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A Principal-Agent Model for Product Specification and
Production
Ananth V. Iyer, Leroy B. Schwarz
Krannert School of Management, Purdue University, West Lafayette, IN 47907
and
Stefanos A. Zenios
Graduate School of Business, Stanford University, Stanford, CA 94305
Abstract1
This paper develops and analyzes a principal-agent model for product specification
and production motivated by “core buying” decisions at Ford Motor Company. This model
focuses on two important elements of the “core” buyer’s responsibility: (1) assessing the
supplier’s capability and (2) allocating some or all of a fixed level of some buyer-internal
resource to help the supplier. Under the contracting scheme we model, the buyer (a principal
whom we call “she”) delegates the majority of product-specification and production activity
to the supplier (an agent whom we call “he”), but retains the flexibility to commit a given,
observable amount of an internally-available resource (e.g., engineering hours) to help the
supplier. The supplier, in turn, allocates his resource (e.g., engineering hours) to produce
the finished product. As in the motivating scenario, both the supplier’s resource allocation
and capability are assumed to be hidden from the buyer. Hence, the principal’s problem
is to determine a menu of (resource-commitment, transfer-price) contracts to minimize her
total expected cost. Drawing on known results from information economics, we identify two
cost structures - “substitutes” and “complements” - and provide the corresponding optimal
“screening” contract. Our contribution is, first, to formulate the product-specification and
production problem as a principal-agent model; second, and more important, to illustrate
the strategic value of a buyer’s level of involvement in the supplier’s production process in
reducing agency losses. In other words our analysis provides one answer to the question:
“Why would/should a buyer provide physical, financial, or intellectual resources to help
a supplier?” The answer: Because the offer of such help during the contracting process
can provide otherwise hidden information about supplier capability. We then describe two
applications of the model - one in inventory management and one in pharmaceutical drug
discovery - to illustrate its applicability and versatility. Finally, we use insights from the
model to suggest hypotheses for empirical study.
June 2001; April 2002
1
The authors have benefited from discussions with Erica Plambeck, Charlie Fine, and Steve Eppinger. Iyer
and Schwarz acknowledge the financial support of the Ford Foundation. Zenios’ research was supported by
the National Science Foundation grant SBER-9982446. An earlier version of this paper was titled “Screening
Contracts for Product and Process Development: A Principal-Agent Model.”
1
Introduction
“Times have changed since Henry Ford made the River Rouge complex in
Dearborn, Michigan, into the ultimate in vertical integration, with iron ore going in at one end and shiny model A’s coming out the other. Now vertical
dis-integration is the order of the day - in autos, in handheld computers, in pharmaceuticals, in ink-jet printers, in health care, in cameras.....” Forbes, April 30,
2001
“Good-bye mergers and acquisitions. In a global market tied together by the
internet, corporate partnerships and alliances are proving a more productive way
to keep companies growing.” Forbes Best of the Web, May 21, 2001
Outsourcing and partnering are changing the nature of companies’ organizational
charts and providing a new source for competitive advantage: the ability to form and manage
effective buyer-supplier relationships. In the automobile industry, for example, Chrysler
outsources over 80% of the parts it assembles into cars; Ford, over 65%, and GM, over 55%.
Cisco System partners provide final assembly for almost half of its switches and routers.
Nearly 80% of Kodak’s reloadable cameras are sourced in Asia, while nearly all of HP’s
printers are made by someone else.
In this paper, we present and analyze a buyer-supplier model for product specification and production motivated by decisions made by “core” buyers at Ford Motor Company.
Each of Ford’s approximately 350 core buyers is responsible for overseeing the relationship
between Ford and one or more of its approximately 1150 suppliers for the component parts or
systems (e.g., brake pedals, seats, car audio systems) that are assembled into Ford products.
More specifically, core buyers are responsible for assessing the capability of each supplier;
negotiating specifications, prices and quantities; and allocating Ford-internal product-design
and/or process-engineering resources to help the supplier in product design, process engineering, etc. These Ford-internal resources are provided at no cost. However, the amount of
these resources available for a given vehicle-development program, and, hence, to any core
buyer, is fixed.
Our model focuses on two important elements of the core buyer’s responsibilities: (1)
assessing the capability of the supplier and (2) allocating some or all of a fixed level of some
available buyer-internal resource to help the supplier. As prescribed by our model, and, as
2
confirmed in practice, the associated decisions are linked. To illustrate, consider the Ford
core buyer responsible for the Sony “head unit”, which is one component of a car audio
system. The ”head unit” fits into the dashboard and provides source selection and control,
one or more sources (tuner, CD, cassette), and speaker control. Ford product designers will
have prepared an initial set of physical, environmental (e.g., heat, vibration), and audio
specifications. The buyer (Ford) and supplier’s (Sony’s) joint goal is to transform the initial
specifications into a finished head unit.
Buyers typically have several different types of resources to help suppliers in transforming specifications into finished components and systems. Our model considers a single
resource, which we will arbitrarily label “engineering-hours” for the purpose of this example. The Ford core buyer may deploy these engineering-hours in many different ways; for
example: (1) to improve the initial design; (2) to cooperate with the supplier in the transformation process; or (3) to working independently, but in parallel with the supplier. To
illustrate: Ford’s engineering-hours might be employed to improving the initial design by
using existing standards (e.g.,the GAP standard dashboard cutout for head units), by eliminating/minimizing conflicts in the initial specifications (e.g., size and features), by applying
design-for-manufacturing techniques, or by improving the communication of a given initial design (e.g., oral description versus written description versus digital files). Or, Ford’s
engineering-hours might be employed to cooperate with the supplier by testing prototypes
in increasingly-sophisticated ways (e.g., CAD simulation) and providing the corresponding
results to the buyer. Finally, Ford might employ its engineering hours independently, in parallel with the supplier’s engineering-hours, on one or more of the steps in the transformation
process.
Regardless of the nature of the buyer’s available engineering-hours or how they are
employed, the nature of the real-world buyer-supplier relationship is complex and interactive.
We model this as a (necessarily simple) process that evolves as follows: the buyer commits
herself to a given, observable number of some available resource, x1 . As in the motivating
example, our analysis assumes that a fixed number of units, R, is available; i.e., x1 ≤ R. The
supplier will then allocate a portion of his own resource, x2 , to the transformation process.
3
Our analysis takes an agency perspective, wherein the buyer (Ford) is the principal who uses
the supplier (Sony) as an agent to produce the system (head unit) according to the buyer’s
specifications. Unlike the classical principal-agent model, however, the principal provides her
own resources, x1 , to reduce total cost. Further, as in the motivating scenario, the supplier’s
resource allocation, x2 , and φ, the supplier’s capability2 to perform the transformation given
x1 and x2 , are hidden from the buyer; the model refers to the buyer’s decision as “resource
commitment” and to the supplier’s decision as “resource allocation” to reflect the assumption
that the former is observable by both parties while the latter is not.
The buyer’s objective is to minimize her total cost, which will include the supplier’s
cost of production plus an agency cost (or information rent) caused by the information
asymmetry. Our analysis explores different contract mechanisms that attempt to achieve this
goal. In the simplest mechanism, referred to as the single resource-commitment contract,
the buyer specifies a single resource-commitment level and a transfer price to be paid to the
supplier. Because the buyer wants the supplier to accept this contract, she offers a price that
is high enough to secure the participation of the least capable supplier. Furthermore, she
uses all her resources because that minimizes the transfer price. As a result, the resources
provided by both parties coincide with first-best, but all the surplus generated from cost
minimization is retained by the supplier; supplier surplus is defined as the difference between
the supplier’s production cost and the payment he receives from the buyer.
