A GAME-THEORETIC PERSPECTIVE ON TRANSACTION COST AND THE DECISION TO MAKE, BUY OR MAKE-AND-BUY December 2001 Khai Sheang LEE* & Wei Shi LIM** RPS #2001-034 (MKTG) * Associate Professor, Department of Marketing, Faculty of Business Administration, Bldg. 1, National University of Singapore, Business Link, Singapore 117591. E-mail: fbaleeks@nus.edu.sg ** Associate Professor, Department of Decision Sciences, Faculty of Business Administration, Bldg. 1, National University of Singapore, Business Link, Singapore 117591. E-mail: fbalimws@nus.edu.sg Copyright Faculty of Business Administration, National University of Singapore.
A Game-Theoretic Perspective on Transaction Cost and The Decision to Make, Buy, or Make-and-Buy Abstract This paper examines a firm s outsourcing decision over time. We identify specific learning and the salvageability of specific learning by suppliers as reasons for a firm to adopt a make-and-buy strategy, even when outsourcing is less costly initially. We show that when specific learning effect is high, the firm follows a makeand-buy strategy, capitalizing on the cost savings in buying, while simultaneously acquiring specific know-how for an eventual switch to a make-only strategy. When specific learning effect is moderate, the firm adopts a make-and-buy strategy, followed by a buy-only strategy. In this way, the firm minimizes the appropriation risk in outsourcing. Finally, outsourcing completely is optimal for the firm only if specific learning effect is low. Key Words: Game Theory, Industrial Marketing, Transaction Cost Economics, Small Numbers Bargaining. 1. Introduction Since Coase's (1937) seminal work on transaction cost, which was later developed by Williamson (1979, and 1981), transaction cost economics (TCE) has been extensively applied to examine the procurement problem faced by firms. According to TCE, transaction cost varies depending on the characteristics of the transaction associated with the exchange relationship, for example, asset specificity, uncertainty, and frequency (Williamson 1985). TCE argues that, buyers should internalize (or make) their supply requirements to preempt against the hazards of opportunism in engaging external agents or suppliers when transaction specific assets are involved in exchange relationships, and outsource (or buy) their requirements otherwise. Based on the arguments of TCE, extensive empirical studies have been conducted to examine the effect of transaction specific assets on a firm s decision to 1
make or buy. Nonetheless, questions of whether a firm should make some of its requirements and buy the rest, or how a firm s governance decision changes over time, have largely been ignored. This is hardly surprising given that the paradigm problem of TCE is on the make-or-buy decision, and that in TCE, "organizational form is often modeled as a binary variable - make or buy" (Shelanski and Klein, 1995, p338). The emphasis of TCE on individual transaction as the unit of analysis ignores how different governance forms can be combined (Rindfleisch and Heidi, 1997). Some researchers have proposed that combined governance forms such as make-and-buy, franchised-and-owned units, and direct-and-indirect distribution channels, could be viewed conceptually as hybrid modes that lie on a continuum, with market exchange at one end and hierarchical integration at the other (Shelanski and Klein, 1995; and Rindfleisch and Heidi, 1997). Challenging this view, Bradach and Eccles (1989) proposed that combined governance forms were more appropriately viewed as plural forms, which they defined as "an arrangement where distinct organizational control mechanisms are operated simultaneously for the same function by the same firm" (Bradach and Eccles, 1989, p112). The authors suggested that, to understand why firms often follow plural forms, like make and buy, the focus must shift away from individual transactions to control mechanisms, and proposed three control mechanisms that govern economic transactions price, authority, and trust. However, like Dutta et al. (1995), we contend that it is not necessary to invoke these control mechanisms, and that plural forms can be examined through the lens of TCE. The objective of this paper is to formally examine how appropriation concerns (Klein et al., 1978; and Walker, 1988) arising from transaction specific assets and small numbers bargaining affect a firm's decision to make only, buy only, or make and buy, their supply requirements. We seek to provide an explanation as to why 2
firms both make and buy their supply requirements, and how their governance decision change over time. As the majority of prior research in TCE are empirical studies (Shelanski and Klien, 1995; and Rindfleisch and Heidi, 1997) a formal analysis following a game theoretic approach could provide useful insights. A distinctive contribution of this paper is that it clarifies the findings (or lack of) in earlier empirical studies. In this paper, we propose that (1) specific learning and (2) the salvageability of this specific learning as two reasons for a buyer to change his governance decision over time and to follow a make-and-buy strategy, even if a supplier could supply at a lower cost initially. When transaction specific assets in the form of specific human capital are involved in an exchange relationship, buyers and suppliers may be "locked-into" transactions asymmetrically (Williamson, 1979 and 1981). This allows a supplier to transfer or salvage, in part or in full, the know-how that he has acquired from the specific relationship (Anderson and Weitz, 1986; and Pisano, 1990) to supply other buyers in the market. Furthermore, this specific learning, that is acquired by a supplier, may not be salvageable nor patentable (Monteverde and Teece, 1982) by a buyer. We show that such asymmetry in the salvageability of specific learning affects the outcome in small numbers bargaining, and hence a buyer s governance decision to make, buy, or make-and-buy. Furthermore, we show that a buyer s optimal governance decision changes as a supplier acquires specific learning over time. The rest of this paper is organized as follows. The next section contains the literature review. Section 3 and Section 4 present a game theoretic model of industrial procurement and the analyses respectively. Section 5 examines the change in governance over time that arises from learning specificity and its salvageability, 3
