. We begin with the case in which fir 1 produces its output doestically so that its arginal cost is c. With fir 2 second sourcing, it produces the bulk of its output in its low cost plant and the residual in its high-cost facility. This iplies that in equilibriu fir 2 s arginal cost is equal to its arginal cost in its highcost plant. Thus, if we use Π ˆ EX ( α) to denote fir 1 s expected payoff fro producing all of its output doestically while its rival is second sourcing, then we have EX (14) Π ˆ ( α ) = απ ( c, + (1 α) π ( c, F 23

24 Now, suppose instead that fir 1 uses to produce all of its output. Then if we use Πˆ ( α) to denote the expected profit earned by fir 1 when it uses while its rival second sources, we have ˆ 2 2 (15) Π ( α ) = α π ( c, + α(1 α)[ π ( c, + π ( c, ] + (1 α) π ( c, F Finally, fir 1 s expected payoff fro second sourcing when its rival also second sources is given by Πˆ ( α) where (16) Πˆ ( α) = α 2 [ π ( c, + ( c k] + (1 α) 2 [ π ( c, + ( c k] + α(1 α)[ π ( c, + ( c k + π ( c, + ( c k] 2F The profit functions in (14)-(16) have any of the sae properties as those depicted in Figure 1. In particular, ˆ EX ˆ Π (0) > Π (0), ˆ EX ˆ Π (1) < Π (1) and the expected payoffs fro and second sourcing are both increasing in α with Πˆ ( α) steeper than Πˆ ( α). The only new wrinkle is that the expected profit fro exporting is now decreasing in α since an increase in α iplies that the fir s rival is ore likely to have a low arginal cost in its foreign plant. This new feature does not alter the qualitative nature of the equilibriu. It is still the case that for low values of α the fir chooses between exporting and second sourcing while for high values of α it chooses between and second sourcing. It follows that if Π ˆ (0) ˆ EX > Π (0) and Πˆ (1) > ˆ Π (1), then the Nash equilibriu is characterized by both firs second sourcing for all α. Proposition 4 provides such a condition for the linear deand case. 24

25 Proposition 4. With linear deand curve (Q = 1 P + δp with 0 <δ < 1) and syetric cost uncertainty ( c = c and c = c + ), both firs second source for all α i i j if 2 ( y + z ) k [ z(2x + z), x y]. This set is non-epty if x >. 1 2z Proof. With the linear deand curve, it can be easily verified that Πˆ (0) > Πˆ EX (0) if k > z[ 2x z + 2 y] and ˆ ˆ Π (1) > Π (1) if k > z[ 2x + z]. 14 ince δ < 1, the latter condition is ore restrictive. Cobining this with our earlier restriction on k, we find that both firs second source for all α if k [ z( 2x + z), x y]. The condition for this set to be non-epty is that 2 ( y + z ) x y > z( 2x + z ), or x >. # 1 2z V. Discussion In this paper, we developed a strategic odel of second sourcing in which the use of ultiple production facilities eets the dual purpose of keeping average cost low while at the sae tie increasing arginal cost. The practice serves as a collusive device because the increase in arginal cost softens product arket copetition and results in higher profits. We couched this theory in the context of a ultinational s decision to sink production capacity in both doestic and foreign countries. The ain reason for developing our theory in the context of international trade was that the cost 14 With the deand curve that we have assued fir 1 s Nash profits fro the price gae are given by c(1 δ ) π ( c1, c2) = x + + c2 y c1z. This forula can be used to deterine the critical values for 2 δ α and α in our earlier analysis and the conditions on k that result in second sourcing eerging as an equilibriu outcoe. 25

26 uncertainty associated with producing in a foreign country provided a natural setting in which to analyze such an issue. In addition, we were able to explain two-way flows between pairs of developed countries, a phenoenon that has been considered a theoretical puzzle 15 in the literature despite its epirical iportance (see Markusen 1995). 16 We conclude with a discussion on how the theory developed in this paper can be applied to other contexts. Voluntary Export Restraints We are not the first to point out that in the presence of strategic copleents firs have an incentive to ake strategic oves to soften copetition. In a two-stage gae in which firs first select capacity and then copete in prices, Kreps and cheinkan (1983) showed that liiting capacity allows firs to support higher equilibriu prices. In the trade literature, Harris (1985) and Krishna (1989) have shown that voluntary export restraints (VERs) can help firs soften copetition in anner siilar to the capacity constraints in Kreps and cheinkan s odel. In particular, they show that a VER set at the free trade level of iports can increase the profits of all firs within the industry. Our odel provides a siilar prediction because the liit on the level of exports plays the sae role as a capacity constraint. Thus, our results can be 15 Brainard (1997a) and Horstann and Markusen (1992) have also provided odels in which equilibriu ay be characterized by two-way. In their odels, this phenoenon arises if sountries are large and have siilar factor endowents and is generated by scale econoies, fir level activities that are joint inputs across plants and transport costs (or tariffs). 16 According to Julius (1990), the share of all direct investent generated by G-5 counties flowing into other G-5 countries has been rising and was estiated to be 70 percent by Our odel is also consistent with the epirical evidence that the nature of ost direct foreign investent in production facilities is horizontal in that ost of the output of foreign production affiliates is sold in the foreign country (Markusen 1995). 26