The second contracting mechanism is a resource-commitment screening contract. Here
it is assumed that the buyer proposes a menu of resource commitment contracts and transfer prices, whereby each commitment level in the menu is tailored to a supplier of certain
capability. The supplier will reveal his capability by the choice he will make. Truthful revelation of the supplier’s capability is achieved by offering a price that includes an information
rent that is increasing in the supplier’s capability. Our analysis shows that the nature of
2
One has to be careful about the interpretation of capability within the context of our model. Our
intended interpretation is that the supplier is capable to pursue the task at hand but at a cost that is not
completely known to the buyer. That is, capability refers to the supplier’s ability to complete the desired
task at low cost.
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the optimal contract depends on the interaction between the buyer’s resource commitment
and the supplier’s capability. Specifically, we consider two cases: One of complements, and
a second one of substitutes. Mathematically, the complements (substitutes) case assumes
that increasing the buyer’s resource commitment (e.g., engineering hours) not only lowers
the total cost, but it also increases (decreases) the cost advantage enjoyed by a more capable supplier relative to a less capable one. In the complements case, the optimal contract
menu includes variations in the resource commitments offered wherein more capable suppliers choose a higher level of buyer resource commitment, and, in exchange receive a higher
information rent. By contrast, in the substitutes case, the contract coincides with the single
resource-commitment contract.
From a conceptual perspective, perhaps our most restrictive assumption is that the
resource available to the buyer is fixed (e.g., x1 ≤ R) and that the resources invested are
costless to the supplier. However, this represents reality at Ford and many other companies.
Nonetheless, it should be noted that in some instances the Ford-internal resource must be
shared among two or more components or systems, and/or allocated among two or more
suppliers, and/or shared by two or more core buyers. Therefore, although direct costs are
not associated with R, opportunity costs are. Except in some parametrization, incorporating
this cost prohibits the development of our propositions. Despite this limitation, our results
are not trivial - in particular, the optimal screening contract does not necessarily use all
available resources. That is, while buyer resources are assumed costless in the first-best
case, they become costly in the principal-agent scenario because of their effect on information
rents.
The basic model presented here has been motivated by the Ford-Sony example, and
we will revisit this example in explaining and interpreting our analytical results, in interpreting practice through the “eyes” of our results, and in offering hypotheses for further
study. However, it should be noted that our model is quite general. In particular, x1 can be
any observable buyer resource (e.g., equipment, capital); x2 can be any “hidden” supplier
investment (e.g., dollars, time), and φ can be any “hidden” supplier capability. For example, the model analyzed here could be used in interpreting the well-know Japanese practice
5
Industry/Activity
Auto Parts
Buyer Resource Commitment Supplier Resource Allocation
Concept (Ford)
Design, Manufacture
(Johnson Controls)
Pharmaceuticals
Drug Development
Scale up and
Manufacturing
(Merck, Pfizer)
Manufacturing (Catalytica)
Pharmaceuticals
Basic Research
Research, Testing
Contract Research
(Merck, Pfizer)
(Covance, Quintiles)
IT Hardware
Concept (Cisco)
SubAssembly, Final
Assembly (Solectron)
Food and Beverage
Brand Management
Bottling, Distribution
(Coca Cola, Redox)
(Bottlers, Korex)
Financial Services
Product, Service Design
Transactions
(PNC, First Union)
(MBNA)
Dot.Com Business
Business Plan
Transactions
Processing and CRM
Table 1: Possible applications of our model.
of “shukko”, under which buyers temporarily transfer employees to work for their suppliers. Table 1 presents several other possible applications of our basic model and proposes
alternative interpretations for buyer and supplier resources.
Literature Review. We are unaware of any studies that examine “product specification and production” from our general, normative perspective. Nonetheless, our models
and analysis are firmly based in the broad area of product development. For example, our
model is related to many of those reviewed by Krishnan and Ulrich (2001). Although their
review is restricted to development projects within a single firm, Krishnan and Ulrich’s
perspective, like ours, is focused on decision making. Further Krishnan and Ulrich’s four
categories of decisions -“concept development”, “supply chain design”, “product design”,
and “production ramp-up and launch” - are quite similar to our model’s two main decision
variables, if both concept development and supply chain design are viewed as part of product
specification (see the examples in Table 1). An interesting backdrop for our model and its
results is also provided by Clark’s study (1989) of parts strategy and supplier involvement
in product development in the world auto industry provides. In fact, it will be argued in
section 5 that our analysis sheds some light to Clark’s empirical findings.
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Agency Models in Managing Buyer-Supplier Relationships. To the best of
our knowledge, Reyniers and Tapiero were the first to model the buyer-supplier relationship
from an operations management perspective. In particular, in (1995a) they model a buyer
and supplier as players in a zero-sum game, wherein the supplier can control the effort invested in the delivery of quality and the buyer may or may not inspect incoming materials.
Reyniers and Tapiero (1995b) examines a similar relationship and models the effect of contract parameters such as price rebates and after-sales warranty cost on the choice of quality
by the supplier.
Kim (2000) examines a buyer-supplier relationship in which the buyer subsidizes supplier effort to reduce cost, thereby increasing channel profit. Baiman, Fischer, and Rajan
(2001) employ an agency model in a buyer-supplier relationship to examine contracting issues with respect to internal and external failures. Their results indicate that in choosing
a product architecture (e.g., bill of material), the buyer should consider both manufacturability and its implications for contractibility and efficiency in managing the buyer-supplier
supply chain.
Liron (1999) examines a joint product-process development contract in a two-party
supply chain similar to our’s and provides sharp insights by considering both a static and
a dynamic model. His analysis focuses on the free-rider problem (that is, when one party
provides less than the desired input because he knows that the other party will cover for
the difference) but it does not consider information asymmetry or contractual limitations.
Whang (1992) develops a game-theoretic model in which an outside contractor is hired to
develop a software for a buyer. That paper shares some common features with our model.
Specifically, like the supplier in our model, the developer of the software in the Whang model
has private information about the production cost. However, in the Whang model the buyer
cannot influence the supplier’s cost by her actions. In fact, one can view our work as a
hybrid that includes features of the Liron model (joint product-process development by two
parties) and of the Whang model (better informed supplier). We believe that both features
are essential to the problem.
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Agency Models in Supply-Chain (Production and Inventory) Management.
Cachon (1998) reviews the literature on supply-chain management from an agency perspective. Corbett and Tang (1998) provide a framework for addressing several questions related
to contracting under asymmetric information. More recently, Van Miegham (1999) examines
three types of contracts between a manufacturer and a subcontractor in a two-stage, twomarket game involving the determination of capacity and production to satisfy stochastic
customer demand. Cachon and Lariviere (1999) use an agency model to examine truthtelling mechanisms involving capacity choice and inventory-allocation policies for a single
supplier and several buyers (i.e., retailers) facing stochastic demand. Cachon and Zipkin
(1999) examine cooperative and competitive inventory policies in a two-stage serial supply
chain facing stochastic demand. Corbett (2001) examines (Q,R) inventory management using an agency model. Corbett and de Groot (2000) and Ha (2001) study optimal quantity
discount policies with information asymmetry. Like our model, their models assume the
supplier has private information about the marginal cost of production.
