تعادل بازار سرمایه با مخاطرات اخلاقی و فناوری های انعطاف پذیر

(Magill, M., Quinzii, M., 2002. Capital market equilibrium with moral hazard. Journal of Mathematical Economics 38, 149–190) showed that, in a stockmarket economy with private information, the moral hazard problem may be resolved provided that a spanning overlap condition is satisfed. This result depends on the assumption that the technology is given by a stochastic production function with a single scalar input. The object of the present paper is to extend the analysis of Magill and Quinzii to the case of multiple inputs. We show that their main result extends to this general case if and only if, for each firm, the number of linearly independent combinations of securities having payoffs correlated with, but not dependent on, the firms output is equal to the number of degrees of freedom in the firm’s production technology.

Magill and Quinzii (2002) showed that, in a stockmarket economy with private information, any state-contingent equilibrium may be generated as a financial market equilibrium provided that a spanning overlap condition is satisfed. Thus, with an appropriate specification of the security structure, the market can avoid the conflict between risk sharing and incentives that is typical of the moral hazard problem. One notable feature of the analysis of Magill and Quinzii relates to the production technology, which is assumed to be characterized by a stochastic production function, with a single scalar input. As observed by Holmstrom and Milgrom (1987), in a standard principal–agent problem, the greater the flexibility available to the agent, the more difficult the problem faced by the principal. For a highly flexible technology, Holmstrom and Milgrom show that the principal can do no better than to offer a payment schedule that is an affine function of output. The object of the present paper is to extend the analysis of Magill and Quinzii to the case of a stochastic production function with multiple inputs. We show that their main result extends to this general case if and only if, for each firm, the number of linearly independent combinations of securities having payoffs correlated with, but not dependent on, the firm’s output is equal to the number of degrees of freedom in the firm’s production technology. The scalar-input stochastic production function technology examined by Magill and Quinzii is the case where the firm has a single degree of freedom. In the other polar case, where the firm has enough independent inputs to span the state space, the first-best can be achieved if and only if the state space is also spanned by ‘outside’ securities, independent of the firm’s observed output.

When state-contingent output is a function of a single scalar input, Magill and Quinzii (2002) prove that the existence of a single outside security appropriately correlated with the output of the firm is sufficient to resolve the problem arising from the fact that holders of securities issued by the firm cannot monitor the effort input of the firm’s owner. In this paper, we have shown that, the more degrees of freedom the firm has available, the greater the number of linearly independent outside securities required to resolve the moral hazard problem. In most cases, it seems reasonable to suppose that the existence of outside securities will mitigate, but not eliminate, the moral hazard problem.