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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: [email protected]
** Associate Professor, Department of Decision Sciences, Faculty of Business
Administration, Bldg. 1, National University of Singapore, Business Link, Singapore 117591. E-mail: [email protected]
Copyright © Faculty of Business Administration, National University of Singapore.
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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 make-and-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
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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
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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,
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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
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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 non-
market 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,
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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
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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 Pi (≥ 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 Cj(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 CS(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
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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 Cj(q) has the following characteristics
(Figure 1).
(a) CB(α) > CS(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) CB(1) < CS(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) Cj(α) is continuous and twice differentiable, such that C’j(α) < 0 and C”j(α) > 0,
that is, Cj(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 Cj(γα) ≥ d/dα Cj(α) (j = B, S) for all γ between 0 and 1, that is, the rate of
decrease of Cj(γα) with respect to α is no more than that of Cj(α). This implies
that, if supplier S is to supply other buyers in the market, his rate of specific
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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) d2/dγ2 Cj(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 P1 is the competitive market price CS(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 Pi, supplier
S decides on whether or not to supply buyer B, while the latter chooses to outsource a
portion αi (∈ [0,1]) of his requirements to the supplier, while producing a portion (1-
αi) of the required supplies himself. That is, B decides on whether to make (αi = 0),
buy (αi = 1), or make-and-buy (αi ∈ (0,1)). Hence, (α1, P1, α2, P2) 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.
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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 CS(γα),
such that CS(0) ≥ CS(γα) ≥ CS(α) (Figure 1), to supply other buyers B' in the market at
a price PS ∈ [CS(γα), P*], where P* = CS(0). Obviously, PS cannot be less than the
production cost CS(γα) but neither can it be higher than the competitive market rate
CS(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(CS(0) - CS(γα)) (≥ 0) , by
charging PS = (ω(γα) + CS(γα)) = (1-ρ)CS(γα) + ρCS(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(CS(0) - CS(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 (CS(α)
+ ω(γα)) from buyer B (Figure 1).
The buyer B chooses a portion α (= {α1, α2}) 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
πB(α1,P1,α2,P2) = [α1P1 + (1 - α1)CB(0)] + [α2P2 + (1 - α2)CB(1-α1)], (1)
where B chooses α to minimize πB(α1,P1,α2,P2).
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A supplier’s unit profit is given by (Pi - CS(αi)), and he bargains over prices P
= {P1, P2} to maximize his payoff, which is given by πS(α) = {α1[P1 - CS(α1)] + α2[P2
– CS(α2)]}.
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 = (P2 - CS(α1)), 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.
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Lemma 1: Given γ, the curve (CS(α) + ω(γα)) is strictly decreasing in α (∈ (0, 1)),
that is, ∂/∂α [CS(α) + ω(γα)] < 0.
Using backward induction, we begin our analysis of the game from the final
period. Suppose buyer B buys α1 and makes (1 - α1) of his requirement in Period 1.
In Period 2, the unit cost of production of supplier S becomes CS(α1), 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 CS(0). The incumbent supplier S therefore has a cost
advantage over other competing suppliers in Period 2, as a result of learning
specificity, since CS(α1) < CS(0), ∀ α1 > 0.
Given the prior production experience of buyer B, his unit cost of production
in Period 2 becomes CB(1-α1). 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 CB(1-α1) or
the competitive market price CS(0), whichever is lower, that is, P2 ≤ Min[CB(1-α1),
CS(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(γα1). Hence, he can demand a price P2 ≥ (CS(α1) + ω(γα1)) from buyer B. We
observe that (CS(α) + ω(γα)) ≤ CS(0), where equality holds when α = 0. The
bargaining outcome in Period 2, P2*, is therefore bounded below by the minimum
price level (CS(α1) + ω(γα1)), if (CS(α1) + ω(γα1)) ≤ CB(1-α1), and bounded above by
the maximum price level Min[CB(1-α1), CS(0)]. That is, (CS(α1) + ω(γα1)) ≤ P2* ≤
Min[CB(1-α1), CS(0)], in which case buyer B also chooses to outsource all his
requirements in Period 2, that is, α2∗ = 1.
