∗
Abstract
Among the several features that distinguish the Modern Manufacturing system, the use of a small number of suppliers is a very visible one. This feature has however been omitted in the theoretical literature. This paper seeks to bridge this gap by studying the complementarity between this feature and the degree of technological freedom allowed to the suppliers.
In order to do so, a model of an ordered good market (that is, a market where a fraction of the design of the product or its manufacturing process is undertaken by the buyer) is presented. The model allows for any form of contracting, endogenous participation and endogenous amount of design undertaken by the supplier.
Using monotone comparative statics and some results from the theory of auctions with endogenous entry, the model predicts that, as observed by Rogerson (1989) in the U.S. Defense Procurement Industry, suppliers should have ex-post positive profits in the optimal contract. It also predicts that deeper participation of the supplier in the design phase leads to a smaller number of suppliers and larger profits for them, as observed in the Japanese automobile parts industry
(Asanuma 1992).
∗ Dept. of Economics, Stanford University. E-mail: lrezende@leland.stanford.edu. A prior version of this work has circulated under the title “A Theory of Ordered Goods
Procurement”. I thank the guidance and encouragement of Tim Bresnahan, Pat Bajari,
Paul Milgrom and Roger Noll. The errors, however, are all mine.
1

Among the several features that distinguish the Modern Manufacturing system, a striking one is the much smaller number of suppliers each firm utilizes.
The very first difference between the Japanese and the American automobile parts industry highlighted by (Asanuma 1992) is that the former has ten to a hundred times less suppliers per manufacturer than the latter (See Table
1, in Section 3).
The potentially important complementary role that the number of suppliers with other features of the Modern Manufacturing system has not yet been investigated by the existing theoretical work, such as Milgrom and Roberts
(1990), Athey and Schmutzler (1995) and Taylor and Wiggins (1997).
The present work aims to contribute to bridge this gap by investigating the complementarity between the choice of the number of supplier and fact that most automobile parts are Ordered goods . Ordered goods, as opposed to marketed goods, are defined as those that “are supplied by outside firms according to specifications issued by the buyer”, rather than those that
“are offered to the public irrespective of the will of the buyer and therefore purchasable by merely selecting from a catalog” (Asanuma 1989, p. 11).
In this paper a model is presented where a buyer seeks to purchase an ordered good yet to be designed from one out of several potential suppliers.
This buyer is allowed to choose any contractual form, number of potential suppliers, and design policy. In spite of the simplicity of the framework, the solution seems to show several features found empirically in two prominent markets of ordered goods: the U.S. Defense Procurement and the “Japanese style” automobile parts industry.
As observed by Rogerson (1989) in the U.S. Defense Procurement context, the model predicts that ex-post profits for the suppliers should be positive, even though ex-ante expected profits are zero.
1 It also predicts that a small number of suppliers is a complement to modern manufacturing practices such as early involvement of suppliers in the design phase. This complementarity has been verified empirically and stressed as one of the most salient characteristics of the Japanese automobile parts industry by Asanuma (1992) and
Kojima (1998).
Both the Modern Manufacturing system (Asanuma 1989, Asanuma 1992,
1 However, some conclusions of the model differ from those in Rogerson (1989). For example, unlike this author the present analysis does not suggest that the Department of
Defense should partially fund the R & D costs of its suppliers.
2

Aoki 1990, Helper 1997, Taylor and Wiggins 1997, Milgrom and Roberts 1990,
Milgrom and Roberts 1995, Athey and Schmutzler 1995) and the Defense
Procurement market (Rogerson 1989, Anton and Yao 1987, Riordan and
Sappington 1989) have been subject of extensive interest in the literature of the last two decades.
Most theoretical works on the Modern manufacturing system (Milgrom and Roberts 1990, Milgrom and Roberts 1995, Athey and Schmutzler 1995,
Taylor and Wiggins 1997) seek to explain the complementarities among productive practices identified in the empirical literature using models where there is only one firm (or one supplier and one buyer) and therefore there is no competition among firms. However, the choice of the number of suppliers is itself an important aspect of the modern manufacturing phenomenon
(Asanuma 1992, Kojima 1998), and it is likely to exhibit potentially important complementarities with other features of the system. It is therefore desirable to obtain a model where the number of participating firms is determined endogenously. This is the contribution sought in the present paper.
A different literature that, similarly to the present paper, explicitly consider the effect of an increased competition on contracting is the one in Second
Sourcing.
2 However, these papers develop theories that are specific to the markets under consideration; they typically focus at the interim choice of introducing a second-source after the design has been made and firms are already in asymmetric positions. They do not provide direct answers to more basic and general questions such as how much competition should be sought in the first place.
The present research follows instead a different method that utilizes results from Auction Theory. This approach has the advantage of simplifying some technical issues and allowing the analysis to focus instead in the comparative statics conclusions.
3
2 Shepard (1987) and Farrell and Gallini (1988) present theories of why licensing a second supplier might be of interest for the original supplier, a practice that is often observed in high tech industries. Anton and Yao (1987) and Riordan and Sappington
(1989) discuss Second Sourcing more specifically in the context of Defense Procurement.
Demski, Sappington, and Spiller (1987) justify second-sourcing in a framework closer to the mechanism design tradition, but in their model the benefit of a second source is to allow for more information about the incumbent supplier’s costs, rather than augmented market competition.
3 Auction theorists have long been interested in the implications of changing the number of bidders (Wilson 1977, Bulow and Klemperer 1996), but this number is usually taken to be exogenous and common knowledge. McAfee and McMillan (1987a) discuss the effect
3

