This paper studies adverse selection problems with a one-dimensional principal instrument and a two-dimensional agent type. We provide an optimality condition that characterizes the bunching of continuum types. The approach is based on a reparameterization of the type space in terms of the endogenous optimal allocation level curves. The condition obtained is related with the optimality of two pooling types in the one-dimensional screening without the single-crossing. We illustrate the method by analyzing one example from the literature as well as a new example far from the linear-quadratic case

中文翻译：

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二维筛选的必要最优条件

本文研究了一维主体工具和二维主体类型的逆向选择问题。我们提供了表征连续体类型的最佳化条件。该方法基于根据内生最优分配水平曲线对类型空间进行重新参数化。获得的条件与在一维筛选中不进行单交叉的两种合并类型的最佳性有关。我们通过分析文献中的一个例子以及远离线性二次方程的新例子来说明该方法。