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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, (CS(α1) + ω(γα1)) > CB(1-α1), 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
α1 in Period 1 affects both the buyer's and the supplier's unit production cost in Period
2, and the appropriation risk τ = (P2*(α1,P1)) - CS(α1)).
Lemma 2: Given (α1, P1) as the decision choices in Period 1, the Nash equilibrium of
the subgame beginning at Period 2 is given by,
(0, CB(1-α1)), if CB(1-α1) ≤ CS(α1) + ω(γα1), (α2
*(α1,P1), P2*(α1,P1)) =
(1, (1 - λ)(CS(α1) + ω(γα1)) + λMin[CB(1-α1), CS(0)]), otherwise.
Next, we shall examine the cases when the effect of specific learning for the
buyer is (i) high, such that CB(1-α1) ≤ CS(α1) + ω(γα1), (ii) moderate, such that CS(α1)
+ ω(γα1) < CB(1-α1) ≤ CS(0), and (iii) low, such that CS(α1) + ω(γα1) ≤ CS(0) < CB(1-
α1). 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
CB(1-α1) ≤ CS(α1) + ω(γα1) for all α1 ≤ α. Note that α always exist, since CS(0) +
ω(0) = CS(0) + 0 > CB(1) but CS(1) + ω(γ) = CS(1) + ρ[CS(0) - CS(γ)] < ρ CS(0) + (1 -
ρ)CS(1) < CB(0). Hence, by the Intermediate Value Theorem, there exists an α in the
interval (0,1) such that CB(1-α) = CS(α) + ω(γα). Similarly, since CB(1 - α) < CS(0)
and CB(0) > CS(0), again by the Intermediate Value Theorem, the existence of
⎯α (∈ [α ,1]) such that CB(1 - ⎯α) = CS(0) is assured. Given that CS(α) + ω(γα) is
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decreasing in α (Lemma 1) and that CB(1-α) is increasing in α, we deduce that
CS(α1) + ω(γα1) < CB(1-α1) ≤ CS(0) for all α1 ∈ [α ,⎯α] and CS(α1) + ω(γα1) ≤ CS(0)
< CB(1-α1) for α1 ∈ (⎯α, 1). Finally, let Γa,b denote the subgame where α1 is between
a and b.
3.1 High Specific Learning Effect: CB(1-α1) ≤ CS(α1) + ω(γα1)
With reference to Figure 1, for values of α1 between 0 and α, since CB(1-α1)
≤ CS(α1) + ω(γα1), Lemma 2 implies that the buyer’s 2-period payoff is given by
πB(α1,CS(0),0,CB(1-α1)) = [α1CS(0) + (1 - α1)CB(0)] + CB(1-α1). Let αa denote the
solution to the first order condition CS(0) - CB(0) - C’B(1-α1) = 0. It is easy to check
that the second-order condition is C’B(1-α1) (> 0). Hence, the buyer’s cost is
minimized when α1 equals αa, 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 Γ0,α, the optimal decisions for buyer B are:
0, if CS(0) - CB(0) > C’B(1-α1), ∀ α1 ∈ [0, α], α1
* = α, if CS(0) - CB(0) < C’B(1-α1), ∀ α1 ∈ [0, α], αa, if ∃ αa ∈ (0, α) such that CS(0) - CB(0) - C’B(1-αa) = 0.
P1
* = CS(0), α2∗ = 0, and P2
* = CB(1-α1*). Furthermore, α1
*, α2*and P1
*, P2* are
independent of γ, ρ, and λ. The appropriation risk faced by the buyer is τ = (CB(1-
α1*) - CS(α1
*)).