while Section 6 discusses the results. The final section concludes and provides directions for future research. All proofs to the lemmas and propositions presented in this paper are included in the Appendix. 2. Literature Review 2.1 TCE and Governance Decision Extensive studies have been conducted to identify and to examine various governance mechanisms as safeguards against the hazards of opportunism in engaging external agents when transaction specific assets are involved in exchange relationships. For example, Williamson (1983, 1984) proposed the use of hostages to credibly commit to exchange relationships. Heidi and John (1990) examined the utility of relationships to safeguard relationship-specific investments and to facilitate adaptation to uncertainty. Stump and Heide (1996) suggested that opportunism by suppliers could be controlled through partner qualification and selection, incentive design, and monitoring. Anderson and Weitz (1992) proposed that pledges in idiosyncratic investments could be effective in reducing opportunism in channel relationships. Klein et al. (1978) proposed that reputation served as collateral against opportunism, while Klein and Leffler (1981) suggested that brand name is a form of specific asset that served as collateral by suppliers to deliver high quality. Others proposed that a multiple sourcing strategy could safeguard against delivery failures (Leavy, 1994; and Wilson, 1994) and suppliers' opportunism post contract award (Seshadri, 1991 and 1995). For small firms, for which internalization is not feasible because of resource limitations (Lee et al. 1999; Lim et al. 2000), Heidi and John (1988) proposed that close bonds with clients safeguard against opportunistic 4
behaviors by principals. In all these studies, the focus is on pure governance forms, rather than plural forms. 2.2 Plural Governance Forms More directly related to our study are those which examined plural forms. For example, Heidi (1994) recommended a typology of three governance forms market governance, hierarchical governance, and bilateral governance, and argued that nonmarket governance cannot be described by a single continuum. However, the author did not identify the determinants of plural governance structures. In Dutta et al. (1995, p194), it was proposed that adding a direct sales force to augment the rep channel serves as a safeguard against lock-in problems with the reps and provides a manufacturer with insight into downstream marketing activities when performance is ambiguous. The authors reported that the degree of lock-in problems faced by a manufacturer and performance ambiguity increases the probability that a dual channel will be used. However, since governance responses were coded as reps only and reps plus house accounts in their study, the authors did not distinguish when increasing asset specificity would increase the probability of dual channels vis-à-vis house accounts only. This is critical, as lock-in problems that arise from specific assets would also increase the probability in following a house accounts only strategy. In Gallini and Lutz's (1992) study of franchisors store-mix decision, it was suggested that, given the information asymmetry between franchisors and potential franchisees, stores owned by new franchisors signal business prospects to potential franchisees. As a result, when this information asymmetry between franchisors and potential new franchisees diminishes, all stores will be franchised. On the other hand, 5
Weiss and Anderson (1992, p106) hypothesized that the more extensively the manufacturer uses house accounts in a sales district, the more likely it is to convert the district to a direct sales force. This suggests that a firm following a make-and-buy strategy would likely switch to a make-only strategy eventually, which is contrary to Gallini and Lutz's (1992) arguments. Compared to these studies, we clarify the conditions when a buyer, who follows a make-and-buy strategy initially, will eventually switch to a buy-only or a make-only strategy. In a related study, Farrel and Gallini (1988) proposed that a monopolist intentionally licenses other firms to utilize his proprietary technology to produce and compete directly with him, because second sourcing or invited competition served as a safeguard for a buyer s specific investment. Although the authors' proposition, which was empirically tested by Dutta and John (1995), provides an explanation as to why firms make-and-license, it is silent as to why firms both make and buy. Another study by Carlton (1979) suggested that partial integration arises because firms integrate and use the market to satisfy the high and low probability demands respectively. Compared to Carlton (1979), we propose an alternative explanation, based on TCE arguments, for the use of plural governance forms by firms. 2.3 Learning Specificity Williamson (1979) described asset specificity as the most important dimension affecting transactions. Although there are various forms of specific assets (e.g., Klein et al., 1978; Williamson, 1981; and Nooteboom, 1993a), we focus on learning specificity or specific human capital in the form technical know-how that arises from learning by doing (e.g., Williamson, 1981; Klein, 1988; Monteverde, 1995; Hart and Moore, 1990). This is because specific human capital has a stronger influence on 6
