Memory, market stability and the nonlinear cobweb theorem

Gaffney, Janice; Pearce, Charles E. M.

doi:10.1017/s1446181100013559

Cited by 5 publications

(8 citation statements)

References 12 publications

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“…given some π 0 and π −1 . Other examples of cobweb models based on nonautonomous equations can be found in [13,18,14,10,15,16]. I notice that, contrary to the previous literature, the non-autonomous nature of the present model is intrinsically connected with the cyclicity of demand/supply functions characterizing the market itself.…”

Section: Modelmentioning

confidence: 76%

“…For example, it is well known that if memory is taken into account in a learning process, as in [10,11,12], then the resulting difference equation is non-autonomous. Some examples of cobweb models with memory in the learning process are [13,14,15,16]. However, in these works the non-autonomous nature of the resulting equation is due to a modification of the expectation formation mechanism.…”

Section: Introductionmentioning

confidence: 99%

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A Cobweb Model with Alternating Demand and Supply Functions

Cavalli

2016

SSRN Journal

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In this work I present a cobweb model for markets characterized by two couples of demand and supply functions which cyclically alternate with period two, in a succession of peak and off-peak market phases. Starting from classical adaptive expectations, a new expectation formation mechanism is presented, to take into account such markets' peculiarity. In particular, to adapt the previous in-phase expected price, agents use both in-phase and out-of-phase expectation errors, suitably weighted through a phase weight. It is shown that the resulting model is described by a nonautonomous difference equation. The local asymptotic stability of the steady state equilibrium is studied, showing that it depends on the expectation weight, the phase weight and on both the relative slopes, at the equilibrium, of the supply functions with respect to the demand functions. Several crucial differences with respect to the classical cobweb model are highlighted, showing the potentially ambiguous role of expectation weight and of relative slopes. It is shown that destabilization can occur both through a flip and a Neimark-Sacker bifurcation, which can occur for the same market conditions and different expectation weights.

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Section: Modelmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

A Cobweb Model with Alternating Demand and Supply Functions

Cavalli

2016

SSRN Journal

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“…The cobweb theorem [3,10] describes price equilibrium where production decisions are taken ex-post, once the current market price is available. This theorem can also be applied to the real estate market.…”

Section: The Model In Real Estate Marketmentioning

confidence: 99%

“…According to the nonlinear cobweb theory [3,10], the price is determined by prior period price and the relation between demands and supply. The formulation can be described as…”

Section: The Model In Real Estate Marketmentioning

confidence: 99%

Analysis of a Game Model with Nonlinear Demand Functions for Real Estate Market

Ma¹,

Mu²

2010

International Journal of Nonlinear Sciences and Numerical Simulation

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In this paper, the nonlinear demand function method was implemented to analyze the complexity of a game model. This work performed a local stability analysis and found out that the stability of Nash equilibrium is lost through period-doubling bifurcation with some parameters varying.Numerical simulations were used to illustrate bifurcation diagrams, maximal Lyapunov exponents and sensitive dependence on initial conditions. Feedback control method was leverage to stabilize the chaotic behavior of the model. (J.H. Ma) establish a model for the real estate market and study the model numerically.

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“…Agricultural markets are the typical competitive market example provided in microeconomics courses, and energy markets have been liberalized in the last twenty years.4 For an introduction and survey on cobweb models we refer toHommes (2013). A first attempt to describe seasonal markets through a cobweb model is proposed in, while the effect of demand seasonality in a monopolistic market model is studied inCavalli and Naimzada (2018).5 It is well known that if agents takes into account in their expectation formation mechanism several previously realized prices, then the resulting difference equation is non-autonomousBischi et al 2015), and this has been already applied to cobweb models(Carlson 1968;Manning 1971;Bischi and Naimzada 1997;Gaffney and Pearce 2004), too. However, in such literature the non-autonomous nature of the resulting equation is due to a refinement of the expectation formation mechanism, while the economic framework under consideration is left unchanged.…”

mentioning

confidence: 99%

Learning in a double-phase cobweb model

Cavalli

Naimzada

Parisio

2021

Decisions Econ Finan

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In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables.

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Memory, market stability and the nonlinear cobweb theorem

Cited by 5 publications

References 12 publications

A Cobweb Model with Alternating Demand and Supply Functions

A Cobweb Model with Alternating Demand and Supply Functions

Analysis of a Game Model with Nonlinear Demand Functions for Real Estate Market

Learning in a double-phase cobweb model

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