As Proposition 1 shows, when the effect of specific learning on the buyer’s
cost is high, such that CB(1 - α1) ≤ CS(α1) + ω(γα1) ≤ CS(0), the optimum choice of α∗
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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 = (CB(1-α1*) - CS(α1
*)). 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 αa (∈ (0, α)) such that the gradient of the buyer’s cost
function at (1 - αa) equals CB(0) - CS(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 CB(1
- α) is greater than CB(0) - CS(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
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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: CS(α1) + ω(γα1) < CB(1-α1) ≤ CS(0)
For the subgame Γa,b = Γα,⎯α, where the specific learning effect is moderate,
the minimum price demanded by supplier S (= CS(α1) + ω(γα1)) in Period 2 is less
than buyer B’s production cost, that is, CS(α1) + ω(γα1) < CB(1-α1) ≤ CS(0) for values
of α1 ∈ [α,⎯α]. Hence, Lemma 2 implies that buyer B will outsource his entire
demand in Period 2, that is, α2∗ = 1. Given that α2
∗ = 1, the buyer’s total cost is
therefore given by, πB(α1,CS(0),1,(1 - λ)(CS(α1) + ω(γα1)) + λCB(1-α1)) = [α1CS(0) +
(1 - α1)CB(0) + (1 - λ)(CS(α1) + ω(γα1)) + λCB(1-α1)]. The buyer’s optimal choice of
α1, which minimizes the buyer’s cost, is therefore the interior solution, αb ∈ (α,⎯α),
such that it satisfies the first order condition
CS(0) - CB(0) + [(1 - λ){C’S(α) - γρC’S(γα)} - λC’B(1-α)] = 0 (2)
However, if αb does not exist, then α1* 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 ∈
17
(α,⎯α) and we have α1* = α. We therefore deduce that α1
* is non-increasing in γ and
ρ. By a similar argument, as λ increases, the left-hand-side of (2) increases since [{-
C’S(α1*) + γρC’S(γα1
*)} - C’B(1-α1*)] > 0 (Lemma 1), which implies that α1
* = α.
We therefore deduce that α1* is non-increasing in λ. These results are summarized in
Proposition 2 below.
Proposition 2: In the subgame Γα,⎯α, the optimal decisions for buyer B are:
α, if [(1 - λ){C’S(α1) - γρC’S(γα1)} - λC’B(1-α1) - CB(0) + CS(0)] > 0, ∀ α1 ∈ [α,⎯α].
α1
∗ = ⎯α, if [(1 - λ){C’S(α1) - γρC’S(γα1)} - λC’B(1-α1) - CB(0) + CS(0)] < 0, ∀ α1 ∈ [α,⎯α].
αb, if ∃ α b ∈ (α,⎯α) such that [(1 - λ){C’S(αb) - γρC’S(γαb)} - λC’B(1-α b) - CB(0) + CS(0)] = 0.
P1* = CS(0), α2
∗ = 1, and P2* = (1 - λ)(CS(α1
*) + ω(γα1*)) + λCB(1-α1
*). Furthermore,
α1* is non-increasing in γ, ρ, and λ, while P2
* is increasing in γ, ρ, and λ. The
appropriation risk τ is given by λ(CB(1-α1*) - CS(α1
*)) + (1 - λ)ω(γα1∗).
When the effect of specific learning is moderate, such that CS(α1) + ω(γα1) <
CB(1-α1) ≤ CS(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 α1*. 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, CS(α1) + ω(γα1) < CB(1-α1) ≤ CS(0) and CS(0) < CB(0),
which suggest that the buyer should outsource his entire requirement in both periods.
18
However, if the buyer outsources his entire requirement in Period 1, then in
Period 2, the premium ω(γα1) 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(CB(1-α1*) - CS(α1
*)) + (1 -
λ)ω(γα1∗), whose gradient with respect to α can be rewritten as λ(-C’B(1-α1
*) –
C’S(α1*)) + (1 - λ)(-ργ C’S(γα)), is positive. The term τ is increasing in α1
*, 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(γα1) is
increasing in γα1 (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 P2* 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 CB(1-α1*) - CS(α1
*) > ω(γα1∗).
As Proposition 2 also shows, the optimal proportion to buy α1* is non-
increasing in γ. This is because increasing salvageability of specific learning by
supplier S increases the premium ω(γα1) that he could command from other buyers B',
thus improving his bargaining position with buyer B. A reduction in the amount
outsourced, α1*, 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
19
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: CS(α1) + ω(γα1) ≤ CS(0) < CB(1-α1).