governance decisions than other forms of specific assets (Masten et al., 1989) and is the most commonly assessed form of specificity in TCE studies (Rindfleisch and Heidi, 1997). For example, it was postulated that specific know-how affects transaction cost and governance decisions (Pisano, 1990), could be a barrier to change (Nooteboom, 1993b), and increases the likelihood of vertically integrated production (Monteverde and Teece, 1982). Indeed, Monteverde and Teece (1982, p206) suggested that, Even if the title to specialized equipment used by the supplier is held by the assembler, this need not provide protection against rent appropriation if transaction specific know-how has been generated". We formalize the authors' argument and extend it to examine the effect of rent appropriation on plural forms over time. 3. A Game Theoretic Model To gain a more precise insight into the hazards of small numbers bargaining (Williamson, 1979; and 1981) when transaction specific assets are involved in exchange relationships, we propose a 2-period bargaining game. We will first describe the game before we discuss some characteristics of the model. In Period i (i = 1, 2), buyer B and supplier S bargain over price P i ( 0). We apply the Nash bargaining solution concept to derive the bargaining outcome. Let the unit cost of production for j (j {B, S}) be C j (q), which is endogenous on q ( 0), the cumulative quantity produced up to Period i for buyer B. Therefore, in Period 1, the supplier s production cost in producing for buyer B is C S (0). We normalize the buyer s purchase requirement per period to be 1, and use α to denote the portion of his requirement that he chooses to buy vis-à-vis to make. We define the learning-by-doing effect as an efficiency gain from cumulative production (Irwin 7
and Klenow, 1994). The learning effect is transaction specific in that a supplier learns, or acquires specific knowledge in production, only if it is awarded the supply contract in part or in full. Learning specificity, as we have defined, is a form of specific human capital that arises from learning-by-doing (Klein et al. 1978; Williamson 1979 and 1981; Schelanski and Klein 1995). Taking into account the effect of specific learning on cost, we therefore assume that the production cost function C j (q) has the following characteristics (Figure 1). (a) C B (α) > C S (α) for all α 0, that is, with the same amount of production experience α, suppliers have a cost advantage over buyer B (Maltz, 1994). This is because a "supplier who aggregates uncorrelated demands can realize collective pooling benefits" (Williamson, 1979, p245). (b) C B (1) < C S (0), that is, because of specific learning, buyer B could acquire a cost advantage over suppliers who did not possess any specific learning, if it chooses to produce in house. Otherwise, it will never be beneficial for the buyer to produce in house. (c) C j (α) is continuous and twice differentiable, such that C j (α) < 0 and C j (α) > 0, that is, C j (α) is strictly decreasing and convex with respect to α. This implies that, by Period 2, if supplier S was awarded a contract to supply α (α > 0), then supplier S would acquire specific learning in producing for buyer B and hence, gain a cost advantage over other suppliers in the market who did not possess such expertise (Monteverde and Teece, 1982). (d) d/dα C j (γα) d/dα C j (α) (j = B, S) for all γ between 0 and 1, that is, the rate of decrease of C j (γα) with respect to α is no more than that of C j (α). This implies that, if supplier S is to supply other buyers in the market, his rate of specific 8
learning in supplying these buyers will be no more than his rate of specific learning in producing for buyer B if he is to continue producing for buyer B. This is not unreasonable given that the specific learning that we are interested in is a form of specific asset and hence, is unique to the B-S dyadic relationship (Williamson, 1979), although it is salvageable (to an extent that is specified) in our model. (e) d 2 /dγ 2 C j (γα) > 0 (j = B, S). This property is similar to the requirement in (c) whereby we have C j (α) > 0. (Insert Figure 1 here) We consider the case when the market is competitive in that supplies are readily available from competing symmetric suppliers. Hence, in the initial period, the suppliers optimal choice of price P 1 is the competitive market price C S (0). However, in the presence of learning specificity, the situation is transformed from one of competitive market into one of small numbers bargaining. For each period i (i = 1, 2), depending on the bargaining outcome P i, supplier S decides on whether or not to supply buyer B, while the latter chooses to outsource a portion α i ( [0,1]) of his requirements to the supplier, while producing a portion (1- α i ) of the required supplies himself. That is, B decides on whether to make (α i = 0), buy (α i = 1), or make-and-buy (α i (0,1)). Hence, (α 1, P 1, α 2, P 2 ) defines the supply contract between buyer B and supplier S for the two-period game. For simplicity, our model consists of two periods instead of an arbitrary n periods. However, it is worthwhile to note that the results obtained are not compromised. 9
Let γ ( [0,1]) denote the degree of salvageability of learning by supplier S outside of the specific buyer-supplier (B and S) exchange relationship. This means that the specific knowledge acquired by S is transferable in that he can use this knowledge, in part or in full to the extent as defined by γ, to produce at a cost C S (γα), such that C S (0) C S (γα) C S (α) (Figure 1), to supply other buyers B' in the market at a price P S [C S (γα), P*], where P* = C S (0). Obviously, P S cannot be less than the production cost C S (γα) but neither can it be higher than the competitive market rate C S (0). In other words, the supplier S could benefit from the salvageability of the specific knowledge that he has acquired, by supplying other buyers B' in the market. In doing so, the supplier S earns a premium ω(γα) = ρ(c S (0) - C S (γα)) ( 0), by charging P S = (ω(γα) + C S (γα)) = (1-ρ)C S (γα) + ρc S (0), where ρ [0, 1] represents the bargaining power of the supplier S vis-à-vis other buyers B' in the market. The premium ω(γα) = ρ(c S (0) - C S (γα)) is maximized when ρ = 1. Note that ω(γα) is non-decreasing in γ and α if ρ = 0 and strictly increasing if ρ > 0 (Figure 1). Obviously, if α = 0, then ω(0) = 0. Given that supplier S earns a minimum premium ω(γα) by supplying other buyers B', he can therefore demand a minimum price (C S (α) + ω(γα)) from buyer B (Figure 1). The buyer B chooses a portion α (= {α 1, α 2 }) of his supply requirement to buy vis-à-vis to make, to minimize his total cost of purchase over the two periods. We assume that, whenever B is indifferent between producing internally and outsourcing, he chooses to produce internally. The payoff (cost) of buyer B over the two-period game is thus given by π B (α 1,P 1,α 2,P 2 ) = [α 1 P 1 + (1 - α 1 )C B (0)] + [α 2 P 2 + (1 - α 2 )C B (1-α 1 )], (1) where B chooses α to minimize π B (α 1,P 1,α 2,P 2 ). 10