The remainder of the paper is organized as follows: Section 2 includes both the description of the model, the derivation of its solution, and presentation of several comparative statics results. Such results are then compared in Section 3 to evidence presented by Asanuma (1989 and 1992) about the
Japanese manufacturing system and by Rogerson (1989) about Defense procurement. Section 4 concludes and suggests possible extensions to the present analysis.
In this section a simple model of an ordered goods market is presented where both contract form and the number of participants are allowed to be chosen endogenously; in this way not only no ad hoc constraints in contractual form are required, but also parties can select more or less competitive arrangements.
A single risk-neutral buyer licenses n risk-neutral suppliers to provide one unit of an input.
It is assumed that the good is a new, customized item. Therefore before production takes place its specifications should be made. The decision of who has the right of making these specifications is taken to be endogenous and modeled in a simple way: It is assumed that there is an index d ∈ [0 , 1] that represents the fraction of the specifications allowed to be made by the suppliers.
In order to be able to provide the item, each supplier has a fixed cost of k ( d ) and, if it is chosen to provide the good, a production cost of c i
( d ). As the subscript suggests, c i varies across firms: for a given d it is a random variable, independently and identically distributed according to a distribution that is of an stochastic number of bidders. Several papers present models where the number of bidders is endogenous and determined by voluntary entry decisions by the bidders:
Johnson (1979), McAfee and McMillan (1987b) and Engelbrecht-Wiggans (1993) study models with a free entry condition where the number of entrants is deterministic; Levin and Smith (1994) and Milgrom (1981) investigates symmetric, mixed-strategy equilibria in the entry decision. Ye (1999) discusses the optimal auction when entry is endogenous and costly.
4

common knowledge. The buyer does not observe c i
; and firm i only observes it after it spends k .
Rather than traditional fixed costs, k should be thought of as a design and set-up cost specific to the provision of the item. It is assumed therefore that k is increasing in d .
c i measures the degree of efficiency/suitability of the supplier to the task at hand. The item is supposed to be a new, customized good, so that this suitability can only be assessed after some spending on planning and technology learning takes place. It is assumed that the larger the d , more room the suppliers have to adapt the specifications of the good to their existing line of production and technological capabilities. Therefore the effect of an increase of d in c i is to make it expected to be smaller and more predictable. As will be seen below, the results do not depend on any assumption on the effect on E ( c i
), but it is going to be important to assume that V ar ( c i
) is decreasing on d . In the Appendix two different interpretations of the design decision are suggested that might make this assumption more palatable.
It is assumed that the buyer has a valuation V of the good.
V may, and possibly should, be considered a function of d . No assumption on the function V ( d ) is required in what follows. For simplicity V is supposed to be large enough so that it is always profitable to buy the good 4 technically, we assume that Pr( c i
+ k < V ) = 1.
5 or, more
For technical reasons, I will assume that for all d the the support of c i is an interval and the distribution of c i is absolutely continuous and regular in the sense of Myerson (1981).
6
Any design not made by the suppliers should be carried out by the buyer.
Its cost however is supposed to be included in V . The buyer has freedom to choose any contract to offer to the potential suppliers.
4 Except possibly for strategic reasons, as is the case of the classic monopsonist model.
Such possibility will be explicitly considered in the model.
5 Notice that this assumption makes the support of c i bounded, so all expectations mentioned below exist.
6 The distribution F of c i is regular if the function ˆ increasing in c in the support of c i
.
f is the density of F .
( c ) = c + F ( c ) /f ( c ) is strictly
5