Agency Models in Economics. The analytical underpinnings for our work are
provided by the principal-agent paradigm. An introductory description of the basic model
is given in Mas-Colell, Whinston, and Green (1995), where its two main variations are
described: hidden action (moral hazard) where the agent’s actions are unobservable, and
hidden information (adverse selection) where the agent has private information about the
difficulty of the task he is to perform on behalf of the principal. The hidden information scenario (which is the one we consider here) generates the so-called mechanism design problem:
design a mechanism that will induce the agent to reveal his private information. Chapter
7 of Fudenberg and Tirole (1991) analyzes the mechanism design problem and provides
numerous references. A more advanced treatment of the topic is provided in Wilson (1995).
The remainder of this paper is organized as follows. Section 2 presents the principalagent model for product specification and production, and the analysis is presented in section
3. Section 4 presents two applications of our model, one in supply chain management and
the second one in pharmaceutical research and development. Section 5 present the main
managerial insights and section 6 provides the concluding remarks. Proofs for the main
8
results are provided in the Appendix.
2
The Principal-Agent Model
In this section, we present a principal-agent model for product specification and production.
The model assumes that the buyer (a principal whom we will refer to as “she”) will purchase
a product from a supplier (an agent whom we will refer to as “he”). The buyer delegates the
majority of product specification and production activities to the supplier, but she retains
some limited and discretionary involvement in the supplier’s activities. The parameters of
the relationship include a technological component that describes the product specification,
production process, and the production-cost function; and an economic component that
specifies the interaction between the two parties.
The technological component assumes that the production cost, which is incurred by
the supplier, depends on the resource commitment made by the buyer x1 , the supplier’s
allocated resource x2 , and the supplier’s capability φ ∈ [φ, φ]. The resources provided by
the two parties are not necessarily measured in the same units. The total production cost
will be denoted by V (x1 , x2 , φ) and is assumed to be decreasing in x1 and φ and to be jointly
convex in x1 and x2 ; that is, φ denotes the least-capable supplier and φ the most-capable
one. In addition, it is assumed that x1 is constrained such that
0 ≤ x1 ≤ R.
(1)
Supplier resources may also be constrained, but this is not recognized explicitly in the model
since the primary objective of the analysis is to study the role of buyer resource commitment
as in the Ford motivating example. For concreteness, the reader can conceptualize x1 as the
buyer resources committed to product specification, and x2 as the supplier resources allocated
to complete product specification and to production. However, different interpretations for
the two decision variables can be valid. Table 1 (in Section 1) provides other examples.
The economic component specifies the sequence of events that underlies the interaction
between the buyer and the supplier, and the information asymmetry. The buyer is the leader
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and the supplier is the follower. In addition, the supplier’s capability is only observable by
the supplier, but not by the buyer. The buyer’s beliefs about the supplier’s capability are
reflected in her prior: π(φ). The economic interaction between the two parties evolves as
follows: The buyer moves first and offers a contract. Because the model reflects an adverseselection problem, the contract is a menu that consists of buyer resource commitment and
corresponding transfer price. In the second step, the supplier chooses among all options
offered the pair (of resource commitment and price) that maximizes his total payoff. In the
final step, the buyer provides the resource commitment chosen by the supplier, the supplier
chooses his resource allocation, incurs the cost, and delivers the final product to the buyer.
Finally, the buyer pays the supplier.
According to the revelation principle, it is sufficient to focus on contracts in which the
supplier will reveal his capabilities by the option choice he makes. Therefore, it is convenient
to index each option in the contract according to the type of the supplier that will choose it.
That is, the menu of options will consist of pairs t(φ) and x1 (φ), where t(φ) is the transfer
price paid to the supplier that chooses resource commitment option x1 (φ).
The basic problem to be studied is: Determine a menu of contracts (x1 (φ), t(φ))φ∈[φ,φ] to
minimize the buyer’s total expected cost
Z
φ
π(φ)t(φ)dφ,
(2)
φ
subject to the incentive-compatibility constraint; i.e., that a supplier of type φ will choose
buyer resource-commitment level x1 (φ),
t(φ) − min V (x1 (φ), x2 , φ) ≥ t(φ̂) − min V (x1 (φ̂), x2 , φ) for all φ̂ ∈ [φ, φ],
x2
x2
(3)
and the participation constraint; i.e., that the supplier’s payoff will exceed the prevailing
expected payoff in the marketplace
t(φ) − min V (x1 (φ), x2 (φ), φ) ≥ u for each φ ∈ [φ, φ];
x2
¯
(4)
For brevity of notation, define the induced cost function Ṽ (x1 , φ) = minx2 V (x1 (φ), x2 , φ)
and assume that the monotonicity of the total cost with respect to x1 is preserved such
10
that Ṽx1 (x1 , φ) < 0. Note that the incentive-compatibility constraint, (3), and participationconstraint, (4), assume that the supplier will choose his resource allocation x2 only after
he decides which pair (x1 (φ), t(φ)) to select. This reflects the implicit assumption that the
supplier has the flexibility to allocate his resources at the last stage of the interaction.
The buyer’s committed resource, x1 , is assumed to be costless to the buyer and to
decrease the supplier’s production cost. There are three reasons behind this assumption:
First, the main objective of our analysis is to examine mechanisms that the buyer can
utilize in order to reduce the “agency costs” in the buyer-supplier relationship. As we
will demonstrate, buyer resources can provide a mechanism to efficiently screen suppliers of
different capabilities. By assuming these resources to be costless to the buyer we focus on
their impact on agency costs. A model in which the buyer’s resources had an explicit cost
would illustrate the same key points, but not as clearly or effectively. The second reason
is analytical tractability: with this assumption, the analysis of the problem is streamlined.
The final reason is empirical. At Ford and at many buyers such resources are costless in the
short-to-medium term.
Several assumptions made in the economic model are also worth discussing. First,
despite the assumed information asymmetry about the supplier’s capabilities, our analysis
assumes that the buyer can determine the optimal level for the supplier’s resource allocation
in the (hypothetical) case where the supplier’s capability is known. Implicitly, this assumes
that the buyer is familiar with the technological aspects of the production process but not
with the exact parameters of the technology. That is, given complete knowledge of the
technology’s parameters, the buyer can specify the optimal course of action.
Similarly, our analysis assumes that the buyer’s resource commitment is observable
and contractible but the supplier’s resource allocation is not. This could happen if the buyer’s
involvement is limited along a well-defined dimension while the supplier’s involvement is
much more elaborate and not easily measurable. An example would be when the buyer
provides physical resources that enhance the supplier’s resources but where the supplier
provides trained and specialized personnel. While the nature of the physical resources is
easily measurable, the training and skill level of the personnel cannot be specified in an
11
enforceable contract.
Another important assumption in the model is that the technology used by the supplier is flexible such that the supplier’s resource allocation can be adjusted after the buyer’s
contract is specified. This implies that, given the contract choice made by the supplier, his
resource allocation minimizes his production cost. However, this flexibility implies that the
buyer can exploit her leadership position to extract the maximum surplus from the supplier.
The supplier might, of course, strengthen his position by investing in capability-dependent
technology that is inflexible such that his resource allocation precedes the choice of contract.
This changes the sequence of events and reduces the power of the buyer’s leadership position.
Our model would be inappropriate in such a scenario.