When α1 ∈ [⎯α, 1] (Figure 1) and Γa,b = Γ⎯α, 1, Lemma 2 implies that buyer B
will choose α2 = 1 and P2* = (1 - λ)(CS(α1) + ω(γα1)) + λCS(0), since CS(α1) + ω(γα1)
≤ CS(0) < CB(1-α1). Hence, in Period 1, the buyer's total cost is given by,
πB(α1,CS(0),1,(1 - λ)(CS(α1) + ω(γα1)) + λCS(0)) = [α1CS(0) + (1 - α1)CB(0) + (1 -
λ)(CS(α1) + ω(γα1)) + λCS(0)]. The first order condition with respect to α1 is
therefore [CS(0) - CB(0) + (1 - λ)(C’S(α1) - γρC’S(γα1))], which is always negative
because CS(0) < CB(0) and C’S(α1) - γρC’S(γα1) < 0 (Lemma 1). The optimal choice
of α1 is thus the boundary solution α1* = 1. Proposition 3 states this result.
20
Proposition 3: In the subgame Γ⎯α, 1, the optimal decisions for buyer B are α1∗ = 1,
P1* = CS(0), α2
∗ = 1, and P2* = (1 - λ)(CS(1) + ω(γ)) + λCS(0). The optimal proportion
α1* is independent of γ, ρ and λ, while P2
* is increasing in γ, ρ, and λ. The
appropriation risk faced by the buyer is given by τ = λ(CS(0) - CS(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, CS(α1) + ω(γα1) ≤ CS(0) < CB(1 - α1)), 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 α1* is independent of γ, ρ, and λ, the bargaining outcome
in price P2*, 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.
21
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 CS(α) and CB(α), one of the following is a subgame
perfect equilibrium.
22
α1
∗
P1
*
α2∗
P2
*
ΠB
(1)
αa
CS(0)
0
CB(1-α1
*) αaCS(0) + (1-αa)CB(0) + CB(1-αa)
(2)
0
CS(0)
0
CB(1-α1
*) CB(0) + CB(1)
(3)
α
CS(0)
0
CB(1-α1
*) α CS(0) + (1-α)CB(0) + CB(1-α)
(4)
αb
CS(0)
1
(1 - λ)(CS(α1
*) + ω(γα1
*)) + λCB(1-α1*)
αbCS(0) + (1-αb)CB(0) + (1-λ)(CS(αb) + ω(γαb)) + λCB(1-αb)
(5)
α
CS(0)
1
(1 - λ)(CS(α1
*) + ω(γα1
*)) + λCB(1-α1*)
αCS(0) + (1-α)CB(0) + (1-λ)(CS(α) + ω(γα)) + λCB(1-α)
(6)
⎯α
CS(0)
1
(1 - λ)(CS(α1
*) + ω(γα1
*)) + λCB(1-α1*)
⎯αCS(0) + (1-⎯α)CB(0) + (1-λ)(CS(⎯α) + ω(γ⎯α)) + λCB(1-⎯α)
(7)
1
CS(0)
1
(1 - λ)(CS(1) + ω(γ)) + λCS(0)
CS(0) + (1-λ)(CS(1) + ω(γ)) + λCB(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.
23
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 make-
and-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.
24
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 make-
and-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.
25
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.
26
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 P1 ≥ CS(0) and P2 ≥ CS(1). These conditions are satisfied by P1* and P2
* in our
results, as evident from Theorem 1. It is also clear that any long-term contract that
27
appropriates all rents from the supplier, that is, P1 = CS(0) and P2 = CS(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 P1 = CS(0) and P2 = CS(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 performance-
assured must therefore necessarily satisfy the condition that (P1 + P2) > (CS(0) +
CS(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).
28
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 vis-
à-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 vis-
à-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).
