A Stochastic Cobweb Dynamical Model
We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability 𝑞_,__0_𝑞_1,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/219653 |
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| _version_ | 1849307998086758400 |
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| author | Serena Brianzoni Cristiana Mammana Elisabetta Michetti Francesco Zirilli |
| author_facet | Serena Brianzoni Cristiana Mammana Elisabetta Michetti Francesco Zirilli |
| author_sort | Serena Brianzoni |
| collection | DOAJ |
| description | We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model,
forward-looking expectations and backward-looking ones are assumed, in fact
we assume that the representative agent chooses the backward predictor with probability
𝑞_,__0_𝑞_1, and the forward predictor with probability (1−𝑞), so that the expected price at time 𝑡 is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory. |
| format | Article |
| id | doaj-art-1fc34d2dfa3046da8b957192c6a1f4b8 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1fc34d2dfa3046da8b957192c6a1f4b82025-08-20T03:54:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/219653219653A Stochastic Cobweb Dynamical ModelSerena Brianzoni0Cristiana Mammana1Elisabetta Michetti2Francesco Zirilli3Dipartimento di Istituzioni Economiche e Finanziarie, Università Degli Studi di Macerata, 62100 Mecerata, ItalyDipartimento di Istituzioni Economiche e Finanziarie, Università Degli Studi di Macerata, 62100 Mecerata, ItalyDipartimento di Istituzioni Economiche e Finanziarie, Università Degli Studi di Macerata, 62100 Mecerata, ItalyDipartimento di Matematica G. Castelnuovo, Università di Roma “La Sapienza”, 00185 Roma, ItalyWe consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability 𝑞_,__0_𝑞_1, and the forward predictor with probability (1−𝑞), so that the expected price at time 𝑡 is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.http://dx.doi.org/10.1155/2008/219653 |
| spellingShingle | Serena Brianzoni Cristiana Mammana Elisabetta Michetti Francesco Zirilli A Stochastic Cobweb Dynamical Model Discrete Dynamics in Nature and Society |
| title | A Stochastic Cobweb Dynamical Model |
| title_full | A Stochastic Cobweb Dynamical Model |
| title_fullStr | A Stochastic Cobweb Dynamical Model |
| title_full_unstemmed | A Stochastic Cobweb Dynamical Model |
| title_short | A Stochastic Cobweb Dynamical Model |
| title_sort | stochastic cobweb dynamical model |
| url | http://dx.doi.org/10.1155/2008/219653 |
| work_keys_str_mv | AT serenabrianzoni astochasticcobwebdynamicalmodel AT cristianamammana astochasticcobwebdynamicalmodel AT elisabettamichetti astochasticcobwebdynamicalmodel AT francescozirilli astochasticcobwebdynamicalmodel AT serenabrianzoni stochasticcobwebdynamicalmodel AT cristianamammana stochasticcobwebdynamicalmodel AT elisabettamichetti stochasticcobwebdynamicalmodel AT francescozirilli stochasticcobwebdynamicalmodel |