Adverse selection problems without the Spence-Mirrlees condition
Humberto Moreira | Araujo, Aloisio
Spence-Mirrlees condition; marginal rate of substitution and rent identities; discrete pooling.
We relax the single crossing property or Spence-Mirrlees condition (SMC) for the adverse selection problem and derive the conditions for incentive compatibility (IC). Economically, this requires that the principal has to take care of wider varieties of strategic behavior of the agent who can now mimic the behavior of other types that are not necessarily nearby. We prove that in order to do that he has to equalize the marginal rate of substitution and the marginal rent between pooling types. This implies a change in the trade off between rent extraction and distortion leading to a lower level of total welfare. Mathematically, our necessary conditions are expressed by a generalized Lagrangian which contains terms other than the standard first and second order conditions of the IC constraints. The incentive compatible contracts can present discrete or continuos pooling and they are discontinuos even under the monotone hazard rate condition. We do not enter into the full complexity of contracts, so we just consider the case of at most one discontinuity. In the space of the limit of continuos contracts, the optimal contract is characterized. In the context of a wider set of contracts we present a class of incentive compatible contracts which approximates the optimal. The non SMC arises naturally when we are dealing with a multidimensional characteristic problem with countervailing incentives (given by the correlation between two sources of asymmetric information). Therefore, our paper also gives a framework to study multi-characteristic adverse selection problems. We give some examples of these in the following contexts: combination of moral hazard and adverse selection, nonlinear pricing, regulation and labor contract.