A remark about quality is also appropriate. Specifically, the model assumes the
quality of the product is fixed and that buyer and supplier resources have no discernible
effect on quality. However, there are various ways in which quality can be incorporated in
the model. The most direct is to interpret buyer resource as being used, in part, to develop
and implement quality specifications, and that these specifications are associated with future
costs (such as warranty costs) incurred by the supplier. A similar interpretation could be
given to supplier’s resource. Another alternative would be to explicitly model quality and its
impact on supplier’s cost and buyer’s desirability for the product. While such an extension
would be worthwhile, it will not be pursued here because it would divert attention from the
key objective of the study, which is to explore the effect of buyer resource commitment on
information rents.
It should also be emphasized that even though our model focuses on the adverseselection problem, there is also a possible double moral-hazard problem in the buyer-supplier
relationship. Both the buyer and the supplier may not “actually” dedicate the planned
amount of resources. However, the double moral-hazard problem is ameliorated because the
buyer’s input is assumed verifiable and because the supplier incurs the total cost of product
development. Therefore, the buyer cannot deviate from the precommitted level of resource
input, and the supplier has every incentive to allocate the appropriate amount of resources.
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3
Model Analysis and Theorems
The analysis proceeds in three steps. First, we consider the first-best case, in which the buyer
knows the supplier’s capability and chooses both decisions: buyer resources and supplier
resources. This solution provides a benchmark that identifies the distortions caused as a
result of decentralization and information asymmetry. Next, we analyze a contract in which
the buyer offers a single resource commitment and transfer price; and finally, a “screening”
contract, where the buyer offers a menu of resource commitments and transfer prices.
3.1
Single-Party Problem: First-Best
In the single-party problem, the buyer knows φ, and chooses x1 and x2 in order to minimize
total cost. The problem is as follows: For each φ ∈ [φ, φ], find x1 (φ) and x2 (φ) to minimize
the production cost
V (x1 (φ), x2 (φ), φ)
(5)
0 ≤ x1 (φ) ≤ R .
(6)
subject to
The optimal (first-best) choice of the two inputs for each type φ ∈ [φ, φ] will be denoted
x∗1 (φ) and x∗2 (φ), respectively.
Proposition 1 The optimal solution to (5)-(6) is:
x∗1 (φ) = R
Vx2 (R, x∗2 (φ), φ) = 0 for each φ ∈ [φ, φ]
3.2
(7)
(8)
Single Resource-Commitment Contract
In this contract the buyer proposes a single resource-commitment and price. The problem
is as follows: The buyer specifies x1 and a price t, and the supplier (assuming he accepts the
13
contract), chooses x2 (φ) that minimizes his total cost, given the buyer resource commitment
specified in x1 . Then the buyer’s problem is to determine x1 ∈ [0, R] and t to
minimize t
(9)
max [t − V (x1 , x2 , φ)] ≥ u for each φ ∈ [φ, φ].
x2
¯
(10)
t,x1
subject to the participation constraint,
It is easy to see that the buyer will set x1 equal to the capacity constraint R, because
otherwise, she would forego some cost savings. In response to this, a supplier of type φ will
choose the resource level x2 that minimizes the production cost V (R, x2 , φ). This coincides
with first-best x∗2 (φ). Hence, the optimal single resource-commitment contract induces firstbest choices by both parties.
Let us now turn to the transfer price t. First, it follows from (10) that t must ensure
the participation of the supplier with the highest cost (i.e. lowest capability φ = φ). Hence,
the price offered by the buyer is equal to this supplier’s cost; that is,
t = u + V (R, x∗2 (φ), φ).
¯
(11)
Note that a supplier with a capability φ > φ is left with a profit (surplus) that reflects his
cost advantage over the least capable (i.e. highest cost) supplier.
In summary, this contract induces first-best choices by both parties, but the price
paid by the buyer must be enough to cover the cost of the least-capable supplier. Therefore,
the buyer cannot exploit any of the cost savings achieved by a more capable supplier.
3.3
Resource-Commitment Screening Contract
The previous analysis suggests that the buyer must utilize a resource-commitment screening
contract in order to optimize her total purchasing cost. That is, for a supplier of type φ, the
screening contract will specify a resource level x1 (φ), and a price t(φ). The intention is that
a type-φ supplier will find it to his best interest to choose the pair x1 (φ).
14
The analysis that will be presented in the remainder of this section will demonstrate
that the nature of the optimal contract depends on whether the cross-partials Ṽx1 φ (x1 , φ)
are positive or negative; these conditions are the well-known single-crossing conditions
from mechanism design, but are reinterpreted in the context of our model. We consider
three cases yielding different results. In the first case, we assume that Ṽx1 φ (x1 , φ) ≤ 0
for all x1 and φ. This implies that the buyer’s efforts and the supplier’s capabilities are
complements:
more buyer resources increase the magnitude of the supplier’s marginal
cost-reduction capability (i.e., it decreases
∂ Ṽ (x1 ,φ)
).
∂φ
In other words, more buyer resources
increase the cost advantage of more capable suppliers. Given complements, we will show
that the optimal menu of contracts separates less capable suppliers by committing fewer
resources compared to the resources that would be committed to a more capable supplier.
In the second case, we assume that Ṽx1 φ (x1 , φ) ≥ 0 for all x1 and φ. This implies that
the buyer’s efforts and the supplier’s capabilities are substitutes:
more buyer resources
decrease the magnitude of the supplier’s marginal cost-reduction capability (i.e., it increases
∂ Ṽ (x1 ,φ)
).
∂φ
That is, more resources diminish the cost advantage of the more capable suppliers.
Given substitutes, we will show that the optimal menu of contracts coincides with the single
resource-commitment contract. The final case is that of mixed complements and substitutes,
in which the sign of the second cross partial depends on the type. In this case, it can be shown
that the optimal contract consists of a screening contract for suppliers with a complementary
relationship and a single resource-commitment contract for the suppliers with a relationship
of substitution. Figure 1 presents a visual example of complements and substitutes. The
example demonstrates that, given complements, increases in buyer resources enlarge the gap
between suppliers of different capabilities. By contrast, given substitutes, increases in buyer
resources reduce this gap (the functions used to draw the graphs in the Figure are the same
ones used in the numerical example in section 4.1.)
The analysis of the mechanism design problem (2)-(4) is standard, and described in
Fudenberg and Tirole (1991), chapter 7. The analysis proceeds in two main steps. First,
for any given menu of resource-commitment options (x1 (φ))φ∈Φ , find the transfer price menu
(t(φ))φ∈Φ that will implement it; i.e., make it desirable for a type-φ supplier to choose the pair
15
Figure 1: A graphical example of complements and substitutes.
(x1 (φ)). Second, obtain the menu of resource commitment options that when implemented
with the pricing mechanism from step 1 minimizes the buyer’s total expected cost.
The main result for step 1 is given below.
Proposition 2
1. Assume that Ṽx1 φ (x1 , φ) ≤ 0. Then a menu of resource-commitment options (x1 (φ))φ∈Φ ,
where x1 (φ) is non-decreasing, is implementable. The transfer price mechanism that
implements this menu is given by
t(φ) = u + Ṽ (x1 (φ), φ) −
¯
Z
φ
Ṽφ (x1 (φ), φ)dφ
(12)
φ
2. Assume that Ṽx1 φ (x1 , φ) ≥ 0.Then a menu of resource commitment options (x1 (φ))φ∈Φ
where x1 (φ) is non-increasing is implementable. The transfer price that implements
this menu is given by (12).
