On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash
On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash
复制标题
关于具有外部性的平稳生产经济的规律性：纳什的竞争均衡
作者：
E. L. del Mercato;Vincenzo Platino
我们考虑了具有消费和生产外部性的私有制经济的一般均衡模型。所有主体（家庭和企业）的选择都可能影响效用函数和生产技术。竞争均衡的分配是纳什均衡。我们提供了一个例子，表明在标准假设下，在一个开放的家庭禀赋集合中，竞争均衡是不确定的。接下来，我们考虑这个模型的一个新版本，在Geanakoplos等人的精神下，考虑企业的禀赋（J Math economics 19:13 13 - 151, 1990）。在我们的模型中，企业的禀赋影响其他企业的技术。然后，我们证明，一般在家庭和企业的禀赋空间中，每个经济体都有有限数量的竞争均衡，并且每个竞争均衡都是基本参数的局部可微映射。
We consider a general equilibrium model of a private ownership economy with consumption and production externalities. The choices of all agents (households and firms) may affect utility functions and production technologies. The allocation of a competitive equilibrium is a Nash equilibrium. We provide an example showing that, under standard assumptions, competitive equilibria are indeterminate in an open set of the household’s endowments. Next, we consider a new version of this model, with firms’ endowments in the spirit of Geanakoplos et al. (J Math Econ 19:113–151, 1990). In our model, firms’ endowments impact the technologies of the other firms. We then prove that, generically in the space of endowments of households and firms, each economy has a finite number of competitive equilibria and each competitive equilibrium is locally a differentiable map of the fundamental parameters.