A supplier s unit profit is given by (P i - C S (α i )), and he bargains over prices P = {P 1, P 2 } to maximize his payoff, which is given by π S (α) = {α 1 [P 1 - C S (α 1 )] + α 2 [P 2 C S (α 2 )]}. Williamson (1979, p242) suggested that in a bilateral monopoly, Although both (buyer and seller) have a long term interest in effecting adaptations of a joint profit maximizing kind, each also has an interest in appropriating as much of the gains as he can on each occasion to adapt. Our model is consistent with the author's argument in that buyer B and supplier S bargain over prices in each period to maximize their individual payoffs. Supplier S in our model is opportunistic in that he maximizes rent appropriation by exploiting the fact that his possession of idiosyncratic know-how makes him difficult to be replaced. The quasi-rent (Klein et al., 1978) appropriable by the supplier, or the appropriation risk faced by the buyer, can be defined as τ = (P 2 - C S (α 1 )), which is also consistent with Monteverde and Teece s (1982) measure of opportunism as price hikes in follow-on periods. In the next section, we will present the formal analysis of the game, first stating the best responses of B and S in the respective subgames, and eventually the subgame perfect equilibrium of the game. 4. Analysis: Make, Buy, or Make-and-Buy We first state the following lemma, which will be useful in our analysis. Essentially, the lemma states that, given a fixed degree of salvageability γ, the minimum price that supplier S can demand from buyer B is strictly decreasing in α, the proportion of the buyer's supply requirement that is outsourced. 11
Lemma 1: Given γ, the curve (C S (α) + ω(γα)) is strictly decreasing in α ( (0, 1)), that is, / α [C S (α) + ω(γα)] < 0. Using backward induction, we begin our analysis of the game from the final period. Suppose buyer B buys α 1 and makes (1 - α 1 ) of his requirement in Period 1. In Period 2, the unit cost of production of supplier S becomes C S (α 1 ), due to learning from the earlier period. In contrast, suppliers who were not awarded any prior supply contract would not benefit from learning specificity, and hence their unit cost of production would remain at C S (0). The incumbent supplier S therefore has a cost advantage over other competing suppliers in Period 2, as a result of learning specificity, since C S (α 1 ) < C S (0), α 1 > 0. Given the prior production experience of buyer B, his unit cost of production in Period 2 becomes C B (1-α 1 ). For supplier S to secure the supply contact in Period 2, he must therefore offer a price that at least matches the buyer s unit cost C B (1-α 1 ) or the competitive market price C S (0), whichever is lower, that is, P 2 Min[C B (1-α 1 ), C S (0)]. On the other hand, since learning is partially salvageable by S outside of the specific buyer-seller relationship, supplier S is assured of a minimum premium ω(γα 1 ). Hence, he can demand a price P 2 (C S (α 1 ) + ω(γα 1 )) from buyer B. We observe that (C S (α) + ω(γα)) C S (0), where equality holds when α = 0. The bargaining outcome in Period 2, P * 2, is therefore bounded below by the minimum price level (C S (α 1 ) + ω(γα 1 )), if (C S (α 1 ) + ω(γα 1 )) C B (1-α 1 ), and bounded above by the maximum price level Min[C B (1-α 1 ), C S (0)]. That is, (C S (α 1 ) + ω(γα 1 )) P * 2 Min[C B (1-α 1 ), C S (0)], in which case buyer B also chooses to outsource all his requirements in Period 2, that is, α 2 = 1. 12
On the other hand, if buyer B could produce at a cost that is lower than the minimum price demanded by supplier S, that is, (C S (α 1 ) + ω(γα 1 )) > C B (1-α 1 ), then obviously buyer B will choose to produce all his requirements in Period 2. Lemma 2 states this result and the bargaining outcome, where λ denotes the bargaining power of supplier S vis-à-vis buyer B in Period 2. As Lemma 2 shows, the buyer's choice of α 1 in Period 1 affects both the buyer's and the supplier's unit production cost in Period 2, and the appropriation risk τ = (P * 2 (α 1,P 1 )) - C S (α 1 )). Lemma 2: Given (α 1, P 1 ) as the decision choices in Period 1, the Nash equilibrium of the subgame beginning at Period 2 is given by, (α 2 * (α 1,P 1 ), P 2 * (α 1,P 1 )) = (0, C B (1-α 1 )), if C B (1-α 1 ) C S (α 1 ) + ω(γα 1 ), (1, (1 - λ)(c S (α 1 ) + ω(γα 1 )) + λmin[c B (1-α 1 ), C S (0)]), otherwise. Next, we shall examine the cases when the effect of specific learning for the buyer is (i) high, such that C B (1-α 1 ) C S (α 1 ) + ω(γα 1 ), (ii) moderate, such that C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0), and (iii) low, such that C S (α 1 ) + ω(γα 1 ) C S (0) < C B (1- α 1 ). Before we proceed with the analysis of the cases stated, we first define a few notations that will be used later. With reference to Figure 1, let α (0,1) be such that C B (1-α 1 ) C S (α 1 ) + ω(γα 1 ) for all α 1 α. Note that α always exist, since C S (0) + ω(0) = C S (0) + 0 > C B (1) but C S (1) + ω(γ) = C S (1) + ρ[c S (0) - C S (γ)] < ρ C S (0) + (1 - ρ)c S (1) < C B (0). Hence, by the Intermediate Value Theorem, there exists an α in the interval (0,1) such that C B (1-α) = C S (α) + ω(γα). Similarly, since C B (1 - α) < C S (0) and C B (0) > C S (0), again by the Intermediate Value Theorem, the existence of α ( [α,1]) such that C B (1 - α) = C S (0) is assured. Given that C S (α) + ω(γα) is 13
decreasing in α (Lemma 1) and that C B (1-α) is increasing in α, we deduce that C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0) for all α 1 [α, α] and C S (α 1 ) + ω(γα 1 ) C S (0) < C B (1-α 1 ) for α 1 ( α, 1). Finally, let Γ a,b denote the subgame where α 1 is between a and b. 3.1 High Specific Learning Effect: C B (1-α 1 ) C S (α 1 ) + ω(γα 1 ) With reference to Figure 1, for values of α 1 between 0 and α, since C B (1-α 1 ) C S (α 1 ) + ω(γα 1 ), Lemma 2 implies that the buyer s 2-period payoff is given by π B (α 1,C S (0),0,C B (1-α 1 )) = [α 1 C S (0) + (1 - α 1 )C B (0)] + C B (1-α 1 ). Let α a denote the solution to the first order condition C S (0) - C B (0) - C B (1-α 1 ) = 0. It is easy to check that the second-order condition is C B (1-α 1 ) (> 0). Hence, the buyer s cost is minimized when α 1 equals α a, if it exists. Otherwise, the buyer s cost is minimized at one of the boundary points, 0 or α. Proposition 1 thus follows. Proposition 1: In the subgame Γ 0,α, the optimal decisions for buyer B are: 0, if C S (0) - C B (0) > C B (1-α 1 ), α 1 [0, α], α 1 * = α, if C S (0) - C B (0) < C B (1-α 1 ), α 1 [0, α], α a, if α a (0, α) such that C S (0) - C B (0) - C B (1-α a ) = 0. P * 1 = C S (0), α 2 = 0, and P * 2 = C B (1-α * 1 ). Furthermore, α * 1, α * 2 and P * 1, P * 2 are independent of γ, ρ, and λ. The appropriation risk faced by the buyer is τ = (C B (1- α * 1 ) - C S (α * 1 )). As Proposition 1 shows, when the effect of specific learning on the buyer s cost is high, such that C B (1 - α 1 ) C S (α 1 ) + ω(γα 1 ) C S (0), the optimum choice of α 14