3. Assume that Ṽx1 φ (x1 , φ) ≤ 0 for φ ≤ φ0 and Ṽx1 φ (x1 , φ) ≥ 0 for φ > φ0 . Then, a menu
of resource commitment options (x1 (φ))φ∈Φ where x1 (φ) is non-increasing for φ ≤ φ0
and it is constant for φ > φ0 is implementable. The transfer payment that implements
this menu is given by (12).
16
The nature of the non-linear transfer payment system (12) provides an important
insight. The total price for a supplier of type φ is equal to the reservation profit margin u,
¯
plus the total cost of production when the supplier chooses the desired resource commitment
x1 (φ), plus an information rent. The information rent is increasing in the supplier’s capabilities, and hence makes it attractive for the supplier to reveal his capabilities by the choice
he makes.
Let us now turn to the second step of the analysis, which is to identify the menu that
will minimize the buyer’s expected total cost when implemented with the pricing mechanism (12). If we ignore the requirement that this mechanism implements policies that are
monotone, then our problem becomes: Find a menu of resource-commitments (x1 (φ))φ∈Φ to
minimize
Z
φ̄
φ
"
Ṽ (x1 (φ), φ) −
Z
φ
#
Ṽφ (x1 (φ), φ)dφ π(φ)dφ;
φ
(13)
where (13) is derived by substituting (12) into (2). An application of integration by parts
implies that this problem is equivalent to minimizing
¸
Z φ̄ ·
1 − P (φ)
Ṽ (x1 (φ), φ) −
Ṽφ (x1 (φ), φ) π(φ)dφ;
π(φ)
φ
(14)
where P (φ) is the cumulative density function for the supplier’s capabilities. Then, the
second step is to obtain the menu (x1 (φ))φ∈Φ that minimizes (14), ignoring the constraints
implied in Proposition 2, and then verify that the constraints are satisfied.
Before we proceed with the analysis, it is worth noting that (14) highlights the tradeoff that needs to be balanced by the optimal screening contract: The buyer wishes for the
supplier to choose a resource level that minimizes total production cost but also wants to
extract some of the cost savings. To achieve this she has to offer the supplier an information
rent. The information rent that would implement the first-best decisions is excessive. Hence,
the menu designed by the buyer proposes a resource commitment that may be different
from first-best; one that may increase the direct product development cost compared to
first-best but with smaller information rents. In summary, delegation of decision-making
authority from the principal to the agent may lead to distortion of buyer and supplier
17
resource commitment in order to induce truthful revelation of the supplier’s capability at a
minimum expected cost to the buyer.
We are now in a position to present our main results. These require two technical
assumptions on Ṽ (x, φ) and π(φ) which ensure that the integrand in (14) is convex (i.e.,
the first-order condition is necessary and sufficient), and that the solution to the first-order
condition satisfies the desired monotonicity condition. The assumptions are: (a) Ṽx21 φ < 0
and Ṽx1 φ2 > 0 ; and (b) That the hazard rate
1−P (φ)
π(φ)
is non-increasing, it is infinite at φ, and
it is zero at φ. In the absence of these conditions, one can still minimize (14) but care must
be taken not to use the first-order condition naively.
Proposition 3 Suppose that the buyer’s resource and supplier’s capability are complements.
Then, the optimal menu of resource commitments satisfies the following conditions for φ≤
∗∗
φ∗∗
L ≤ φU ≤ φ

for φ ≤ φ∗∗
x∗∗

1 (φ) = 0
L
∗∗
∗∗
∗∗
0 ≤ x1 (φ) ≤ R for φL ≤ φ ≤ φU
.

∗∗
∗∗
x1 (φ) = R
for φU ≤ φ
(15)
∗∗
∗∗
The buyer’s optimal resource commitment x∗∗
1 (φ) and thresholds φL , φU are derived as fol-
lows:
1−P (φ)
Ṽx1 φ (x∗∗
1 (φ), φ) =
π(φ)
∗∗
1−P
(φ
)
L
Ṽx1 (0, φ∗∗
Ṽx1 φ (0, φ∗∗
L ) − π(φ∗∗
L ) > 0,
L )
∗∗
1−P (φU )
∗∗
Ṽx1 (R, φU ) − π(φ∗∗ ) Ṽx1 φ (R, φ∗∗
U ) < 0.
U
Ṽx1 (x∗∗
1 (φ), φ) −

∗∗

0 for φ ∈ [φ∗∗
,
φ
]

L
U




(16)
The optimal resource allocation for a type-φ supplier, x∗∗
2 (φ), chosen in response to the
optimal screening contract satisfies
∗∗
Vx2 (x∗∗∗
1 (φ), x2 (φ), φ) = 0.
The pricing system that implements the optimal contract is given by
Z φ
∗∗
∗∗
t (φ) = u + Ṽ (x1 (φ), φ) −
Ṽφ (x∗∗
1 (φ), φ)dφ.
¯
φ
(17)
(18)
If, on the other hand, the buyer’s resource and supplier’s capability are substitutes, then the
optimal screening contract coincides with the single resource-commitment contract.
18
One can say more by considering the hybrid complements/substitutes case where the
relationship is complementary with suppliers of capabilities φ ≤ φ0 and it becomes one of
substitution when φ > φ0 . In that case, it can be shown that the optimal contract is derived
by separating the region of types into two parts: the region of complements and the region
of substitutes. Then the solution is obtained by pasting together the pieces corresponding
to the two parts. The end-result is a contract in which x∗∗ (φ) = R for φ > φ0 , while for
φ ≤ φ0 , the optimal x∗∗ (φ) is derived from the solution to (16).
Insights from the Propositions. The main insight from our analysis is that the
buyer’s optimal commitment of resources depends on their interaction with supplier capability. When supplier capability and buyer resources are substitutes, increasing the buyer’s
involvement achieves two objectives: it reduces the total cost of product specification and
production and the corresponding information rents. The latter occurs because the increased
involvement by the buyer reduces the supplier’s marginal capability that drives the information rents. It follows that it is optimal for the buyer to use all her resources irrespective of
the supplier’s capability.
By contrast, in the case of complements, buyer resources can increase the supplier’s
marginal capability and that will increase the information rents. Therefore, the buyer finds
it advantageous to restrain her involvement in order to effectively price-discriminate: she
provides contracts with limited involvement (low x1 ) and contracts with a more extensive
involvement (higher x1 ) but, potentially, at a price discount (lower t). Then, the more
capable supplier finds it advantageous to choose the more extensive involvement at a lower
price because he can better integrate this involvement in his processes and achieve larger
cost reductions. Therefore, even though the price paid to a more-capable supplier is lower
than the one paid to a less-capable one, the former is left with a higher surplus because he
takes advantage of the buyer’s involvement.
An important observation here is that in the case of complements, the buyer’s ability
to offer a menu of contracts reduces the supplier’s surplus compared to the single resourcecommitment contract. In other words, the buyer exploits her involvement in the product
development project to extract some of the supplier’s surplus. While the supplier with a
19
high level of capability retains more of the surplus than the less capable supplier, he is worse
off compared to the case of a single resource-commitment contract.
This concludes our discussion of the general model. The main contribution, so far, has
been to demonstrate that the product-specification and production problem can be analyzed
at a fairly abstract level using a standard model from information economics, and to illustrate
the strategic value of the buyer’s involvement in the supplier’s production process. In the
next section, we present two applications of the model in order to operationalize the concepts
of complements or substitutes, and to illustrate the main insights extracted from the generic
model.
