Competition and Unanimity Revisited
用简单例子讨论竞争性股票市场理论的新发展，质疑了文献中关于股东一致性的核心观点，特别是市场完全性（spanning）的必要性，并证明完美竞争可以在没有完全市场的情况下存在。
Some recent developments in the theory of competitive stock markets are discussed and illustrated in this paper, using simple examples. These developments challenge the central role played by in the literature dealing with unanimity among shareholders. Harry DeAngelo's 1981 article gives a clear account of some popular views about the central importance of spanning, and is used to focus my presentation. In DeAngelo's article, there are three basic claims: (a) If all initial shareholders in a firm have perfectly competitive conjectures and there is spanning, net market value maximization will be unanimously favored by initial shareholders as the objective of the firm whether or not there are short sales of the firm's shares (perfect competition plus spanning imply unanimity). (b) Perfectly competitive conjectures only make sense when there is spanning (perfect competition implies spanning). (c) For perfectly competitive conjectures to be correct, there must not only be spanning, but also constant returns to scale, and hence zero profits (profits are inconsistent with perfect competition). In this paper, I show that claim (a) can be true even without spanning. In particular, (i) If all initial shareholders in a firm have correct and perfectly competitive conjectures, then net market value maximization will be unanimously favored by them as the objective of the firm, at least if there are no short sales of the firm's shares by initial shareholders (perfect competition, with or without spanning, implies unanimity). (ii) Claim (b) above is false; that is, perfect competition can exist without spanning. (iii) Claim (c) is false, whether or not there is spanning; that is, positive profits and perfect competition are perfectly consistent. Since the assumption of spanning is tantamount to the assumption of complete markets (for example, if there is free disposal plus spanning then markets are complete (D. M. Kreps, 1979), assertion (i) significantly extends the scope of the unanimity result. In particular, it extends the result to environments with incomplete markets in which firms market unique securities. Assertion (ii) shows such environments exist, and (iii) shows they can be nontrivial, that is, ones in which shareholders care about the firm's objective beyond whether or not the objective implies nonnegative profits. Assertions (i)-(iii) are easily demonstrated once it is realized that the old textbook maxim-for perfect competition there must be many buyers and sellers of a commodity (for example, a particular type of security)-is simply false. While many buyers and sellers may be sufficient for perfect competition, it is not necessary. Indeed, (iv) There may be only one seller of a commoditywithout any good substitutes -yet that seller will face a perfectly elastic demand if he is small relative to his market. The import of (iv) is that spanning is basically irrelevant for perfect competition;'