Infinite Memory Expectations in a Dynamic Model with Hyperbolic Demand
Infinite Memory Expectations in a Dynamic Model with Hyperbolic Demand
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具有双曲线需求的动态模型中的无限内存期望
DOI：
10.1023/a:1020405907640
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
E. Michetti
中科院分区：
文献类型：
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作者：
C. Mammana;E. Michetti
在这项研究中，我们将研究一个具有双曲线需求，S形供给和向后看的期望创造机制的蛛网型模型所表现出的动态，其中系统的新状态是从所有以前的状态中获得的，这些状态是通过ρ区域中指数递减权重的加权算术平均值来观察的。本文提出的研究旨在确认由于无限记忆的存在而存在稳定效应，因为在所有其他条件开始相同的情况下，存在一个记忆率>，在该记忆率下市场均衡是一个水槽。因此，一个不稳定的系统在具有无限历史记忆的足够抵抗性预期的存在下会变得稳定，尽管这种向稳定的转变伴随着混乱的开始。因此，所产生的效果是“定性不稳定”之一，这是指所产生的定性动态性能，与“定量稳定”相关联，也就是说，参考相关动态发生的不变集的宽度减小。
In this study we will research the dynamics shown by a cobweb-type model with hyperbolic demand, sigmoidal supply and with backward-looking mechanism of expectation creation, whereby the new state of the system is obtained from all the previous states observed by weighted arithmetical mean with exponentially decreasing weights in the ρ region. The study herewith presented aims at confirming the existence of a stabilising effect due to the presence of infinite memory since, with all the other conditions begin the same, a memory rate> exists at which market equilibrium is a sink. An unstable system, therefore, becomes stable in the presence of sufficiently resistant expectations with infinite historical memory, although this transition to stability is accompanied by the onset of chaos. The resulting effect, therefore is one of “qualitative destabilisation,” that is with reference to the qualitative dynamic performance produced, associated to a “quantitative stabilisation,” that is to say with reference to the decreasing width of the invariant sets within which relevant dynamics occur.