4
Examples
We will present two examples: The first is an inventory-management example based on the
EOQ model; and the second is a sequential-experimentation model in pharmaceutical drug
discovery. Our goal is twofold: First, to demonstrate the versatility and applicability of the
model; second, to add more structure to the general findings from section 3.
4.1
Inventory Management
The buyer requires a product from the supplier at a fixed rate D per unit time. Demand is
met from finished-goods inventory maintained by the supplier. Shortages are not allowed.
Production is assumed to be instantaneous, but there is a production setup cost and an
inventory-holding cost, both incurred by the supplier. The setup cost depends on the buyer’s
specifications, which in turn, depend on the buyer’s resource commitment, x1 , and on the
supplier’s setup capability, φ. Hence, the setup cost will be denoted by K(x1 , φ). The
supplier’s decision is the production lot size x2 . The holding cost is h per item per unit time.
Then, the supplier’s cost function is
V (x1 , x2 , φ) =
DK(x1 , φ) h
+ x2 .
x2
2
20
(19)
According to our analysis, it is sufficient to consider the induced cost function Ṽ (x1 , φ) =
p
minx2 Ṽ (x1 , x2 , φ). It is easy to show that Ṽ (x1 , φ) = 2DhK(x1 , φ). We assume that each
setup consists of a number of steps, N(x1 , φ), that depend on both product specification and
supplier capability, and that the cost of each step is capability-dependent, and denoted by
s(φ) i.e., K(x1 , φ) = N (x1 , φ) × s(φ).
Next, we will describe circumstances under which the buyer resource and supplier
capability are complements versus substitutes. First, it is natural to assume that the cost
ds(φ)
< 0), that the number of steps
dφ
1 ,φ)
more resources (i.e. ∂N(x
< 0), and, also, that the
∂x1
1 ,φ)
in the supplier’s capabilities (i.e. ∂N(x
≤ 0). To obtain
∂φ
per step decreases for more capable suppliers (i.e.
decreases as the buyer commits
number of steps is non-increasing
a cost function that satisfies the substitutes case it is sufficient to have the number of steps
be independent of φ (i.e.
On the other hand, when
∂N(x1 ,φ)
∂φ
∂N(x1 ,φ)
∂φ
= 0). Simple algebra then shows that Ṽx1 φ (x1 , φ) ≥ 0.
< 0 and
∂ 2 N(x1 ,φ)
∂x1 ∂φ
< 0 then it is possible to construct
examples that satisfy the complements case i.e., Ṽx1 φ (x1 , φ) ≤ 0 (Note that one must use
the functional form of Ṽ to find regions where the condition for complements holds). In
summary when the buyer’s resource reduces the number of steps, and when the supplier’s
capability only influences the cost of each step but not the number of steps, then we have
a case of substitutes. On the other hand when, when the supplier’s capability influences
both the cost of each step and the number of steps, it is possible to either have a case of
complements or a case of substitutes.
A Numerical Example. For the case of substitutes, let N(x1 , φ) = (1 − (x1 /4))
√
and s(φ) = (1 − φ). Assume that R =2, 2hD = 1, that supplier capability φ takes a
value between 0 to 1 and is uniformly distributed between 0 and 1. The corresponding
1
K(x1 ,φ)
≥ 0. It can then be verified that it is optimal to set x∗1 (φ) = 2
√
and thus offer a transfer payment of t(φ) = 0.5 = 0.707 to all suppliers regardless of
√
√
capability. The corresponding surplus for a supplier with capability φ is 1/ 2[1 − 1 − φ],
Ṽx1 φ (x1 , φ) =
√
16
which is increasing in the supplier type. Figure 2A plots the supplier surplus as a function of
capability. Note that the surplus is equal to zero for the least capable supplier (when φ = 0)
and the contract provides a surplus for all other suppliers. This corresponds to the results
21
A. Substitutes Case:
Supplier Surplus vs supplier capability
Supplier
Surplus
x1**(φ)
B. Complements Case: Buyer Resource Commitment
vs Supplier Capability φ
2
0.7
0.6
1.5
0.5
0.4
1
0.3
0.5
0.2
0.1
0.2
0.4
0.6
0.8
Supplier Capability φ
C. Complements Case:
Transfer Price vs Supplier Capability φ
t(φ)
0.2
1
0.4
0.6
0.8
1
Supplier Capability φ
Supplier
Surplus
D. Complements Case: Supplier Surplus
Vs Supplier Capability φ
Supplier Capabilityφ
0.15
0.15
0.2
0.4
0.6
0.8
1
0.98
0.98
0.125
0.125
0.96
0.96
0.1
0.1
0.94
0.94
0.075
0.075
0.92
0.92
0.05
0.05
0.9
0.9
0.025
0.025
0.88
0.88
0.2
0.86
0.86
0.4
0.6
0.8
Supplier Capability φ
1
Figure 2: Results for EOQ Numerical Example
for the single resource-commitment contract.
For the case of complements, let N (x1 , φ) = (1 − φx1 /4) and s(φ) = 1; all other model
components are the same as above. Note that the benefit from a given x1 is greater for more
p
capable suppliers; i.e., a complements relationship. The associated Ṽ = 1 − (φx1 /4) and
the cross partial
∂ 2 Ṽ
∂φ∂x1
= (−8 + (φx1 ))/[8(4 − (φx1 )]3/2 ; this is negative for all feasible values
of x1 (i.e., x1 ≤ 2).
It can also be verified that the optimal menu of contracts would set x∗1 (φ) = 0 for
φ ≤ 0.5, x∗1 (φ) = 8((2φ) − 1)/(φ((3φ) − 1)) for 0.5 < φ ≤ 0.5425 and x∗1 (φ) = 2 for
φ > 0.5425. This contract (plotted in Figure 2B,C) shows that the buyer offers a contract
22
that induces the least-capable suppliers to choose no involvement by the buyer, while the
most capable suppliers choose full use of buyer resources. (Note that the value 0.5425 was
obtained by identifying the value of φ such that the x∗1 (φ) hits the value of R = 2). The
associated menu of payments offered to suppliers is t(φ) = 1 for φ ≤ 0.5, t(φ) = 0.8601
Rφ
for φ > 0.5425 and t(φ) = Ṽ (x∗1 (φ), φ) − 0 Ṽφ (x∗1 (φ), φ)dφ for 0.5 < φ ≤ 0.5425
(see Figure 2C). Figure 2C shows that the payments offered to the less capable suppliers
are higher than that for more capable suppliers i.e., the payments decrease with capability.
However, Figure 2D also shows that supplier surplus increases with capability, thus providing
stronger incentives for the more capable suppliers. Since the more capable suppliers use buyer
resources more efficiently, they see a greater cost reduction.
4.2
Pharmaceutical Drug Discovery
Our second example is drawn from the lead-identification step in drug discovery. In this step,
thousands of molecules are tested using a biological assay that reflects a particular disease.
Molecules that are found to block some of the disease-specific biological activities are called
“leads” and progress to the second stage of development.
