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Evolution in a General Equilibrium framework
Journal of Mathematical Economics ( IF 1.3 ) Pub Date : 2021-03-18 , DOI: 10.1016/j.jmateco.2021.102513
E. Accinelli , Humberto Muñiz

In this paper, we consider a general equilibrium model in which the economies are characterized by the distribution of firms on a set of branches of production; we will show that based on the decisions of the managers of the firms, it is possible to build a dynamic system whose solutions reproduce the possible trajectories of the economy. Once the initial state of an economy is known, that is, the initial distribution of firms, we will have a unique solution for this dynamic system, which will coincide with the evolution of the economy, that is, the evolution of prices and equilibrium allocations.

The investment decisions of the administrators of the companies will change the distribution over the set of existing productive branches, which in turn will produce changes in the wealth of consumers who are also shareholders of the companies and then as a consequence, their demand will change, and therefore the equilibrium allocations and prices will too.

In most cases, these decisions lead to an improvement in the efficiency of the productive side of the economy and an increase in the welfare of the economy as a whole, but, as we will show, under some particular circumstances, even when it comes to rational decisions from the point of view of administrators, this can lead to undesirable repercussions on the welfare of consumers. Besides, in a neighborhood of a critical economy, even when these decisions may involve small changes in the distribution of companies, they can cause abrupt and unexpected changes in the behavior of the economy, or in other words, they can cause an economic crisis. These are characterized by large changes in the prices, in the demand, and in the supply of goods. In contrast, in a sufficiently small neighborhood of a regular economy, small changes in the distribution of firms produced by the investment decisions of managers do not lead to large changes in the subsequent behavior of the economy. We will exemplify these statements with several numerical examples.



中文翻译:

一般均衡框架中的演化

在本文中,我们考虑一个一般均衡模型,其中经济的特征是企业在一组生产部门上的分布;我们将证明,基于公司经理的决策,有可能建立一个动态系统,其解决方案再现经济的可能轨迹。一旦知道一个经济体的初始状态,即企业的初始分布,我们就会得到这个动态系统的唯一解,它与经济体的演化,即价格和均衡分配的演化相吻合.

公司管理人员的投资决策将改变现有生产部门的分配,这反过来又会导致同时也是公司股东的消费者财富发生变化,因此,他们的需求将发生变化,因此均衡分配和价格也会如此。

在大多数情况下,这些决定会导致经济生产方面效率的提高和整个经济福利的增加,但是,正如我们将要展示的,在某些特定情况下,即使涉及到从管理者的角度来看理性决策,这可能会对消费者的福利产生不良影响。此外,在关键经济体附近,即使这些决策可能涉及公司分布的微小变化,它们也可能导致经济行为发生突然和意外的变化,或者换句话说,它们可能导致经济危机。它们的特点是价格、需求和商品供应的巨大变化。相比之下,在一个足够小的正规经济区,由管理者的投资决策引起的公司分布的微小变化不会导致经济随后行为的巨大变化。我们将用几个数值例子来说明这些陈述。

更新日期:2021-03-18
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