Given the ex-ante symmetry among suppliers, we know that the optimal contract can be described in the following form: n suppliers will be licensed 7 ; the buyer will allow them to determine a proportion d of the specifications and they will be charged a fee φ . This fee is allowed to assume a negative value, and is assumed to be the same for each supplier due to their ex-ante symmetry. After the firms learn their cost types, the buyer is allowed to offer any pricing scheme and any rule to assign the supplier.
However, this pricing subgame that occurs among the licensed suppliers and the buyer is exactly like an independent private values procurement auction with a fixed number of bidders with i.i.d. types. So optimal auction theory (Myerson 1981) tells us that, in the symmetric regular case, the optimal mechanism will be a second-price auction with a reservation price that we will call γ . So our task is reduced to find the d , n , φ and γ that maximize the buyer’s profit. These numbers are announced before the suppliers spend k , and the buyer is not allowed to change it later (that is, the contract is enforceable in court).
Taking further advantage of the auction analogy, we know that if the firms bid their dominant strategies, the winning bidder is the firm with the smallest cost, 8 c
(1: n )
, and pays for that c
(2: n )
, as long as these values are below
γ . If c
(2: n )
> γ , γ is the price paid; and if c
(1: n )
> γ , the item is not traded.
We can therefore write each supplier ex-ante expected profit, and use it to establish the participation constraint for firm i :
Pr( c i
E [ γ − c
(1)
|
= c
(1)
) E [ c
(2)
− c
(1)
| c
(2) c
(1)
≤ γ < c
(2)
] Pr( c
(1)
≤ γ ] Pr( c
(2)
≤ γ ) +
≤ γ < c
(2)
) − k − φ ≥ 0 .
The expected profit for the buyer, here called Π, is
Π = V − E [ c
(2)
| c
(2)
≤ γ ] Pr( c
(2)
≤ γ ) + ( V − γ ) Pr( c
(1)
≤ γ < c
(2)
) + nφ
Since it is increasing in φ , the participation constraint binds, and we can substitute φ out of the expression for Π, which since Pr( c i
= c
( i )
) = 1 /n 9
7
In principle the buyer could prefer to adopt a mixed strategy, that is, to select a distribution over n . This however is suboptimal: Ye (1999) has shown that in an analogous setting the buyer’s profit is concave in n .
8 We write c
( j : n ) for the (bottom-up) j -th order statistics of c i of n , or c
( j )
9 for short.
Since the distributions of c
1
, . . . , c n out of a random sample are identical, the probability of cost is the same as any other supplier; that is, it equals 1 /n .
i having the lowest
6

becomes:
Π = V − E [ c
(1)
| c
(2)
≤ γ ] Pr( c
(2)
≤ γ )
+ V − E [ c
(1)
| c
(1)
≤ γ < c
(2)
] Pr( c
(1)
≤ γ < c
(2)
) − nk or
Π = V − E [ c
(1)
| c
(1)
≤ γ ] Pr( c
(1)
≤ γ ) − nk =
Z
γ
( V − x ) dF
(1)
( x ) − nk,
0 where F
(1) is distribution of c
(1)
. Clearly a maximizing value for γ is γ = V .
The economic interpretation for this choice is quite simple. In a traditional auction, γ is usually chosen below V : as a monopsonist, the buyer prefers to introduce some inefficiency (in the form of a positive probability of no trade) in order to lower the price paid. Here, however, the buyer has at his disposal the possibility of collecting through φ all expected profits form the bidders.
Since there is risk neutrality in both parties, the buyer is really obtaining the total (expected) surplus of the market, and is not in its interest to introduce any inefficiency through γ .
Since we are assuming that Pr( V > c i
) = 1, Π simplifies further to
Π = V − E [ c
(1: n )
] − nk.
So Π turns out to be the social surplus of the transaction: it is the value of the good, V , minus the expected cost of producing it, E [ c
(1: n )
], and the total design cost incurred by the n potential suppliers, nk .
The optimal choice of the number of suppliers will be the one that maximizes Π with respect to n . Notice that, since E [ c
(1)
] is bounded by the compact support of F , lim n
→∞
Π = −∞ , and this solution is well defined.
Likewise the optimal d will be the one that maximizes Π. Again this is a well-defined problem, since d ∈ [0 , 1] is compact and the function to be maximized is continuous (as long as the functions of d that enter Π are continuous).
10
It is convenient to rewrite the contract parameters chosen by the buyer:
1
φ = E [ p − c
(1)
] − k, n
10 The discrete character of n is not a problem, since one can apply the Theorem of the
Maximum (Berge 1963) to Π( d ) = max n
Π( d, n ).
7