While several technological platforms are available for lead identification, one novel
technology, called “combichem”, is now becoming dominant; (see Thomke, 2001). In this
technology, several molecules are generated using combinatorial chemistry and then tested
using automated methodologies referred to as “high-throughput screening”. This technology
has typically been developed by small companies (startups) who sell their services to pharmaceutical corporations. In a typical scenario, the pharmaceutical corporation (buyer) enters
into an agreement with the startup (supplier) in which the latter will use its proprietary
technology to identify one or more leads.
Lead-identification by the supplier can be modeled by a sequence of independent
experiments, with the probability of success in each experiment denoted 1 − p, where
p = exp(φ); the parameter φ (φ ≤ 0) is the supplier’s private information that reflects
his proprietary technology. The supplier contracts with the buyer to identify a lead. The
23
supplier’s decision (x2 ) is a stopping rule. We will assume that he will stop (running experiments) when the first lead is identified. If the cost of each experiment is c, then the
supplier’s total expected cost of experimentation is c/(1 − p).
The buyer can share resources with the supplier that can be used to perform several
parallel experiments. That is, if the buyer’s resources committed to lead identification are
denoted x1 , then each experiment consists of x1 + 1 independent experiments. In addition,
there are two possibilities: Either the buyer’s resources are used to perform experiments
using the supplier’s technology, or using the buyer’s own technology. In the former case, the
probability of success in each round of experiments becomes 1 − px1 +1 , while in the latter it
becomes 1 − pq x1 ; where q denotes the probability of failure in experiments performed using
the buyer’s technology. In addition, to reflect a scenario where the supplier has access to a
novel technology while the buyer uses established technology it is natural to assume that q
is known to both parties but p is only known to the supplier.
In the case where the buyer’s resources are used with the supplier’s technology, then
the production cost function Ṽ (x1 , φ) = c/{1 − exp[φx1 + φ]}. By contrast, when the buyer’s
resources are used with buyer’s own technology, then production cost function Ṽ (x1 , φ) =
c/{1 − exp[βx1 + φ]}; where β = ln(q). Then, straightforward algebra demonstrates that
the former scenario reflects a case of complements while the latter is a case of substitutes.
One can use the general framework developed in section 3 to obtain the optimal contracts.
However, because the special structure of the cost functions violates some of the technical
assumptions, one must be careful with the first-order conditions in (16) and must check the
conditions on the boundaries of the feasible region for x1 .
This example demonstrates that when buyer resources will be used in conjunction
with supplier technology, then the buyer may find it beneficial to offer a menu of resourcecommitment options in order to elicit information about the supplier’s capabilities and minimize the information rents. If, on the other hand, buyer resources cannot be integrated
with the supplier’s technology but only with the buyer’s own technology, then the buyer is
better off committing all her resources in the relationship.
Other Examples. For another example of substitutes, consider the printing in24
dustry where digital files are used by the printer to generate a product that satisfies buyer
specifications. As the buyer increases the effort to provide a cleaner digital file to the printer,
the cost to generate a prototype that satisfies buyer specifications not only decreases, but
the gap between more and less-capable printers (with the same equipment) also decreases.
Thus, we see that less-capable suppliers receive a greater absolute benefit than more-capable
suppliers. Hence a cost structure that resembles substitutes.
Finally, consider the use of Computer-Aided Design (CAD) technology for transmitting buyer specifications, which permits the use of computer simulation to develop and test
product specifications. As the buyer increases the role of computer simulation to adjust
product specifications, the benefit to more-capable suppliers (i.e. with more effective engineering talent, and, thus better ability to integrate these files to reduce production costs) is
higher. Such a cost relationship represents “complements.”
5
Model Insights and Observations on Practice
In this section we will highlight the insights the analysis of our model provides for product
specification and production contracting. In particular, using the model we will interpret
anecdotes and empirical observations about buyer-supplier partnerships, and will propose
hypotheses that relate these observations to the parameters of our model. Empirical verification of the hypotheses is beyond the scope of this manuscript.
The Value of Providing Buyer Resources to a Supplier. “Why would/should a
buyer provide physical, financial, or intellectual resources to help a supplier?” This question
has haunted other manufacturers ever since learning that Honda, Toyota, and other Japanese
manufacturing companies have elaborate programs to do just that. Our analysis of a stylized
model provides one answer: that if such offers are used during the contracting process,
the corresponding “screening contract” provides otherwise hidden information about the
supplier’s capability. Our numerical results indicate that this yields cost savings compared
to a single-resource commitment contract.
The Importance of the Buyer-Supplier Relationship on Optimal Buyer
25
Resource Commitment and Total Cost. Our analysis also demonstrates the importance
of complementarity versus substitutabilty in determining the amount of a resource that the
buyer should commit. In particular, depending on the nature of the relationship - substitute
or complement - and the supplier’s capability, the optimal level of buyer commitment either
equals zero; the maximum possible, R, or something strictly in-between.
Hence, it is important that the buyer assess the nature of its relationship - complementary or substitute - with suppliers and potential suppliers: first, in order to provide
the appropriate level of resource commitment; and, second; if appropriate, to influence the
nature of that relationship. Further, if both complementarity and substitutability do exist,
then their existence provides one important motive for manufacturers to “qualify” suppliers
(see Ford, 1996) and/or offer programs such as those described by Dyer and Nebeoka (2000)
to align suppliers or potential suppliers.
An important question is how to make such an assessment? The examples presented
in section 4 suggest a general principle: When the buyer resource will be integrated into
the supplier’s processes and technology then the relationship is one of complements. If on
the other hand, when the buyer resource will be used to complete tasks that could have
otherwise been completed by the supplier, then we have a case of substitutes.
Can Outsourcing Go Too Far? For example, in outsourcing its head units, seats,
or tires, should Ford eliminate it own in-house resources for these components and systems?
A few years ago, such reductions/eliminations were commonplace.
More recently, the Wall Street Journal reports that Ford is planning to hire more than
500 engineers to coordinate with suppliers to reduce quality problems and improve supplier
production processes. Chrysler plans to use 1500 engineers in a war room to work with
suppliers to decrease costs. Discussions with managers in the auto industry suggest that
the significant reduction in Original Equipment Manufacturer (OEM) engineering base and
the elimination of testing labs and technical expertise at the OEMs may have resulted in a
decline in product quality and increases in costs.
This is consistent with our model — for low values of R, there is little difference
between the cost of single resource-commitment contracts and the alternatives. Hence, our
26
analysis suggests that management decisions to reduce/eliminate in-house resources reduced
the potential to fine tune designs and decrease supplier-delivered costs. It also decreases the
buyer’s ability to use the incentive of cooperation to improve total costs.
Reflections on Japanese and US manufacturing partnerships. There is, of
course, considerable literature describing Japanese manufacturers’ use of partnerships as
contrasted with US manufacturers. For example, Lee and Ansari (1985), in a comparative
analysis of traditional US and Japanese JIT purchasing practices, characterize the Japanese
as providing “loose” specifications, wherein “the buyer relies more on performance specification (i.e., concept specification) than on product design” (i.e., product specification).
In contrast, they characterize traditional US purchasing as providing “rigid” specifications,
wherein the buyer relies more on the opposite. However, Kamath and Liker (1994) observe
that even with respect to their first-tier suppliers, the Japanese “typically regard only a
handful as partners and assign more limited roles to the rest”. Indeed, Kamath and Liker
describe four classes of suppliers, which can be viewed as representing the spectrum of buyer
involvement with suppliers (i.e., the range of possible values of x1 (φ)). Liker and Wu (2000)
describe partnering arrangements that Honda and Toyota’s transplanted US assembly plants
have with their US suppliers, and describe how these companies use their relationships to
manage the capability of these suppliers. Dyer and Nebeoka (2000) describe how Toyota’s
“knowledge-sharing network” to manage supplier capability.
