The value of information and optimal organization.

Such customer strategy can be easily explained in the framework of this article. Because software applications for related business areas typically have some degree of overlap and duplication, purchasing such applications from a single source is similar to procuring substitutable inputs from a single supplier. As our results show, the pitfall of this strategy is that a single supplier of such software applications would be able to extract more rent from a customer after the initial purchase--in the form of service and consulting fees, and payments for upgrade modifications--than the sum of what a customer would expect to pay for such services and upgrades to two different suppliers. If the degree of substitutability between the products if sufficiently large, then this factor would be more important than possible economies of scope from using an integrated software suite. So it would, indeed, be optimal for customers to purchase ERP software from different suppliers, consistent with Proposition 3 below. On the other hand, if the degree of substitutability is fairly small, then the customers would be better off with an integrated business software suite, as follows from Proposition 4. So far, the practices in this industry suggest the former to be the case.

The results of this article can also be used to explain the regularities in the bicycle manufacturing industry. Similarly to business software, the bicycle production process has historically been modularized. Different components of a bicycle (frame, tires, wheels, brakes, gears and shifters, pedals, and saddle) are produced independently of each other and then assembled either by specialized designers or by frame manufacturers. Established international standards ensure that the components are interchangeable and can be easily mixed and matched in the final bicycle assembly. So coordination between manufacturers of different components is unnecessary, and innovations are introduced in each component separately, as pointed out by Galvin and Morkel (2001). The number of suppliers of each component does not exceed two or three. For instance, there are only two main producers of gear shifters and moving mechanical parts in the world, Shimano and SRAM, and one fringe supplier--Campy. The situation is similar in the production of other components (for more details, see Chang, Saloner, and Shimano, 2006). Furthermore, antitrust litigation between suppliers has led to elimination of bundling.

With few oligopolistic component manufacturers competing on quality rather than price and quality being the main determinant of the consumers' valuations, this environment fits quite well with the model that I study below. Interestingly, the structure of supplier relationships in the bicycle industry is generally consistent with the predictions of this article. A bicycle normally contains components manufactured by several suppliers. Yet, it is typical for bicycle assemblers, such as Trek, Specialized, or Giant, to procure components that have functional complementarities--such as gear shifters and wheel hubs, headsets, and forks--from a single supplier, although they can easily be procured from different suppliers, as no coordination between suppliers is required. Such practices are consistent with our results saying that it would be more cost effective for a bicycle assembler to procure complementary parts from a single supplier (see Proposition 1).

Finally, the results of Section 6 on delegation can be applied to explain the structure and supplier relationships in vertical supply chains. In particular, in recent years, major suppliers of electronic products (OEMs), such as HP, Motorola, and IBM, have to a large extent outsourced manufacturing to subcontractors. One of the issues that these OEMs have faced is whether they should allow subcontractors to negotiate and purchase materials and components used in production (which is equivalent to the delegation mode in our analysis) or whether the OEMs should negotiate and procure the components themselves and then hand them over to contract manufacturers (which is equivalent to a decentralized mechanism in our analysis). HP has always pursued the latter route. Motorola originally delegated component procurement to subcontractors, but it has recently reversed its policy (see Sullivan, 2003 for details). Motorola found that it could increase its profits by engaging in procurement and directly negotiating with component suppliers. Higher profitability of direct negotiations can be explained by referring to our results. If the contract manufacturers' productivity is significantly affected by the characteristics of the components, that is, the degree of substitutability or complementarity between the subcontractors' inputs and the necessary components is large, then, as Propositions 5-7 predict, it would be optimal for OEMs to procure the components directly, rather than to delegate. The reversal of Motorola's policy can be interpreted to indicate that this is, indeed, so.