γ = V, 11 n = argmax m
V − E [ c
(1: m )
] − mk, d = argmax
δ
V ( δ ) − E [ c
(1: n )
( δ )] − nk ( δ ) .
The price paid by the good, p , is p = c
(2)
, if n > 1,
γ, if n = 1.
In the following section we study how the contract parameters relate to each other and the exogenous elements of the model.
In order to discuss the impact of the distribution of costs on the contract form we need to parameterize it. A natural way to do it is to normalize the costs defining
( i )
= c
(
σ
2 Doing so we obtain i )
− ¯
, where ¯ = E [ c i
] and σ = V ar [ c i
].
12
Π = V − ¯ − σE [
(1: n )
] − nk.
2.3.1
Number of Suppliers
It is very easy to obtain comparative statics results on decreasing in n ; and from
(1: n )
≥
(1: n +1)
, we know that increasing in n . Therefore Π is supermodular 13 n
−
.
E [
∂ Π
∂k
(1)
=
] =
− n
∂ Π
∂σ is is in ( n, σ, − k ), and we have shown that
Proposition 1 The optimal n is a (weakly) increasing function of σ , a decreasing function of k , and invariant to V or ¯ .
11 Actually, any value for γ above the support of c i can be chosen by the buyer; γ = V has however the advantage of being economically intuitive and of being the solution also when Pr( c
12 i
> V ) > 0.
Assuming that these moments exist is without loss of generality, since any distribution with bounded support has mean and variance.
13
Throughout this section results from the Monotone Comparative Statics Theory are going to be used. See Topkis (1978) or Milgrom and Shannon (1994). For an application to modern manufacturing, see Milgrom and Roberts (1990).
8

Suppose now that the effect of a change in d in the distribution of c i is a change in ¯ and σ only, that is, the distribution of i is not affected by d .
14
Suppose further that σ is decreasing in d . Under these conditions Proposition
1 leads to
Proposition 2 The optimal n is a decreasing function of d .
2.3.2
Price
An initial difficulty in doing price comparative statics is to identify in the model what should be considered its appropriate measure. There are at least three potential interpretations: the price that is paid in the auction subgame, p ; the amount of money the winning supplier collects, p − φ , and the total amount paid by the buyer, p − nφ .
A this point it is helpful to state this simple and yet remarkable result, due to McAfee and McMillan (1987b) and Engelbrecht-Wiggans (1993): 15
Proposition 3 The optimal entry fee φ is close to zero, in the sense that the optimal n is the same as if φ = 0 .
16
Proof: Through φ the buyer is able to extract all expected surplus. So the optimal n (call it n ∗ ) maximizes expected surplus. The effect of an increase in n in the total surplus is ∆ S ( n ) = E [ c
(1: n
− 1) we have ∆ S ( n ∗
− c
(1: n )
] − k . At n
) ' 0 (in the sense that ∆ S ( n ) ≥ 0 and ∆ S ( n + 1) ≤ 0).
∗ ,
Consider now n
0
, the number of suppliers that would accept to enter if the fee were set to zero.
n
0 is the highest number where the entrant still expects a positive profit, that is,
E [ c
(2: n )
− c
(1: n )
] − k .
π ( n
0
) ' 0 (in that same sense), where
π ( n ) = 1 n
It seems like ∆ S and π are different functions; however, calling F the distribution of costs, we can write
E [ c
(2: n )
Z
=
− c
(1: n )
] = xn ( n − 1)(1 − F ) n
− 2 F dF −
Z xn (1 − F ) n
− 1 dF
14
One case where this happens is when the effect of a larger d is to scale down the distribution of the
15 c i
’s; for example, if c i
( d ) =
1 d c i
(1).
In these models n is the outcome of an entry game by the bidders, rather than a variable of choice by the auctioneer; however, the basic insight that the auctioneer collects all surplus and therefore entry is optimal is present.
16 Or, in other words, φ = 0 except for the fact that n is not continuous.
9

= n
Z x [( n − 1) F − (1 − F )](1 − F ) n
− 2 dF
= n
Z x [( n − 1) − n (1 − F )](1 − F ) n
−
2 dF
= n
Z x ( n − 1)(1 − F ) n
− 2 dF −
Z xn (1 − F ) n
− 1 dF
= n E [ c
(1: n
− 1)
− c
(1: n )
] , so ∆ S ( n ) = π ( n ) and n
0
= n ∗ .
Corollary 3.1
φ ≥ 0 .
Proof: φ has two effects on Π; a positive direct one and a negative indirect one, through a decrease in n . If φ < 0, by Proposition 3 an increase to 0 would not affect n , and would therefore increase profits. So φ < 0 cannot be optimal.
Intuitively, Proposition 3 states that φ is not used to attract or repel potential suppliers, but rather to extract any residual expected profit that the licensed potential suppliers might have because n is discrete. It is not necessarily true that φ is always insignificant, particularly in markets where n is small. But Proposition 3 provides a bound to it: namely, φ cannot be larger than the loss in each supplier’s expected profit if one extra supplier were licensed.
The previous discussion suggests that the behavior of any of the price concepts considered, p , p − φ and p − nφ , might move together. However, for the sake of completeness, the comparative statics of each concept is discussed in turn.
The behavior of the price p can be easily linked to n , given that γ > c
(2: n )
≥ c
(2: n +1)
.
k affects p only indirectly through n , while ¯ does so only directly, since p = ¯ + σ
(2)
, if n = 1. Because of this we easily obtain 17
Proposition 4 The price p is a (weakly) decreasing function of n , and therefore an increasing function of k .
p is also an increasing function of ¯ .
17 In doing comparative statics of a random variable such as p , we mean that for any fixed realization of the underlying random variables {
1
,
2
, . . .
} the result holds. Note incidentally that this implies that the result also holds in expected value.
10

