An Adverse Selection Model with Finite Number of Types and Informational Rents

In the paper we analyze a contractual relationship between two economic agents using a standard Principal-Agent approach from the theory of incentives. The Principal wants to delegate a production activity to an Agent privately informed about his marginal cost of production. This problem corresponds to a classical model of adverse selection. We first present the standard model with two types of agent and then we generalize it, assuming that the type of agent belongs to a finite set of values. We provide a full characterization of the Principal’s optimization problem and we solve it using Kuhn-Tucker techniques. Focusing on the economic interpretation of the optimal solution, we also use a change of variables. The optimization problem is next expressed in terms of the new variables, the informational rents. In the last part of the paper we derive and summarize the characteristics of the optimal contracts in the situation of asymmetric information.