When does Shareholder Unanimity obtain? A review and discussion of the famous "shareholders unanimity result" or questionning the foundations of modern corporate finance.

The purpose of this note is to review and understand what is called the shareholders unanimity result in the finance literature. We first will stress that "unanimity" is an equilibrium concept, which requires that an investment decision in a largely held firm be taken only if all shareholders agree upon it. We stress that this concept is suited to the case of complete financial markets, since it automatically holds. The unanimity concept is less satisfactory in the case of incomplete markets. In fact, overly stringent conditions on the fundamentals are required to have unanimity among shareholders hold. The literature proposes two classes of conditions for which unanimity obtains. A first class of auspicious cases for unanimity is that for which the economys aggregate production set is generated by a finite set of vectors. This is classically called the spanning condition. A second class of favorable conditions is when preferences are of the Hyperbolic Absolute Risk Aversion type. We shall wonder what is it about HARA functions that saves unanimity? Finally we shall discuss the following: can we think of other classes of preferences, maybe non additive for which the unanimity based criterion survives?