A Didactic Example of Linear (Multidimensional) Screening Contracts

Abstract

This short paper proposes a didactic example on how to solve a multidimensional screening problem in the linear case. In the proposed example, shareholders of a cash-constrained firm propose to the firm management a recapitalization in counterpart of the distribution of future dividends. The capacity of the firm to distribute future dividends depends on its production costs and its technology, which are private information of the management. Thus shareholders face a (multidimensional) screening problem. We completely characterize the optimal menus of contracts that shareholders offer. Notably, we show that there always exist optimal menus of contracts with at most two contracts offered: a low dividend, low recapitalization contract and a high dividend, high recapitalization contract. This is an extreme case of bunching.