29
Integrating channel distribution theory and ecology theory of organizational
change, Weiss and Anderson (1992) examined a firm’s intention to change from one
pure form of governance to another. The authors reported that there was considerable
inertia shown by firms in changing from a rep to a direct sales force, which they
attributed to managerial perceptions of high switching costs. Weiss and Anderson
(1992, p110) concluded that, “we provide one explanation for why specific
distribution channel arrangements do not change as readily as prior theory may
suggest”. On the contrary, our analysis shows that the arguments based on TCE alone
are sufficient to explain why firms do not change readily from one pure form to
another, as given by Corollary 5.
7. Conclusion
While this paper has provided some insights and a more precise understanding
of the effect of specific asset and its salvageability on governance decisions over time,
there are several limitations that are worth noting. We have not considered reputation
effects, which may deter players from opportunistic behaviors (Klein and Leffler
1981). The issue of collusion among suppliers has been also omitted. However,
given that collusion is illegal in many countries, this is a reasonable omission. Of the
many types of specific assets identified (e.g., Klein et al. 1978; Williamson 1981; and
Nooteboom 1993a), we have focused only on one type of specific assets, that is,
specific human capital. Future studies could investigate the impact of the various
types of specific assets on governance decisions. Although Williamson (1979, p245)
stressed that “the object is to economize on the sum of production and transaction
costs”, few studies have examined the combined effects of both these costs on
governance decisions (Rindfleisch and Heidi, 1997). An analysis of the impact of
30
both production and transaction costs on plural forms is another direction for future
research.
Rindfleisch and Heidi (1997, p50) noted that "though a large body of
empirical evidence has been generated on the use of various governance mechanisms,
a discriminating theory of governance choice is still at an early stage of
development." Towards this end, our paper is a modest attempt. However, we have
only examined plural forms in terms of make, buy, and make-and-buy, and showed
that the standard arguments of TCE are sufficient to explain such forms. The ability
of TCE to explain other plural forms like franchising, joint ventures and licensing
appears promising as another direction for future research. Finally, another logical
extension would be to conduct an empirical verification of the theoretical propositions
derived in this study.
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Figure 1: Impact of Specific Learning on Unit Cost
CS(α) CB(1-α) CB(0) CS(0) CB(1-α) (CS(α) + ω(γα)) Curve ω(γ) CS(γα) CB(1) CS(γ) CS(α) CS(1) ω(0) α 0 α ⎯α 1
35
Table 1: Impact of Specific Learning and its Salvageability on Decision to Make, Buy, or Make-and-Buy
Specific Learning Effect
Low:
Case(iii) CS(α1) + ω(γα1) ≤ CS(0) < CB(1-α1)
Moderate: Case(ii)
CS(α1) + ω(γα1) ≤ CB(1-α1) ≤ CS(0)
High: Case(i)
CB(1-α1) ≤ CS(α1) + ω(γα1) ≤ CS(0)
High
Salvage-ability
Make-and-Buy
Followed by Buy-Only
α1
∗ ∈ {α, αb⎯,α} such that α < αb <⎯α
α2
∗ = 1
Low
Salvage-ability
Buy-Only
α1∗ = 1
α2∗ = 1
Make-and-Buy
Followed by Buy-Only
α1
∗∗ ∈ {α, αb⎯,α} such that α < αb <⎯α
α2
∗ = 1
α1∗ < α1
∗∗
Make-and-Buy Followed by
Or Make-Only Followed by Make-Only
α1
∗ ∈ {0, α, αa} such that 0 < αa < α
α2
∗ = 0
36
Appendix
Proof of Lemma 1 d/dα (CS(α) + ω(γα)) = d/dα (CS(α) + ρCS(0) - ρCS(γα))
= CS’(α) - ργ CS’(γα) < CS’(γα) - ργ CS’(γα) (as given by (d) on Page 8) = (1 - ργ) CS’(γα) < 0.