Unfortunately, the impact of σ on p cannot be signed in general.
For the second definition, we can write
Ep − φ = ¯ + σ n − 1
E [ n
(2)
] +
1 n
E [
(1)
] + k, but this does not lead us far, since the effect of n on the term in brackets depends n the particular distribution of i
.
In the third case, it is easy to obtain comparative statics results because
Π = V − E [ p − nφ ]. Therefore n minimizes E [ p − nφ ] = ¯ + σE [ and by the Envelope Theorem we know that
(1)
] + nk
Proposition 5 The expected amount spent by the buyer is increasing in k and ¯ and decreasing in σ , if n > 1 . If n = 1 , it is constant in σ .
It is instructive to ask how the solution of the model relates to contractual forms observed empirically, such as closed-door bilateral negotiations and market competition.
Rather than exogenously imposing these two mechanism formats to the agents, I allowed the mechanism form to be selected endogenously. In this way I avoid the problem of selecting one specific form of contract and justifying why other forms might not be feasible/desirable. Because of the specific assumptions imposed in the environment, it turns out that the optimal auction assumes a convenient, intuitive form and it can be summarized by four decision variables: the specifications decision d , the number of suppliers n , a license fee φ and a reservation price γ .
I argue that this class of mechanism can encompass both a competitive market (on the supply side) and a bilateral contract. In fact, a perfectly competitive market (in both sides) would prevail in the case of φ = 0, γ = V and n → ∞ . In the other hand, a closed-door contract can be represented by n = 1 and φ and γ used to implement any pricing scheme convenient to the buyer. In the very simple environment studied here, any pricing scheme boils down to the amount of money transferred before the uncertainty is resolved ( φ ) and the amount used to decide the allocation of the good after the uncertainty is (partially) resolved ( γ ); so this mechanism encompasses all contract choices relevant in this framework.
11

Under this interpretation the choice of n can be used as an appropriate scale to see how far the mechanism choice is from pure market competition.
Proposition 1 states that the mechanism tends to be less competitive when it is more costly to prepare a supplier for production and there is less uncertainty about the production cost/efficiency. This is hardly surprising, since the basic trade-off that drives the model is between the social cost of setting up many suppliers and the benefit of screening the most efficient supplier among a large group.
18
Proposition 2 provides a more interesting conclusion: there is less competition in markets where suppliers have freedom to determine a larger share of the design of the good. Also, in these cases the supplier obtains a higher price.
The aim of this section is to investigate whether some of the theoretical predictions of the model are observed empirically. Two industries are going to be considered: The U.S. Department of Defense Procurement for development and production of aerospace projects, and the automobile parts industry in
Japan. I will draw heavily on evidence about these industries presented by
Rogerson (1989) and Asanuma (1989 and 1992), respectively.
A market that fits the assumptions of the model is the government procurement of a new technology good, since there is a sole buyer, presumably with bargaining power to choose the contractual form, and the R & D cost allocation is of great concern.
One such market is the one studied by Rogerson (1989): the procurement by the U.S. Department of Defense of new aerospace projects. Due perhaps to the great amount of uncertainty and the large sums involved, this market has been object of a significant interest in the Regulation Literature.
19 In
18 Nalebuff and Stiglitz (1983a) and Nalebuff and Stiglitz (1983b) argue that one of the advantages of competition vis-` other contractual arrangements is its flexibility; when unexpected contingencies arise, the market adapts itself and costly renegotiation is avoided. This suggests that competition should be preferred in more uncertain environments. The same conclusion is obtained in the present model.
19 Besides Rogerson, see Anton and Yao (1987) and Riordan and Sappington (1989).
12