is independent of γ, ρ, and λ, and is driven solely by the effect of specific learning. This is consistent with Williamson's (1979) suggestion that asset specificity is the single most important factor that drives transaction cost and governance decision. Note also that, when the effect of specific learning is high, appropriation risk τ, and hence governance decision, is driven by the relative difference in production costs of the buyer vis-à-vis the supplier, that is, τ = (C B (1-α * 1 ) - C S (α * 1 )). This perhaps provides an explanation for Walker and Weber s (1984) observation that comparative production cost is the strongest predictor of governance decision, in their empirical study. When there exists α a ( (0, α)) such that the gradient of the buyer s cost function at (1 - α a ) equals C B (0) - C S (0), the buyer adopts the make-and-buy policy in Period 1. This is because, if the buyer chooses a make-only strategy in Period 1, then he is not capitalizing on the cost savings from outsourcing, given that his initial unit cost is higher than that of the supplier's. On the other hand, if the buyer chooses a buy-only strategy in Period 1, then he could not credibly internalize the production of his requirement in the next period. The buyer therefore optimizes by following a make-and-buy strategy initially, but switches to the make-only strategy when he has acquired a cost advantage over the supplier. Obviously, the greater the effect of specific learning on cost reduction, the earlier the buyer switches to the make-only strategy, to the extent that he would follow a make-only strategy right from the beginning if the effect of specific learning is sufficiently high. This happens when the gradient of the buyer's cost function C B (1 - α) is greater than C B (0) - C S (0) (Proposition 1). Proposition 1 therefore implies that, even though the effect of specific learning is high, which suggests that the buyer internalizes his production, he could do better 15
by following the make-and-buy strategy initially. An external supplier is engaged initially for part of the buyer s requirements, until the latter has acquired sufficient specific learning to produce more efficiently. Corollary 1 therefore follows. Corollary 1: When the effect of specific learning is high, a make-only strategy right from the beginning is not optimal. The buyer is better off following a make-and-buy strategy initially, then switching to a make-only strategy when he has acquired a cost advantage over his supplier. The buyer's decision is independent of the salvageability of specific learning by his supplier. 3.2 Moderate Specific Learning Effect: C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0) For the subgame Γ a,b = Γ α, α, where the specific learning effect is moderate, the minimum price demanded by supplier S (= C S (α 1 ) + ω(γα 1 )) in Period 2 is less than buyer B s production cost, that is, C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0) for values of α 1 [α, α]. Hence, Lemma 2 implies that buyer B will outsource his entire demand in Period 2, that is, α 2 = 1. Given that α 2 = 1, the buyer s total cost is therefore given by, π B (α 1,C S (0),1,(1 - λ)(c S (α 1 ) + ω(γα 1 )) + λc B (1-α 1 )) = [α 1 C S (0) + (1 - α 1 )C B (0) + (1 - λ)(c S (α 1 ) + ω(γα 1 )) + λc B (1-α 1 )]. The buyer s optimal choice of α 1, which minimizes the buyer s cost, is therefore the interior solution, α b (α, α), such that it satisfies the first order condition C S (0) - C B (0) + [(1 - λ){c S (α) - γρc S (γα)} - λc B (1-α)] = 0 (2) However, if α b does not exist, then α 1 * is one of the boundary points α or α. When γ or ρ is sufficiently large, the left-hand-side of (2) is positive for all α 16
(α, α) and we have α * 1 = α. We therefore deduce that α * 1 is non-increasing in γ and ρ. By a similar argument, as λ increases, the left-hand-side of (2) increases since [{- C S (α * 1 ) + γρc S (γα * 1 )} - C B (1-α * 1 )] > 0 (Lemma 1), which implies that α * 1 = α. We therefore deduce that α * 1 is non-increasing in λ. These results are summarized in Proposition 2 below. Proposition 2: In the subgame Γ α, α, the optimal decisions for buyer B are: α, if [(1 - λ){c S (α 1 ) - γρc S (γα 1 )} - λc B (1-α 1 ) - C B (0) + C S (0)] > 0, α 1 [α, α]. α 1 = α, if [(1 - λ){c S (α 1 ) - γρc S (γα 1 )} - λc B (1-α 1 ) - C B (0) + C S (0)] < 0, α 1 [α, α]. α b, if α b (α, α) such that [(1 - λ){c S (α b ) - γρc S (γα b )} - λc B (1-α b ) - C B (0) + C S (0)] = 0. P 1 * = C S (0), α 2 = 1, and P 2 * = (1 - λ)(c S (α 1 * ) + ω(γα 1 * )) + λc B (1-α 1 * ). Furthermore, α 1 * is non-increasing in γ, ρ, and λ, while P 2 * is increasing in γ, ρ, and λ. The appropriation risk τ is given by λ(c B (1-α 1 * ) - C S (α 1 * )) + (1 - λ)ω(γα 1 ). When the effect of specific learning is moderate, such that C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0), Proposition 2 shows that both the salvageability of specific learning γ and the bargaining power of supplier S (ρ and λ) affect the buyer s decision in the optimal amount to outsource α * 1. At equilibrium, since the supplier s unit cost is lower than the buyer s unit cost, the buyer chooses the buy-only strategy in Period 2. However, in Period 1, the buyer chooses the make-and-buy strategy. This is rather counter intuitive, as the buyer s unit cost is always higher than that of the supplier s in both Periods 1 and 2, that is, C S (α 1 ) + ω(γα 1 ) < C B (1-α 1 ) C S (0) and C S (0) < C B (0), which suggest that the buyer should outsource his entire requirement in both periods. 17
