The value of information and optimal organization.

Further, when the degree of substitutability is sufficiently large, it becomes too costly in terms of efficiency losses to use a mechanism in which the quantity of one input increases in the quantity of the other input. But when the ordering of quantities is reversed, the value of information in the single-agent mechanism becomes superadditive because of the extra deviation factor: a low-cost producer of both inputs obtains more profits by misrepresenting both input costs as high. This "coordinated" deviation is infeasible in the two-agent mechanism, so the two-agent mechanism is optimal in this case.

Another interesting set of issues arises in the context of delegation. A delegation mechanism cannot be more profitable than the two-agent mechanism, and the two are equivalent if the primary contractor could not exploit her position of an informational intermediary to increase her profits. Thus, the key issue is whether the primary contractor benefits from intermediating the subcontractor's cost information or simply passes it on to the principal. Potentially, she could benefit from this role in two ways. First, she could try to appropriate some of the subcontractor's informational rent. Second, she could manipulate the report regarding the subcontractor's type to increase the rent on her own information.

I consider four delegation structures which differ in the extent of the principal's contractual abilities. Although the exact conditions under which the two-agent and delegation mechanisms are equivalent vary with the contractual framework, the main conclusion remains the same. The primary contractor benefits from her role of an informational intermediary if the quantity of one input has a significant effect on the marginal product of the other input, that is, if the degree of complementarity or substitutability between the inputs is sufficiently large. To understand this result, note that under these conditions the quantity of the input produced by the primary contractor and hence her informational rent are sensitive to the subcontractor's information. Hence, the primary contractor has stronger incentives to manipulate the latter.

In the context of delegation, I also consider the issue of the optimal choice of the primary contractor. To the best of my knowledge, this issue has never been addressed in the literature before. I identify the conditions determining whom of the two agents the principal should employ as the primary contractor. Specifically, I show that the primary contractor should be the agent who produces an input that has a smaller effect on the marginal product of the other input and who is more likely to be a high-cost producer.

The issues of incentives in organizations and optimal organizational structure have been studied by a number of authors. (4) Baron and Besanko (1992), Gilbert and Riordan (1995), Da Rocha and de Frutos (1999), and Jansen (1999) examine the issue of optimal organization under perfect complementarity between the inputs. Baron and Besanko (1992) and Gilbert and Riordan (1995) show that the single-agent mechanism is superior, and the optimal allocation can also be implemented via delegation. (5) In contrast, Da Rocha and de Frutos (1999) demonstrate that the two-agent mechanism becomes superior under perfect complementarity when the supports of the two cost distributions are sufficiently asymmetric.

Dana (1993) focuses on the effect of correlation in the cost structure under separability of the production function in the two inputs. He shows that the two-agent mechanism is optimal when correlation is sufficiently strong, which allows the principal to exploit relative performance evaluation. Jansen (1999) attains a similar conclusion under perfect complementarity and limited liability assumptions. Demski, Sappington, and Spiller (1987) study the effect of cost correlation on a different organizational choice--optimal input supplier switching. "Informational economies of scope" discussed by Dana under separability are similar to the effect of our internalization factor. Yet, in contrast to his approach, this article focuses on technological interdependency between inputs and its effect on the relative strength of internalization and extra deviation factors.

Perfect complementarity and separability are interesting but quite special cases. Gilbert and Riordan (1995) point out that their analysis of the optimal regulatory regime for the electric power and natural gas industries "depends on the fixed proportions production technology. This is perhaps questionable even in the electricity example, because optimizing the transmission grid may reduce the need for the new generation capacity"; that is, the quality of the grid and the volume of electric power appear to be substitutes. On the other hand, a higher quality of the grid means a higher stability of the network and a lower probability of outages. This may allow consumers to use more electricity and rely less on other forms of energy. So, the same two inputs may be complements. Other examples with some degree of complementarity or substitutability include express and regular mail, long-distance and local telephony, internet and telephone communication, defense systems and municipal projects with multiple components. The results of this article can be applied to obtain conclusions regarding the optimal regulatory regime and optimal purchasing and procurement decisions for these goods and services. Our analysis can also be used to explain the structure of the bicycle manufacturing industry, as well as

the trends in enterprise soft-ware and procurement decisions in the electronics industry. I discuss these examples in greater detail in Section 2.

In a related contribution, Mookherjee and Tsumagari (2004) study a model with a homothetic benefit function of the principal and a continuous type distribution. They show that the single-agent organization dominates under complementarity when the input costs are identically exponentially distributed, whereas the two-agent organization performs better under substitutability. These results are similar to Propositions 1 and 3 in this article. The difference between their paper and this one boils down to two aspects of the model which, in turn, generate two substantive differences in results. First, the assumption of homotheticity of the benefit function implies a stable relationship between the marginal products of the two inputs which guarantees that nonlocal incentive constraints are never binding in Mookherjee and Tsumagari (2004). In contrast, I allow for an arbitrary benefit function. This leads me to show that, when the benefit function is sufficiently asymmetric, the extra deviation factor becomes effective under complementarity via binding horizontal incentive constraints, and as a result the two-agent mechanism becomes optimal (see Proposition 2).

Second, the definitions of substitutes (complements) in Mookherjee and Tsumagari (2004) are based on the properties of the optimal two-agent (single-agent) mechanism and, thus, do not refer directly to the parameters of the model. In contrast, I define complements and substitutes on the basis of the sign of the cross-partial derivative of the principal's benefit function. Then I show that a single-agent mechanism is optimal under a small degree of substitutability (see Proposition 4). However, it would be impossible to classify this case in Mookherjee and Tsumagari (2004), as it satisfies both their definition of substitutability (the optimal quantity of an input in the two-agent mechanism is increasing in the cost of the other input) and their definition of complementarity (the optimal quantity of an input in the single-agent mechanism is decreasing in the cost of the other input).

The comparison of the single-agent and two-agent mechanisms provides additional insights regarding the potential for collusion in organizations. Laffont and Martimort (1997, 1998) have studied this issue in a similar framework under perfect complementarity. (On the issue of collusion, see also Laffont and Martimort, 2000, and Faure-Grimaund et al., 2003.) They have shown that the potential for collusion exists only under additional restrictions on contracts, such as anonymity. Our results allow us to explain why a stake of collusion does not exist without such restrictions: under complementarity the value of information is typically subadditive, and so the principal prefers informational centralization. Thus, the principal would actually benefit if the agents could collude in the two-agent mechanism and coordinate their strategies to maximize their joint profits. (6) More generally, I show that a stake of collusion always exists under substitutability. Under complementarity, it exists if the two-agent mechanism is optimal (e.g., under the conditions of Proposition 2).