this market not only the assumption of a sole buyer is a natural one, but also this buyer has great freedom to choose the rules under which the market operates. Indeed, complex forms of contracting and regulation are implemented. Also, the large cost of R & D and the incentive problems associated with its allocation are one of the main issues in this market.
One of the objects of concern about this industry is that suppliers seem to enjoy excessive profits in the production phase. The main point of Rogerson
(1989) is that these positive economic profits production should be thought of not as evidence of inept or captured regulation, but rather as prizes for innovation: the possibility of getting them has an important incentive effect on the initial R & D phase.
To empirically support his interpretation, Rogerson reports evidence on shifts in the suppliers’ expected profits (as measured by changes in their stock returns) in the days surrounding the announcement of the winner in
12 major aerospace systems projects, from 1964 to 1977.
The results show that the announcement has a significant positive effect on the winner’s profit, a significant negative effect on the loser’s profit and, perhaps more interestingly, the overall effect is not significantly different from zero.
Such evidence matches closely the predictions of our model: according to it, the supplier’s expected profit conditional in winning ( p − φ − E [ c
(1) should indeed be positive, the losers incur a loss ( − φ − k ), 20
] − k ) while the total profits, being equal to the ex-ante expected profits, should be 0.
Furthermore, when the design costs are very large, the number of potential suppliers is small, and this makes the apparent differences in profits larger. Indeed this seem to be the case in defense procurement: the number of firms that participate is 2 or 3 in each project in Rogerson’s sample, and it is does not seem unreasonable to presume that R & D expenses are extremely high in this industry.
The fundamental rationale behind Rogerson analysis and the current one is the same, even though Rogerson’s argument relies more in the moral hazard aspect of R & D investment. However, the current analysis contributes to the discussion because it is simpler and more formal, and may lead to obtain further predictions and policy implications.
20 This is negative, by Corollary 3.1. Also p − φ − E [ c
(1)
] − k should be positive, otherwise total suppliers’ expected profits would be negative and the participation constraint would be violated.
13

As an example, consider the debate on whether indirect R & D (I R &
D), that is, direct subsidy to R & D investment, should be provided. One implication of the current model is that monetary transfers in the development phase ( φ ) if anything should be negative 21 , and therefore I R & D should not be used, contrary to implication 8 in Rogerson (1989).
Of course such an implication should be interpreted with care, given that the model incorporates the R & D investment decision in a very crude way and does not consider moral hazard issues.
22 But it illustrates how a more formal treatment can provide a basis to investigate several implications of the theory in an integrated way.
As mentioned before, one market that motivates this research is the automobile parts industry. The market for one particular part roughly fits the assumptions made in the model. Since in many cases parts are customized for one particular model, there is typically one large buyer with bargaining power to license suppliers and design the contract scheme it prefers. Differences in design complexity and flexibility are likely to generate large variation in the amount of set-up costs and relationship-specific investing ( k ) across different parts industries.
An interesting aspect of this market is that there is a dramatic variation in relationship practices across different buyers. There are at least two markedly different systems: the so-called “American”, which in our typology would be market-oriented, and the “Japanese”, that relies more in closer, long-term relationships.
23
Asanuma (1989 and 1992) describes many aspects in how these systems differ, and a few of them seem to agree with our model. This section discusses two of these aspects: the large differences across the “systems” in the number of suppliers and in their degree of involvement in design.
21 Corollary 3.1.
22 However, one intuitively expects that in an unobservable effort model there seems to be even less reason to adopt an ex-ante subsidy rather than an ex-post prize as an incentive device.
23 The American and Japanese labels refer to the place where each system originated, and not to any characteristic intrinsically national. In fact, nothing in principle precludes a firm from one country to utilize the other system. This is what many American firms pursued during the mid-eighties. Also, many Japanese manufacturers, such as Mazda, have systems that are not quite “Japanese” (Asanuma 1992).
14

Asanuma (1992) reports staggering differences in number of suppliers per company. The figures collected by him (p. 102) show that American firms have 1 or 2 orders of magnitude more suppliers than the Japanese.
Such numbers are summarized in Table 1. It is hard to believe that, with such strikingly different figures, the number of suppliers does not play a preeminent role in the logic behind the differences in the systems.
24 Asanuma also provides evidence that the number of suppliers per plant is also much larger among American companies, in spite of the fact that their plants are typically half the size of their Japanese counterparts.
Firm Number of suppliers
GM
Ford
Chrysler
Toyota
Nissan
Mazda
5500–35000
2500
2000–15000
172–224
163
338–1288
Table 1: Number of suppliers per company in 1986.
It is a difficult, and probably impossible, task to identify the single cause of such large differences in the number of suppliers. As many authors emphasize (Asanuma 1989, Asanuma 1992, Aoki 1990), the relationship with suppliers in the Japanese system is distinct from more standard practices in many different aspects, and such aspects exhibit strong complementarities that prevent them from being adopted in isolation (Milgrom and Roberts
1990).
One can still identify partial complementarities in the practices and use them to evaluate the validity of the theoretical predictions. Asanuma discusses several aspects of the Japanese system that are complements to a smaller number of suppliers. One such aspect relates very closely with the analysis made here: the larger degree of involvement of Japanese suppliers
24 The ranges in the figures are due to alternative classification criteria for suppliers; c.f.
Asanuma for details. Notice that, according to the view that Mazda’s system is not quite
“Japanese” Asanuma (1992, p. 121–2), its number of suppliers is somewhat larger. Since
Mazda is not particularly large, this indicates that the difference can be partly, but not completely, due to differences in sizes of each manufacturer.
15