However, if the buyer outsources his entire requirement in Period 1, then in Period 2, the premium ω(γα 1 ) that supplier S can command outside of the specific buyer-supplier exchange relationship increases, thereby increasing the appropriation risk that the buyer faces. The appropriation risk τ = λ(c B (1-α * 1 ) - C S (α * 1 )) + (1 - λ)ω(γα 1 ), whose gradient with respect to α can be rewritten as λ(-c B (1-α * 1 ) C S (α * 1 )) + (1 - λ)(-ργ C S (γα)), is positive. The term τ is increasing in α * 1, which implies that appropriable quasi rent is increasing in the specific assets that the supplier acquires, just as Monteverde and Teece (1982) hypothesized. In addition, the appropriation risk τ is also increasing in salvageabiltiy γ, as the premium ω(γα 1 ) is increasing in γα 1 (Figure 1). Hence, while the lower cost in buying suggests that buyer B should follow a buy-only strategy in Period 1, the resulting higher bargaining outcome P * 2 and appropriation risk faced by buyer B in Period 2 suggest that buyer B should follow a make-only strategy in Period 1 instead. Taking these opposing forces into consideration, the buyer therefore optimally chooses to make-and-buy in Period 1. The buyer s production experience in Period 1 reduces the supplier s ability to engage in opportunistic bargaining (Walker and Weber, 1984), thereby reducing the bargaining outcome in price when the buyer switches to a buy-only strategy, in Period 2. As expected, the appropriation risk τ, is increasing in λ, the bargaining power of supplier S vis-à-vis buyer B, since C B (1-α * 1 ) - C S (α * 1 ) > ω(γα 1 ). As Proposition 2 also shows, the optimal proportion to buy α 1 * is nonincreasing in γ. This is because increasing salvageability of specific learning by supplier S increases the premium ω(γα 1 ) that he could command from other buyers B', thus improving his bargaining position with buyer B. A reduction in the amount outsourced, α * 1, therefore reduces the appropriable quasi rent by supplier S. Similarly, when the bargaining power of supplier S, vis-à-vis buyer B (as denoted by 18
λ) and other buyers B' (as denoted by ρ) increases, the amount that buyer B outsources in Period 1 reduces. Proposition 2 therefore implies that, under moderate specific learning effect, even though the buyer s unit cost is always higher than that of the supplier s, which suggests that the buyer should outsource his entire requirements in both Periods 1 and 2, he could do better by following the make-and-buy strategy initially. An external supplier is engaged to produce a portion of the buyer s requirements initially, which reduces as the salvageability of specific learning increases. Corollary 2 thus follows. Corollary 2: When the effect of specific learning is moderate, even though the buyer s unit cost is always higher than that of the supplier s, a buy-only strategy right from the beginning is not optimal. The buyer is better off following a make-and-buy strategy initially, reducing the quantity outsourced as the salvageability of specific learning by his supplier increases, and switches to a buy-only strategy eventually. 3.3 Low Specific Learning Effect: C S (α 1 ) + ω(γα 1 ) C S (0) < C B (1-α 1 ). When α 1 [ α, 1] (Figure 1) and Γ a,b = Γ α, 1, Lemma 2 implies that buyer B will choose α 2 = 1 and P * 2 = (1 - λ)(c S (α 1 ) + ω(γα 1 )) + λc S (0), since C S (α 1 ) + ω(γα 1 ) C S (0) < C B (1-α 1 ). Hence, in Period 1, the buyer's total cost is given by, π B (α 1,C S (0),1,(1 - λ)(c S (α 1 ) + ω(γα 1 )) + λc S (0)) = [α 1 C S (0) + (1 - α 1 )C B (0) + (1 - λ)(c S (α 1 ) + ω(γα 1 )) + λc S (0)]. The first order condition with respect to α 1 is therefore [C S (0) - C B (0) + (1 - λ)(c S (α 1 ) - γρc S (γα 1 ))], which is always negative because C S (0) < C B (0) and C S (α 1 ) - γρc S (γα 1 ) < 0 (Lemma 1). The optimal choice of α 1 is thus the boundary solution α * 1 = 1. Proposition 3 states this result. 19
Proposition 3: In the subgame Γ α, 1, the optimal decisions for buyer B are α 1 = 1, P * 1 = C S (0), α 2 = 1, and P * 2 = (1 - λ)(c S (1) + ω(γ)) + λc S (0). The optimal proportion α * 1 is independent of γ, ρ and λ, while P * 2 is increasing in γ, ρ, and λ. The appropriation risk faced by the buyer is given by τ = λ(c S (0) - C S (1)) + (1 - λ)ω(γ). Obviously, when the effect of specific learning on the buyer s cost function is low, such that it is not possible for the buyer to produce at a cost lower than the competitive market price (that is, C S (α 1 ) + ω(γα 1 ) C S (0) < C B (1 - α 1 )), the buyer optimal choice is to buy-only in both periods, regardless of the salvageability of specific learning γ and bargaining power ρ and λ. The appropriation risk that the buyer faces is limited by the low effect of specific learning. Proposition 3 therefore is consistent with the central argument of TCE that transaction specific assets gives rise to hazards of opportunism (Klein et al. 1978; and Williamson, 1979 and 1981), and hence, firms should outsource only under conditions of low asset specificity. However, although α * 1 is independent of γ, ρ, and λ, the bargaining outcome in price P * 2, and hence the appropriation risk τ, are both increasing in γ, ρ, and λ. This means that, as the supplier acquires increasing specific learning, and as the salvageability of specific learning increases, he can credibly demand an increasingly higher price in future negotiations. Corollary 3 thus follows from Proposition 3. Corollary 3: When the effect of specific learning is low, a buyer follows a buy-only strategy right from the beginning, and pays an increasingly higher price as his supplier acquires increasing specific learning and as the salvageability of specific learning by his supplier increases. 20
Corollaries 1 and 3 are in general agreement with the central thesis of TCE in that, in the long run, firms should internalize and outsource under conditions of high and low specific assets respectively, which has been extensively tested and found to possess high predictive validity (Shelanski and Klein, 1995; and Rindfleisch and Heidi, 1997). However, prior empirical research in TCE has overlooked the implications of moderate specific asset condition, under which, the salvageability of specific assets affects governance decision in terms of the optimal quantity to make vis-à-vis to buy (Corollary 2). We next examine how a buyer s decision to make, buy, or make-and-buy, changes over time as a result of learning specificity and its salvageability by the supplier. 5. Change in Governance over Time From Propositions 1, 2, and 3, we obtain Theorem 1, which states that specific learning and its salvageability by a supplier interact to affect a buyer's decision in following a make-only, a buy-only, or a make-and-buy strategy. Observe that the buyer s payoff in (3) and (5) in Theorem 1 are the same by the definition of α. Theorem 1: Depending on the parameters of the game: γ the degree of salvageability of specific learning by a supplier, ρ and λ the bargaining power of the supplier vis-à-vis other buyers B and buyer B respectively, and the effect of specific learning on the cost functions C S (α) and C B (α), one of the following is a subgame perfect equilibrium. 21