Hence, CS(α) + ω(γα) as defined by CS(α) - ρCS(γα) + ρCS(0) has a negative derivative with respect to α, and is therefore decreasing in α. Proof of Lemma 2
In Period 2, B chooses (α2(α1,P1), P2(α1,P1)) to maximize his current period payoff, which is given by [α2P2 + (1 - α2)CB(1-α1)]. If CB(1-α1) ≤ CS(α1) + ω(γα1), then B will never buy from S in Period 2. If however, CB(1-α1) > CS(α1) + ω(γα1), the buyer will outsource his entire requirement to the supplier S. The existence of an outside option ω(γα1) implies that P2 is bounded below by CS(α1) + ω(γα1), and bounded above by Min{CB(1-α1), CS(0)}. The Nash bargaining solution is therefore as given in the statement of the lemma.
Proof of Proposition 1 Since CB(1 - α1) ≤ CS(α1) + ω(γα1) ≤ CS(0), ∀ α1 ∈ [0, α], Lemma 2 implies
that α2 = 0. The buyer’s payoff can then be simplified as πB(α1,CS(0),0,CB(1-α1)) = [α1CS(0) + (1 - α1)CB(0)] + CB(1-α1). It is then easy to show that πB(α1,CS(0),0,CB(1-α1)) is minimized at αa, if it exists, such that C’B(1-α1) = CS(0) - CB(0), or at one of the boundary points, 0 or α.
Substituting the solutions P2* = CB(1-α1*) and α1* into τ = (P2 - CS(α1)), it
follows that τ = (CB(1-α1*) - CS(α1
*)).
Proof of Proposition 2 Since CS(α1) + ω(γα1) < CB(1-α1) ≤ CS(0), ∀ α1: α < α1 ≤ ⎯α, it is
straightforward to deduce from Lemma 2 that the buyer will choose α2 = 1. Hence, in Period 1, the optimal proportion to outsource to the same supplier α1 is selected to minimize the total cost, given by, πB(α1,CS(0),1,(1 - λ)(CS(α1) + ω(γα1)) + λCB(1-α1)) = [α1CS(0) + (1 - α1)CB(0) + (1 - λ)(CS(α1) + ω(γα1)) + λCB(1-α1)]. The optimal choice for α1 is thus the interior turning point αb, if it exists, or one of the boundary points α or⎯α.
When γ or ρ is sufficiently large, the first-order-condition of πB(α1,CS(0),1,(1 - λ)(CS(α1) + ω(γα1)) + λCB(1-α1)) is positive for all α ∈ (α,⎯α) and we have α1
* = α. We therefore deduce that α1
* is non-increasing in γ and ρ. By a similar argument, as λ increases, the first-order-condition increases since [{-C’S(α1
*) + γρC’S(γα1*)} -
C’B(1-α1*)] > 0 (Lemma 1), which implies that α1
* = α. Hence, we deduce that α1* is
non-increasing in λ.
37
Proof of Proposition 3 Since CS(α1) + ω(γα1) ≤ CS(0) < CB(1-α1),∀ α1:⎯α < α1 ≤ 1, it is
straightforward to deduce from Lemma 2 that the buyer will choose α2 = 1 and P2* =
(1 - λ)(CS(α1) + ω(γα1)) + λCS(0). Hence, the buyer’s objective function becomes, πB(α1,CS(0),1,(1 - λ)(CS(α1) + ω(γα1)) + λCS(0)) = [α1CS(0) + (1 - α1)CB(0) + (1 - λ)(CS(α1) + ω(γα1)) + λCS(0)], for which the first order condition is given by [CS(0) - CB(0) + (1 - λ)(C’S(α1) - γρC’S(γα1))], which is always negative (Lemma 1). Hence, the minimum point is the right end-point, that is, α1
* = 1.
Proof of Theorem 1 Let Δa,b denote the subgame perfect equilibrium of the subgame Γa,b, that is,
Δa,b is of the form (α1, P1, α2(α1,P1), P2(α1,P1)). We know from Propositions 1, 2, and 3 that the subgame perfect equilibrium of the game Γ is given by,
The subgame perfect equilibria (1), (2) and (3) follows from Proposition 1, while the subgame perfect equilibria (4), (5) and (6) are results of Proposition 2. Finally, subgame perfect equilibrium (7) is a direct result of Proposition 3.
).(minarg1,,,0 ,,
* Δ=ΔΔΔΔ=Δ
Bπαααα