Classification Buyer: Examples ordered Drawings I provides minute goods supplied manuf. instructions
II provides blueprints
III provides rough
Assembly of small parts
Stamping of small outer parts
Small plastic drawings parts of dashboard
Drawings IV has substantial knowSeats approved ledge of manuf. process
V has interm. knowledge Brakes, bearings, of manuf. process tires
VI has limited knowledge Radios, electronic of manuf. process injection systems, batterys marketed goods
VII selects from supplier catalog
Table 2: Asanuma’s parts and suppliers classification scheme.
in the design phase, both of the product and its production technology.
In order to investigate this feature, Asanuma develops a taxonomy of 7 different degrees of involvement in design. Such taxonomy is presented in
Table 2.
The first two columns of Table 2 present the two more conventional distinctions made in the Japanese Industry. The dichotomy between ordered
( gaichuhin ) and marketed goods ( shihanhin ) is a traditional one in Japan, and is often used in official statistics (Asanuma 1989). The classification of ordered goods in “Drawings Approved” (DA) or “Drawings Supplied” (DS) 25 is a more recent one, and reflects an increase in the variety of the degree of involvement of suppliers in design that occurred in some industries.
Such an increase is due mostly to an expansion of DA practices and an increase in the responsibility of the suppliers in the industries that are associated with the “Japanese system” such as the automobile parts industry.
Indeed the shared responsibility of the suppliers in the design of the product and the line of production and in keeping high quality standards is one of
25 In Japanese, shoninzu and taiyozu , respectively (Asanuma 1989, p. 12).
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the central features of the Japanese system (Asanuma 1992).
Asanuma’s I–VI scale for ordered goods is very closely related to d in our model. A firm that adopts a “Japanese system” is likely to procure more of its parts in a DA fashion, that is, to select more often higher values of d .
Under this interpretation the striking differences in the number of suppliers shown in Table 1 might be explained by Proposition 2.
Some of the incentive practices typical of the Japanese system also indirectly provide support to another prediction of the model. As Asanuma discusses, a large component of the incentive system for the suppliers is the possibility of being “upgraded” from lower degrees in the I–VI scale to higher ones. This indicates that profits are perceived to be larger in the DA categories — again, as our model predicts, supplier profits are larger when n
(and d ) is higher.
The task undertaken in this paper was to obtain a model of ordered goods procurement that would satisfy the following wish list: i) allow for agents to choose any contractual form; ii) generate testable implications; and iii) be as simple as possible.
The postulation of a simple, symmetric environment allowed to characterize any form of contract with a small number of economically meaningful variables. Results from Monotone Comparative Statics and Optimal Auction Theory lead to some testable results that, within the boundaries of the model, do not depend on specific functional assumptions.
In section 3 such results were confronted to the evidence collected from the work of Rogerson and Asanuma about the Defense procurement and the Japanese automobile parts industry, respectively. The results of this comparison were encouraging; the evidence does not seem in a first look to falsify the main predictions of the model. This cannot however be interpreted as a full-fledged test of the model, first because the evidence utilized comes from secondary sources, that collected it for other purposes; and second because several implications of the theory are intuitively natural ones, that could possibly be obtained by other models. Therefore a more thorough empirical testing is left for another occasion, when both primary data and deeper theoretical predictions would hopefully be available.
The focus on simplicity also left many probably interesting and impor-
17