α 1 P 1 * α 2 P 2 * Π B (1) α a C S (0) 0 C B (1-α 1 * ) α a C S (0) + (1-α a )C B (0) + C B (1-α a ) (2) 0 C S (0) 0 C B (1-α 1 * ) C B (0) + C B (1) (3) α C S (0) 0 C B (1-α 1 * ) α C S (0) + (1-α)C B (0) + C B (1-α) (4) α b C S (0) 1 (1 - λ)(c S (α * 1 ) + ω(γα * 1 )) + λc B (1-α * 1 ) (5) α C S (0) 1 (1 - λ)(c S (α * 1 ) + ω(γα * 1 )) + λc B (1-α * 1 ) (6) α C S (0) 1 (1 - λ)(c S (α * 1 ) + ω(γα * 1 )) + λc B (1-α * 1 ) (7) 1 C S (0) 1 (1 - λ)(c S (1) + ω(γ)) + λc S (0) α b C S (0) + (1-α b )C B (0) + (1- λ)(c S (α b ) + ω(γα b )) + λc B (1-α b ) αc S (0) + (1-α)C B (0) + (1-λ)(C S (α) + ω(γα)) + λc B (1-α) αc S (0) + (1- α)c B (0) + (1- λ)(c S ( α) + ω(γ α)) + λc B (1- α) C S (0) + (1-λ)(C S (1) + ω(γ)) + λc B (0) From Theorem 1, it is evident that, when a buyer follows a make-and-buy strategy, he does so only for the initial period, but eventually adopts a buy-only and a make-only strategy under conditions of moderate and high specific learning effects respectively. Hence, from Theorem 1, Corollary 4 follows. Corollary 4: When a buyer follows a make-and-buy strategy, he does so only for an initial period. Eventually, he switches to a buy-only and a make-only strategy under conditions of moderate and high specific learning effects respectively. Conversely, as Theorem 1 implies, a buyer following a pure form of governance (that is, make-only or buy-only) would not change to a plural form nor another pure form, based on asset specificity considerations alone. 22
Corollary 5: When a buyer follows a make-only (buy-only) strategy, he would not switch to a buy-only (make-only) strategy or a make-and-buy strategy, based on specific learning considerations alone. Corollaries 4 and 5 thus describe and clarify how governance decision, in terms of make-only, buy-only, or make-and-buy, changes over time under different asset specificity conditions, which is an important issue that has generally been neglected by prior TCE research. Compared to earlier studies on plural governance forms (Dutta et al., 1995; Gallini and Lutz, 1992; and Weiss and Anderson, 1992), Corollary 4 shows that, a firm that follows a make-and-buy strategy will eventually switch to a buy-only and a make-only strategy when specific learning effects are moderate and high respectively. (Insert Table 1 here) Table 1 summarizes our results and illustrates the interaction effect of specific learning and its salvageability on governance decision over time. Under conditions of high and low specific learning, a buyer's decision to make-only, buy-only, or makeand-buy, is driven solely by the effect of specific learning, while the salvageability of specific learning by a supplier has no effect on the decision. However, under moderate effect of specific learning, salvageability of specific learning by a supplier reduces the amount a buyer outsources when he follows a make-and-buy strategy. 23
6. Discussion The marketability of the know-how acquired by a supplier outside of a specific buyer-supplier exchange relationship improves the supplier s bargaining position. The supplier could therefore demand a higher price in future negotiations, thereby increasing the appropriation risk that the buyer faces. A make-and-buy strategy enables a buyer to acquire production experience, which improves his bargaining position vis-à-vis his supplier s in future renegotiations. Hence, when specific learning effect is moderate, such that it is not possible for a buyer to acquire a cost advantage over his supplier through specific learning, although the buyer s optimal strategy in the long run is to outsource completely, his optimal strategy is to makeand-buy initially. This is despite the fact that it is less costly initially to outsource completely. In addition, when following the make-and-buy strategy initially, the buyer should also reduce the quantity outsourced as the salvageability of specific learning by his supplier increases. Doing so reduces the price premium that arises from the supplier s market option, thereby reducing the appropriation risk that the buyer faces in future renegotiations. On the other hand, when the effect of specific learning on cost reduction is high, such that it is possible for a buyer to acquire a cost advantage over his supplier, a make-and-buy strategy allows the buyer to capitalize on the cost savings in buying initially. At the same time, the buyer could acquire specific know-how in production for the eventual switch to the make-only strategy, when he has acquired a cost advantage over his supplier. As the buyer could (and would) credibly internalize eventually, salvageability of specific learning by the supplier therefore does not affect the buyer s outsourcing decision in this case. 24
Obviously, when the effect of specific learning on cost reduction is low, such that it is not possible for a buyer to produce at a cost lower than the competitive market price, a buy-only strategy right from the beginning is optimal. It is also obvious that, in this case, the salvageability of specific learning by a supplier would not affect the buyer s outsourcing decision. Our analysis and results contributes to the understanding of TCE and its application to governance decision-making in several research areas, which we shall next discuss. 6.1 Transaction Cost Economics and Long Term Contracts Uncertainty has been identified as a factor that affects transaction costs, and hence governance decision (Williamson; 1985), and has received much research attention (e.g. Walker and Weber, 1984 and 1987; Balakrishnan and Wernerfelt, 1986; Weiss and Anderson, 1992; and Stump and Heidi, 1996). We did not include uncertainty in our analysis. This is because we wish to show that the presence of specific learning and its salvageability by a supplier are sufficient to give rise to appropriation risk, and hence to affect governance decisions, even in the absence of uncertainty. Like Grossman and Hart (1986) and Hart and Moore (1994), we examine the implications of the hold-up problem, when a firm cannot costlessly replace an agent if the latter possesses specific human capital. However, unlike Grossman and Hart (1986) and Hart and Moore (1994), who focused on the make-or-buy decision and the optimal debt repayment path, respectively, our concern is on plural forms in terms of make-only, buy-only, or make-and-buy. 25
