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Stability Analysis Of Some Dynamical Models For Prices With Distributed Delays

Author

Listed:
  • Nicoleta SÎRGHI

    (Department of Economics and Modelling, West University of Timişoara)

  • Gabriela MIRCEA

    (Department of Business Information System, West University of Timişoara)

  • Mihaela NEAMŢU

    (Department of Economics and Modelling, West University of Timişoara)

  • Laura Mariana CISMAŞ

    (Department of Economics and Modelling, West University of Timişoara)

  • Camelia HAŢEGAN

    (Department of Accounting, West University of Timişoara)

Abstract

In the present paper, we study two nonlinear systems which describe the price dynamics of a single commodity market. The market price is expressed with the demand and supply functions for the commodity. The distributed time delay is introduced in the demand and supply prices. It is assumed that the consumer and producer behavior depends on the weighted function of the past prices. The demand can take into account the recent price and the past demand price. The producer can consider the past supply price. Thus, we obtain two nonlinear mathematical models for the price dynamics. In some conditions, there is only one positive equilibrium point. The stability of the equilibrium point and the existence of periodic solutions are investigated. We find the conditions so that the equilibrium point is locally asymptotically stable. The numerical simulations illustrate the effectiveness of our results and some conclusions and future research are provided.

Suggested Citation

  • Nicoleta SÎRGHI & Gabriela MIRCEA & Mihaela NEAMŢU & Laura Mariana CISMAŞ & Camelia HAŢEGAN, 2016. "Stability Analysis Of Some Dynamical Models For Prices With Distributed Delays," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(3), pages 135-152.
    • Handle: RePEc:cys:ecocyb:v:50:y:2016:i:3:p:135-152
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    References listed on IDEAS

    as
    1. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
    2. Gabriela MIRCEA & Mihaela NEAMŢU & Laura Mariana CISMAŞ, 2015. "Dynamical Models for Prices with Distributed Delays," Timisoara Journal of Economics and Business, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 8(1), pages 91-102, June.
    3. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
    4. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    price dynamics; delay economic models; equilibrium point; local stability; distributed time delay;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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