tant extensions for the future. In the remaining of the text I briefly discuss examples of such extensions.
When one first thinks about arrangements where specification responsibilities are shared such as the ones discussed here, the most important information asymmetry that seems to exists is the one related to unobservable effort, or moral hazard, rather than the one considered here.
Indeed, this is also clear in the applied papers discussed in Section 3: the central information asymmetry in Rogerson is the inability of the government to monitor the firms’ R & D investment; likewise, several contractual features in the Japanese system are meant to discipline and motivate, and not to screen existing unobserved capabilities.
It is important to address in the future how would the results of the model change if the underlying unobserved variable were object of choice of the agents, rather than exogenously given.
A multi-period extension of the model would be very valuable in order to study more carefully the Japanese supplier relationship, given that dynamics play at least two important roles in the “modern manufacturing” phenomenon. Since these roles are distinct, I discuss each in turn.
4.2.1
Long-term Relationships
Students of the Japanese system such as Asanuma point out the existence and importance of long-term relationships between buyers and suppliers as one of the main sources of cooperation.
In a paper that seeks to explain exactly the supplier incentives in each system, Taylor and Wiggins (1997) model a different trade-off that has as a central feature these long-term relationships. According to their model, the
Japanese supplier delivers quality products in order to keep a profitable longterm relationship, while its American counterpart does so because the buyer regularly makes quality inspections. Their model is interesting because it shows how in a repeated game environment long-term relationships can have
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an important effect in fostering both efficiency and a cooperative, rather than adversarial, environment.
Since all these aspects seem to be central in the Japanese system by the account of Asanuma, it seems important to allow for repeated interaction in our model in order to obtain a more realistic representation of the Japanese system.
However, the Taylor and Wiggins model does not take into account the role of market competition in fostering efficiency, in spite of the title of the paper. I am convinced by the evidence discussed in Asanuma (1992) that market competition, rather than quality inspections, play the central role in the American system, so the present model in spite of its simplicity contributes to the debate.
A natural and important direction of research would be therefore to seek a model that allow for the possibility of equilibria sustained by long term relationships (rather than a vague notion of non-market contracting) or by market competition (rather than relatively unimportant quality inspections).
4.2.2
Flexibility and Evolution
Two other dynamic aspects of the modern manufacturing phenomenon deserve mention and can be subject to study in the future. One is its historical evolution; the complementarity of the practices within each system generates momentum (Milgrom, Qian, and Roberts 1991) that prevents gradual change. The mid-eighties experience of American auto manufacturers trying to shift to the Japanese system can be valuable to investigate the validity of this theory and to highlight the existing complementarities.
26
Another aspect that is puzzling for me is to assess how flexible each system is. Many authors stress as one of the main advantages of the Japanese system its flexibility with respect to technological change and its ability to customize its product line to satisfy demand needs. On the other hand, the system seems to be quite resilient to adapt itself to the recent worsening led by the recession and the appreciation of the Yen. It would be useful to have a model capable of explaining the nature of this asymmetric response to different kinds of shocks that the Japanese system presents.
26
Another valuable historic evidence is the recent experience of Japanese manufacturers in installing plants abroad, to test how much of the Japanese system can indeed be efficiently “exported”.
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This appendix suggests two ways in which one could model the decision in the specifications that would generate as a “reduced form” the functional forms considered in the text (and, in particular, V ar ( c i
) = σ 2 decreasing in d ).
d
In this interpretation 27 the parameter d is a measure of the time at which the suppliers get involved in the design process: From period 0 to 1 − d the design is done by the buyer; at time 1 − d the suppliers are called to participate and from then on, until time 1, they take care of the design.
The true production cost is only known once the design phase is completed, at time 1. Since they are selected at time 1 − d , they should base their behavior in the estimate of the cost at that point in time. Call this estimate c i
. So c i
= E [cost | Information at 1 − d ], and the fact that information improves with time implies that the variance of c i is decreasing in d .
It is important to note that under this interpretation k should be seen not as the design cost itself but rather as an information gathering and bid preparation cost. If the supplier is chosen before the design takes place, only one supplier will actually invest in finishing the design, and the supplier’s design cost does not affect the choice of n . (It will still affect the choice of d , though.) d
Suppose the set of possible specifications s is a region A of a normed, complete space, say R n . Production costs depend on how well the technological capabilities of the supplier fit the chosen specifications; in the spatial metaphor this is equivalent to say that the cost c i is a an increasing function of the distance between s and an “ideal specification” s ∗ i from the point of view of supplier i : c i
= C ( k s − s ∗ i k ). Likewise we assume that there is an ideal specification s ∗
0 for the buyer, and V = V ( k s − s ∗
0 k ).
We model partial specification by the buyer in the following way: The buyer chooses a set D ⊂ A ; the supplier is then allowed to select a specification s ∈ D . In this interpretation the parameter d , the amount of freedom
27 I thank Paul Milgrom for suggesting me this interpretation.
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the supplier has, measures the relative size of the set D with respect to A .
Note that D ⊂ D 0 ⇒ min s
∈
D
C ( k s − s ∗ i k ) ≥ min s
∈
D 0
C ( k s − s ∗ i k ), so productions costs are expected to be smaller. It is also intuitively reasonable to expect a decrease in uncertainty, since a larger set D implies that the chosen s is closer to s ∗ i
, and therefore is expected to fall in a smaller region of A . (For example, if the only source of uncertainty in c i is the choice of the specification, then a large D would lead to many interior solutions for min s ∈ D
C ( k s − s ∗ i k ), and therefore c i increasing in d .) would be a constant with probability
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