Essay about Cobweb

A COBWEB MODEL WITH RANDOM ANTICIPATIONS

Serena Brianzoni, UniversitГ degli studi dalam Macerata

Cristiana Mammana, UniversitГ degli studi di Macerata

Elisabetta Michetti, UniversitГ degli studi dalam Macerata

Francesco Zirilli, Università di Roma ‘La Sapienza'

EXTENDED ABSTRACT

1 . Launch

The cobweb model is known as a dynamical system that identifies price fluctuations as a result of the interaction among demand function depending on current price and provide function based on expected value.

A classic meaning of the cobweb model is definitely the one provided by Ezekiel (1938) who proposed a thready model with deterministic stationary expectation. The smallest amount of convincing aspects of the initial formulation is the linearity of the functions describing the market and its simple expectations. Therefore several work have been produced over time to enhance the original model. In a number of functions non-linearities have already been introduced inside the cobweb style (see Holmes and Manning (1988)) whilst other creators considered different varieties of price objectives (see, amongst others, Nerlove (1958), Chiarella (1988), Hommes (1994), Gallas and Nusse (1996)). More recently in Mammana and Michetti (2003, 2004) an infinite storage learning system has been released in the non-linear cobweb style. In this job we look at a stochastic non-linear cobweb style that generalizes the type of Jensen and Urban (1984) assuming that the representative businessperson chooses among two several predictors in order to formulate his expectations: •

backward predictor: the expectation of foreseeable future price is the arithmetical imply of previous observations with decreasing dumbbells, according to a geometrical progress of ρ region; one particular •

forward predictor: the organization mechanism of this expectation considers the market equilibrium price whilst considering that the present price will converge to it just in the long run.

The representative business owner chooses the backward predictor with possibility q ( 0 < q...

Sources: [1] Ahmad, N., Bischi, G. I., Gardini, L., 1996. Unlimited distributed memory in under the radar

dynamical systems

[2] Aicardi, F., Invernizzi, S., 1992. Memory effects in discrete dynamical systems.

[3] Department, W., McGough, B., 2005. Misspecification and consistent objectives in

stochastic non-linear financial systems

[4] Brock, W. A., Hommes, C. H., 97. A logical route to randomness. Econometrica sixty-five,

1059-1160.

[5] Chiarella, C., 1988. The cobweb style: its lack of stability and the start chaos. Monetary

Modelling 5, 377-384.

[6] Evans, G. V., Honkapohja, S., 98. Stochastic lean learning in the cobweb style.

[7] Ezekiel, M., 38. The cobweb theorem. Quarterly Journal of Economics 52, 255-280.

[8] Gallas, L. A. C., Nusse, They would. E., 1996. Periodicity vs chaos in the dynamics from the

cobweb versions

[9] Holmes, J. M., Manning, Ur., 1988. Memory and market stability: the case of the cobweb.

[10] Hommes, C. H., 1994. Mechanics of the cobweb model with adaptive objectives and

nonlinear supply and demand

[11] Jensen, Ur. V., City, R., 1984. Chaotic price behaviour in a nonlinear cobweb model.

[12] Mammana, C., Michetti, At the., 2003. Unlimited memory targets in a energetic model

with hyperbolic require

[13] Mammana, C., Michetti, E., 2005. Backward and forward-looking objectives in a

chaotic cobweb unit

[14] Mann, W. R., 1953. Suggest value methods in iterations. Proceedings of the American

Mathematical Society 5, 506-510.

[15] Michetti, Elizabeth., 2000. Damage and learning effects in cobweb models. Rivista dalam politica

economica 12, 167-206.

[16] Sraffa, P., 1986. Le leggi della produttivitГ in program di concorrenza. In L. Sraffa (ed. ),

Saggi (pp



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