The Principal-Agent Relationship: Two Distributions Satisfying MLRP and CDFC.

The first-order approach, which consists in replacing the incentive compatible constraint by the agent's first order condition, is widely used in agency problems where the principal cannot observe the level of effort chosen by the agent. This substitution is valid with the Monotone Likelihood Ratio Property and the Convex Distribution Function Condition. Unfortunately, revenue distributions seldom present both properties. In this note, we provide two examples of revenue distributions that satisfy MLRP and CDFC. We also give their counterpart in terms of loss distribution.