Clark’s study (1989) found systematic differences between Japanese automakers and
their US and European counterparts with respect to what we model as buyer resource commitment in product design. Clark found that “black box” parts - “those parts whose functional specification is done by the assemblers (buyers), while detailed engineering is done by
parts suppliers” - account for 62 % of the Japanese automakers’ total procurement costs, but
only 16 % and 32 % for the US and European automakers, respectively. Correspondingly,
“detail-controlled” parts - “those parts that are developed entirely by the assemblers (buyers), from functional specifications to detailed engineering drawings” - account for only 30%
of Japanese purchases, compared to 81% and 54% for the US and European automakers.
We believe that our model can be used to reconcile these different findings. To visual27
ize the link, consider a total-effort pie-chart (x1 (φ) and x2 (φ)) for a product for a given level
of supplier capability (φ). Assume that x1 (φ) can be divided into two parts: buyer resources
used for product-design related effort (x11 (φ)) and the buyer resources used for process specification related effort (x12 (φ)). Similarly consider such a split of supplier resources (x2 (φ))
into x21 (φ) and x22 (φ). Clark’s study focused primarily on empirical data regarding the composition of design-related effort; that is, his study focused on the relative values of x11 (φ)
and x21 (φ). Clark finds that the x11 (φ) for US automakers (buyers) is higher than that for
typical Japanese automakers. However, Kamath and Liker (1994) focus on the composition
of x12 (φ) and x22 (φ) and suggest that the value of x12 (φ) for Japanese automakers is larger
than that for US automakers. Liker and Wu (2000) can be interpreted as suggesting that
Honda and Toyota use screening contracts to adjust the value of x1 (φ) based on supplier capability. Similarly, Dyer and Nebeoka (2000)’s paper suggests the role of adjusting x12 (φ) by
Japanese automakers to manage their suppliers. Note that each of our suggestions generates
testable hypothesis regarding the relative values of x11 (φ), x12 (φ), x21 (φ) and x22 (φ) and the
interaction between these variables and supplier capabilities. In particular, if one assumes
that everything else is kept constant and that the buyer-supplier relationship reflected in
these empirical studies is similar to the principal-agent model analyzed in this paper, then
our analysis suggests that buyer resources used for product design complement the supplier’s
capability in Japanese manufacturer’s but not in US ones. By contrast, buyer resources used
for process specification substitute for the supplier’s capability in Japanese manufacturer’s
but complement the capability of US ones.
6
Conclusions and Extensions
We have developed a principal-agent model for product specification and production. This
model enables us to suggest the optimal use of resources in a screening contract. Our
analysis concludes that this decision depends on the cost relationship between the buyer’s
commitment of resources and its impact on the supplier’s ability to decrease costs (based
on his capability). We introduce two cost structures — substitutes and complements — and
28
provide the optimal screening contract. The complements cost structure suggests that it may
be optimal for the buyer to use less than all her available resources to optimize the total cost
— which consists of the supplier product cost, reservation profit and information rent. We
provide two applications of the model to illustrate its versatility — one considers inventory
management in the context of an EOQ model and the other models product development
in the pharmaceutical industry. The managerial implications of this model are explored to
suggest links to observed choices made in the auto industry.
Extensions of the model could proceed in several directions which include incorporation of a supplier auction to determine the supplier with whom the buyer is to contract, the
addition of learning about supplier capability in a multi-period contracting process, and a
more detailed model of the link between supplier capability and product quality.
Appendix
Proof of Proposition 1: Suppose that the constraint is not binding for some φ0 .
Then, x1 (φ0 ) < R. But, it is assumed that
∂V (x1 ,x2 ,φ)
∂x1
< 0, hence one can decrease the total
cost by increasing x1 (φ0 ) until x1 (φ0 ) = R. Therefore, the resource constraint is binding for
each φ.
Proof of Proposition 2: The implementability of the menu of resource commitments follows from Theorem 7.3 in Fudenberg and Tirole (1998), page 261. To derive the
expression for the transfer price we proceed as follows (the method is described in Fudenberg
and Tirole (1998), and is replicated here for completeness). First, define the indirect utility
function
V1 (φ) = max t(φ̃) − Ṽ (x1 (φ̃), φ).
φ∈Φ
(20)
Then, Theorem 7.3. of Fudenberg and Tirole (1991) implies that the incentive compatibility
constraint under the conditions spelled in the Proposition can be restated as follows:
dx1 (φ)
dt(φ)
− Ṽx1 (x1 (φ), φ)
= 0;
dφ
dφ
(21)
which is equivalent to the statement φ = arg maxφ̃∈Φ t(φ̃) − Ṽ (x1 (φ̃), φ̃). Equation (21),
together with an application of the envelope theorem (see Mas-Colell, Whinston, and Green
29
(1995), page 964) to (20), implies that:
dV1 (φ)
= −Ṽφ (x1 (φ), φ).
dφ
It follows that
V1 (φ) = u¯
Z
(22)
φ
Ṽφ (x1 (φ), φ)dφ.
(23)
φ
Hence,
t(φ) = u + Ṽ (x1 (φ), φ) −
¯
Z
φ
Ṽφ (x1 (φ), φ)dφ.
(24)
φ
Parts (b) and (c) can be similarly proven.
Proof of Proposition 3: We proceed in three steps. First, we obtain the first order
conditions for (14) and provide a characterization for their solution. Then verify that the
first order conditions are necessary and sufficient for optimality.
10 . The first order conditions for (14) can be written as
Ṽx1 (x1 (φ), φ) − η(φ)Ṽφx1 (x1 (φ), φ) = 0.
(25)
There are two cases to consider: a) If Ṽφx1 (x1 (φ), φ) > 0, then the left hand side of (25)
is negative for all values of x1 (φ). Hence, it is optimal to set x1 (φ) = R for all φ. b) If
Ṽφx1 (x1 (φ), φ) < 0, then the left hand side of (25) is positive for φ in the neighborhood
of φ (because η(φ) À 1 in that neighborhood), and it is negative in the neighborhood of
φ (because η(φ) ' 0 in that neighborhood). This implies that the solution the first-order
condition (25) is given by (16).
20 . Now, the second order conditions are
Ṽx1 x1 (x1 (φ), φ) − η(φ)Ṽφx21 (x1 (φ), φ) ≥ 0;
(26)
the non-negativity follows because V (x1 , x2 , φ) is assumed jointly convex in x1 and x2 , and
because Ṽφx21 (x1 (φ), φ) < 0. Next, it remains to confirm that x∗∗
1 (φ) is non-decreasing in φ.
Totally differentiating (25) with respect to φ implies:
dx∗∗
1 (φ)
=
dφ
dη(φ)
Ṽφx1 (x1 (φ), φ)
dφ
+ η(φ)Ṽφ2 x1 (x1 (φ), φ)
Ṽx1 x1 (x1 (φ), φ) − η(φ)Ṽφx21 (x1 (φ), φ)
≥ 0;
30
(27)
because both
dη(φ)
dφ
and Ṽφx1 (x1 (φ), φ) are non-positive, Ṽφ2 x1 (x1 (φ), φ) > 0, and the denom-
inator is the second-order condition 26 which is positive.
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