The value of information and optimal organization.

Our analysis of delegation in hierarchial mechanisms is related to the work of Melumad, Mookherjee, and Riechelstein (1995). Of the four delegation mechanisms that we consider, two ([H.sub.1] and [H.sup.ep.sub.D]) were first studied by these authors, whereas the other two ([H.sub.D] and [H.sup.ep.sub.1]) have not been considered previously. Melumad, Mookherjee, and Riechelstein (1995) establish that the delegation mechanism [H.sub.1], in which the primary contractor reports her cost to the principal before communicating with the subcontractor and only has to break even in the interim, is equivalent to the two-agent mechanism in the case of a continuous distribution of types. Interestingly, we show that such equivalence does not hold when the set of types is finite. Intuitively, this is due to the fact that in the continuous type case, incentive constraints which involve the primary contractor misrepresenting both her own and the subcontractor's costs hold if the incentive constraints involving a misrepresentation of only one of the two costs are satisfied. However, this is not true in the discrete case under a large degree of substitutability or complementarity (for a more detailed explanation, see footnote 12). In particular, under these conditions, in our model the binding incentive constraint involves the primary contractor reporting her own low cost as high and claiming that the subcontractor's cost is low, irrespective of the true level of the latter, whereas the incentive constraints involving only a misrepresentation of the primary contractor's cost are nonbinding.

As for the hierarchy [H.sup.ep.sub.D], in which the primary contractor accepts the contract offered by the principal only after contracting with the subcontractor and which is equivalent to hierarchy [H'.sub.1] in Melumad, Mookherjee, and Riechelstein (1995), the added value of the analysis in this article consists of deriving the exact conditions--in particular, a small degree of complementarity--under which [H.sup.ep.sub.D] attains the performance of the two-agent mechanism.

The two new hierarchies introduced in this article, [H.sub.D] and [H.sup.ep.sub.D], capture alternative and realistic scenarios of contracting. In [H.sub.D], the primary contractor accepts the principal's contract without reporting her cost. She then contracts with the subcontractor and reports both costs to the principal, but does not have an option to withdraw from the contract after learning the subcontractor's cost. In contrast, in [H.sup.ep.sub.D] the primary contractor first reports her cost to the principal, but can withdraw from the contract at a later stage after receiving the subcontractor's cost report.

The analysis of the single-agent mechanism in this article involves solving a screening problem with a two-dimensional type distributed over a discrete domain, and an arbitrary benefit function of the principal. By characterizing the optimal mechanism in this case and identifying the conditions under which the extra deviation factor is effective and hence nonlocal incentive constraints bind, the article contributes to the literature on multidimensional mechanism design (see Matthews and Moore, 1987; McAfee and McMillan, 1988; Armstrong, 1996; Rochet and Chone, 1998; Wilson, 1993). The paper in this literature that is most closely related is Armstrong and Rochet (1999), who provide a complete characterization of the optimal screening mechanism with two-dimensional agent's type under separability between the goods, but with an arbitrary degree of correlation between the parameters of the agent's type. This article complements theirs, as I characterize the optimal two-dimensional screening mechanism for an arbitrary degree of complementarity or substitutability between the goods but with independently distributed type parameters.

On a more technical side, the contribution of this article lies in demonstrating how the homotopy technique can be applied to compare the performance of different organizational forms. Specifically, I connect the sets of the first-order conditions characterizing the optimal mechanisms in different organizational forms homotopically, that is, via a continuous transformation, and use this to compute the difference between the principal's expected payoffs in the two organizations. I believe that this technique can be used more broadly in the analysis of organizational and contractual problems.

The rest of the article is organized as follows. In Section 2, I discuss several examples and applications of the results presented in this article. In Section 3, I present the model, characterize optimal mechanisms, and describe the results for the symmetric case. Section 4 deals with the complementarity case, and Section 5 deals with the substitutability case. Section 6 studies delegation. Section 7 addresses the issue of collusion. The proofs of Propositions 1 and 2 are in the Appendix. The rest of the proofs are in the online supplement available at http://www.severinov.com/organization_AppendixB.pdf.

2. Examples and applications

* This section discusses how the results of this article, which will be established in the rest of the paper, can be applied to explain the prevailing forms of organization and to provide recommendations regarding the optimal structure and regulation in several industries.

First, consider the regulation of the electric power industry. As discussed in the Introduction, it is conceivable that the two main components there--the electric power itself and the quality/capacity of the transmission grid--could be either substitutes or complements. This is ultimately an empirical question. In particular, the amount of power and the transmission grid are substitutes if a higher quality of the grid reduces losses and hence demand for the electric power. If the degree of substitutability between these inputs is sufficiently large then, according to Proposition 3, the optimal regulatory regime involves disintegration. It is notable that current regulatory policies in several U.S. states (e.g., California) are gradually moving in this direction. Disintegration is also optimal if these two inputs are complements, but there is a large asymmetry between them (see Proposition 2). This situation is also plausible, because the marginal benefit of an extra unit of power is likely to be as sensitive to an increase in the quality of the grid as to an increase in the volume of energy.

As a related point, this article also suggests (see Proposition 3) that it is optimal to use different providers for regular and express mail, as these are substitute services with a significant degree of substitutability between them. Therefore, the legislative restrictions curbing the ability of the U.S. Postal Service to develop its express mail capabilities could be justifiable.

My results can also be used to explain the regularities in the market for enterprise applications software (often referred to as ERP software). These software applications automate different corporate functions, such as sales, finance, customer relations management, manufacturing, human resources, inventory control, supply chain management, and so on. At the early stages of this market, different software applications were offered for each corporate function, and a limited number of vendors competed in each category, such as Peoplesoft in human resources, SAP in finance, Siebel in sales, i2 in supply chain management, and so on. As the ERP software market evolved and consolidated through mergers, two larger and more successful companies, SAP and Oracle, started offering integrated software serving most corporate functions. However, the market acceptance of such integrated software suites was and remains fairly low. (See Symonds, 2003 for a detailed account of the competition in this industry and the limited success of Oracle's strategy of offering an integrated suite of business applications.) Customers are particularly reluctant to use software from a single supplier for more closely related functions, such as sales, finance, and customer relationship management, or manufacturing and supply chain management. Instead, the corporations are more willing to use software from different providers in related areas, despite the fact that this involves certain functional and data duplication (for example, sales software from one provider and finance software from a different provider would both contain information about order flow and would be capable of producing statistical reports regarding it), and then integrate diverse applications with the help of third-party system integrators, such as IBM or Accenture.