27 viewed as a natural extension of Kreps and cheinkan to a setting in which firs can use ultiple production facilities or as an extension of Harris and Krishna in which second sourcing plays the role of the VER. One advantage of our odel is that we can derive the collusive role of VERs even in the presence of foreign direct investent as long as the capacity in the host country is not sufficient enough to eet all the deand in that country. The ost proinent exaple of a VER is the one applied to Japanese iports in the North Aerican autoobile industry in the 1980s. However, after the iposition of the VER ajor Japanese autoobile anufacturers set up production facilities in the U. The odels of Harris and Krishna are unable to generate the collusive effects of a VER once foreign direct investent is taken into consideration. Thus, it is hard to explain the ajor Japanese auto anufacturers decision to engage in foreign direct investent in the U in their odels. econd ourcing and the Make or Buy Decision econd sourcing is a coon practice in the seiconductor industry. 17 For exaple, in this industry it is coon for an innovating fir to license its technology to one or ore copeting firs in an effort to create ultiple sources of supply (e.g., Intel allowed IBM to produce Intel s icroprocessors internally provided that IBM agreed not to sell to a third party). In addition, firs in this industry often enter into agreeents to purchase inputs fro ultiple suppliers. hepard (1987) attributes the forer practice to the innovating fir s desire to enhance deand for new technologies by aking the product ore attractive to potential buyers. Others have argued that the latter practice reduces the risk of being unable to obtain a key input when a supplier runs out of its 17 ee, for exaple, hepard (1987). 27

28 stock. Our odel provides an alternative strategic rationale for such practices. Provided that the fir can credibly coit to obtaining a fixed aount fro the low-cost source (which can be accoplished through contracting), second sourcing softens product arket copetition. Another coon feature of any industries is that firs often both ake and buy any of the coponents used to produce their final product. For exaple, in a recent study of a high-tech engineering fir Knez and iester (2002) found that the fir obtained eighteen of its coponents fro both an internal and an external supplier. 18 The production anageent literature has ephasized efficiency considerations and bargaining costs as key factors in deterining whether a fir should ake its parts or buy the the presuption is that there is rarely any incentive to do both. Knez and iester interviewed anagers at this fir and asked why they relied on both internal and external suppliers. The standard response was that since external suppliers tend to provide the parts at lower cost, the fir obtains ost of its supply externally. However, since there are instances in which parts are needed faster than the external supplier can deliver the, the fir obtains the residual parts internally. Eccles and White (1988) also suggest that soe copanies ake it a policy to source a certain percentage of their needs externally on internally transferred products as a way of getting realistic arket prices. Our theory suggests that if a fir has arket power and copetes in prices in an oligopolistic arket then this practice of siultaneously aking and buying parts ay have unintended positive consequences. By relying on a relatively inefficient internal 18 ee also Monteverde and Teece s (1982) study of the auto industry. In investigating Ford and GM s decisions of whether to ake or buy coponents, they labeled a coponent as ade if over 80% of its supply was produced internally. The use of this criterion suggests that a significant nuber of coponents were provided by both an internal and external supplier. 28

29 supplier for its residual parts, the fir ay be effectively softening product arket copetition with its rivals. The idea that a fir can gain strategically by anipulating its sourcing decision also appears in a recent paper by Chen (2001). This paper provides a odel of vertical erger in which one upstrea fir is ore efficient than others. In equilibriu, one of the downstrea firs erges with the ore efficient fir and the reaining downstrea rival chooses the integrated fir as its supplier even when the latter s input price is higher than prices of alternative sources. The reason for this paradoxical result is that vertical integration creates ulti-arket interaction between the integrated fir and its downstrea rivals; when the unintegrated fir selects the integrated fir as its supplier, the vertically integrated fir behaves less aggressively in the downstrea arket since its aggressive pricing can cut into its profits in the upstrea arket. This odel is siilar in flavor to ours in that the sourcing decision is otivated not only by cost iniization but also by strategic considerations in the output arket. Chen s (2001) odel, however, rules out the possibility of second sourcing by assuing either switching costs due to relationship-specific investent or the use of requireent contracts in the input arket, under which a downstrea fir is required to purchase all inputs fro a certain supplier at soe unit price. If second sourcing is allowed in his odel, a better strategy for the unintegrated downstrea fir would be to arrange a dual sourcing agreeent to buy soe fixed aount fro an independent supplier who offers the lowest price and the residual (variable aount) fro the integrated fir at a higher price. In this way, the unintegrated fir can save on input 29

30 costs while keeping the integrated fir s strategic incentives intact. 19 The welfare effects of ultiple sourcing would be unabiguously negative in this odel. First, the integrated fir would be able to charge a higher price and sustain a ore collusive outcoe since the effects of a higher acquisition price fro the integrated fir on the unintegrated downstrea fir s total input costs would be lessened. econd, the integrated fir is a ore efficient producer even though its price is higher than those of alternative producers. Thus, any shift of input production fro the integrated fir to alternative sources is inefficient. 19 The dual sourcing strategy could have an added advantage of itigating the potential hold-up proble ephasized in the incoplete contract/transactions cost literature of vertical integration. 30