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.

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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