Cristiana Mammana | PubMed Health

PubMed2004

Backward and forward-looking expectations in a chaotic cobweb model.

In this study we research the dynamics shown by a cobweb-type model with linear demand, non-invertible supply function and with forward-looking expectations associated to backward looking ones. The study of the dynamics exhibited by our model will show how the presence of forward-looking expectations represents a stabilising factor: As the weight attributed to the above mentioned foreseeing form increases, the system becomes less and less complex until it only generates orbits converging either to the fixed point or to a cycle-2. It is particularly interesting to analyse at the same time the role played by the two forms of expectations considered, both of which contribute to market stabilization.

Journal Article↗

PubMed2003

Infinite memory expectations in a dynamic model with hyperbolic demand.

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 rho 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 ('rho) 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.

Humans↗