3. Model and preliminaries

* A central entity, or principal, needs to procure two different goods or inputs. The principal's benefit is measured by the production/benefit function v([q.sub.1], [q.sub.2]), where [q.sub.i] is the quantity of input i, for i [member of] {1, 2}. I assume that v(., .) is increasing in both arguments, twice continuously differentiable, and concave. The cross-partial derivative [v.sub.12](., .) has a constant sign over the relevant domain. We will say that the inputs are complements (substitutes) if [v.sub.12](., .) [greater than or equal to] 0 ([v.sub.12](., .) < 0). To ensure that the optimal quantities are positive, I impose the Inada boundary condition: [lim.sub.q1 [right arrow] 0] [v.sub.1]([q.sub.1], [q.sub.2]) = [infinity] for all [q.sub.2] > 0. This condition is dropped when I consider specific examples.

I will compare the performance of three organizational forms illustrated in Figure 1: centralized organization (one agent produces both inputs), decentralized organization (each input is produced by a different agent), and delegation mechanism where the agents are organized in a hierarchy and the principal contracts only with the supplier of one input, who in turn contracts with the supplier of the second input. (7) In each organizational form, the principal offers a contract(s) to the agent(s), who may either accept or reject the offer. If the contract(s) is (are) accepted, the agent(s) produces and delivers the goods/inputs to the principal and gets paid according to the contract(s). Additional contracting stages in the delegation mechanism are described in Section 6.

[FIGURE 1 OMITTED]

The principal maximizes her expected benefit net of the expected payments for the inputs. The agents(s) are risk neutral and decide whether to accept a contract after privately learning their production cost(s). An agent's reservation utility level is normalized to zero. An agent cannot produce the good which she is not assigned to. The marginal costs of production are constant and are independently distributed across goods and across agents. Specifically, it is common knowledge that the marginal cost of good i is low ([C.sub.L]) with probability [P.sub.i], and is high ([C.sub.H]) with the complementary probability, where [C.sub.H] > [C.sub.L] > 0. Let [DELTA] = [C.sub.H] - [C.sub.L]. Because the benefit/production function v(., .) can be arbitrarily asymmetric, the assumption that the distributions of input costs have a "common support" is equivalent to a less-restrictive "common ratio" assumption [C.sup.1.sub.L]/ [C.sup.1.sub.H] = [C.sup.2.sub.L]/ [C.sup.2.sub.H] from which common supports can be obtained by simple renormalization of units. Independence of distributions is assumed in order to abstract from factors on the cost side.

Let us now describe the contracts offered by the principal in the single-agent and the two-agent mechanisms. By the Revelation Principle (see e.g., Baron, 1989), we can restrict attention to incentive-compatible direct mechanisms in which every agent reports her cost truthfully. Recall that a direct mechanism is a mapping from the set of possible cost types {[C.sub.L], [C.sub.H]} x {[C.sub.L], [C.sub.H]} (or states of the world) into the set of quantities and transfers: [R.sup.2.sub.+] x [R.sup.2] (in two-agent mechanism) or [R.sup.2.sub.+] x R (in a single-agent mechanism). The four possible states of the world are denoted by LL, LH, HL, and HH. In this notation, the first (second) letter indicates the marginal cost of the first (second) good.

Let [q.sup.i] = ([q.sup.i.sub.LL], [q.sup.i.sub.HL], [q.sup.i.sub.HH] denote the vector of quantities of good i [member of] {1, 2} assigned in the two-agent mechanism. By convention, the first letter in the subscript refers to the marginal cost of good i. For example, in the state LH, the mechanism assigns quantities [q.sup.1.sub.LH] and 2 [q.sup.2.sub.HL]. Let [t.sup.i.sub.KJ] denote the transfer to the agent producing good i, in the case when she announces cost [C.sub.K] and

the other agent announces cost [c.sub.J](K, J [member of[ {L, H}). The two-agent mechanism has to satisfy the following interim incentive and individual rationality constraints for each i and j [member of {1, 2}, i [not equal to] j:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

[FIGURE 2 OMITTED]