In our model, the appropriation risk is endogenous on specific learning and its salvageability. This ex-post cost differs from the agency cost that arises from the private information that agents have of their own productivity (Olsen, 1996). Several researchers applied the principal-agent approach in examining long term contracts (e.g., Aghion et al., 1994; Dewatripont and Maskin 1995; and Holden 1999), which were proposed as a substitute for vertical integration (e.g., Kleindorfer and Knieps 1982; and Joskow 1987). The underlying theme of the majority of the studies on long-term contracting (Aghion et al., 1994; Chung, 1991 and 1995; Dewatripont, 1988; Dewatripont and Maskin, 1995; Grout, 1984; Hart and Moore, 1988; Holden, 1999; Huberman and Kahn, 1988; and MacLeod and Malcomson, 1993) is one of ensuring an efficient level of investment when re-negotiation is possible. Compared to these studies, which followed the risk-sharing principal-agent approach, we follow the risk neutral transaction cost approach, in examining governance issues. It is worthwhile to note that Allen and Leuck (1995) reported that the transaction cost approach has a greater predictive validity than the former approach. We did not explicitly examine long term contracts between the supplier and the buyer. However, from our analysis, it can be shown that, any long-term contract that is re-negotiation and performance proof must take the form of subgame-perfect equilibrium (7) (Theorem 1) in our model, where the buyer adopts a buy-only strategy. The argument is as follows. Klein and Leffler (1981, p615) showed that a necessary and sufficient condition for (contractual) performance is the existence of price sufficiently above salvageable production costs. Applied to our model, this means that any performance assured long-term contract must satisfy the conditions that P 1 C S (0) and P 2 C S (1). These conditions are satisfied by P * 1 and P * 2 in our results, as evident from Theorem 1. It is also clear that any long-term contract that 26
appropriates all rents from the supplier, that is, P 1 = C S (0) and P 2 = C S (1), cannot be re-negotiation proof. This is because the supplier possesses a market option, which earns him a premium ω(γ) from other buyers in the market, and which arises from the transferable specific assets that he has acquired. Hence, if P 1 = C S (0) and P 2 = C S (1), unless the contract is re-negotiated, the supplier would stop or disrupt supplies in Period 2. Any long term contract that is re-negotiation proof and performanceassured must therefore necessarily satisfy the condition that (P 1 + P 2 ) > (C S (0) + C S (1)), and in particular, take the form of subgame perfect equilibrium (7) as described in Theorem 1. 6.2 Empirical Studies on TCE and Procurement In a study that examines how small numbers bargaining and appropriation concerns affect firms procurement decisions, Pisano (1990) reported that a firm s historical propensity to procure R&D internally does not affect its R&D procurement decision. In the author's study, historical propensity is measured as a ratio of the number of own, to total, R&D products in development. This suggested that the firms sampled in the author's study were following a make-and-buy strategy, which the author regarded as a hybrid mode when measuring governance responses. Our analysis suggests that combined governance forms were more appropriately viewed as plural forms, instead of hybrid modes, and that asset specificity conditions be accurately categorized into three low, moderate, and high, instead of the usual two high and low, as in Pisano s (1990) study. These are important considerations because, given that the firms sampled were following a make-and-buy strategy, Corollary 4 implies that they will eventually follow a buy-only and a make-only strategy under moderate and high asset specificity conditions respectively (Table 1). 27
Our results, which are derived theoretically, are in agreement with previous empirical findings by Masten et al. (1989) and Pisano (1990). The former reported that specific human capital has a positive and significant influence on the percentage of the component produced in-house while the latter found that small-numbers bargaining problems and the accumulation of specific technical capabilities influenced firms to internalize their R&D. These findings of theirs are in agreement with Propositions 1, 2, and 3 here, which imply that learning specificity has a positive effect on the proportion of a buyer s supply requirements that he chooses to make visà-vis to buy (Table 1). However, Masten et al. (1989) and Pisano (1990) did not examine how governance decision might change over time, or how it could be affected by the salvageability of specific human capital by the supplier. 6.3 Empirical Studies on TCE and Channels of Distribution Anderson (1985) examined how specific assets affect a firm s decision to internalize its sales function. It was reported that, when salespeople had high specific assets in their interactions with their clients, firms were more likely not to internalize their sales function. This observation, the author suggested, is contrary to basic TCE prediction. However, our analysis suggests that Anderson s observation could be explained by the asymmetry in the salvageability of specific assets by salespeople visà-vis the firms. Client related specific assets are likely to be more salvageable by the salespeople, than by the firm. Given that this is the case, Corollary 3 implies that firms are likely to outsource their entire sales function eventually, if they had started with a plural form initially. However, under sufficiently high specific asset condition, firms will internalize their entire sales function eventually (Corollary 1). 28