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Learning in a double-phase cobweb model

Author

Listed:
  • Fausto Cavalli

    (University of Milano-Bicocca)

  • Ahmad Naimzada

    (University of Milano-Bicocca)

  • Lucia Parisio

    (University of Milano-Bicocca)

Abstract

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.

Suggested Citation

  • Fausto Cavalli & Ahmad Naimzada & Lucia Parisio, 2021. "Learning in a double-phase cobweb model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 579-611, December.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:2:d:10.1007_s10203-021-00335-w
    DOI: 10.1007/s10203-021-00335-w
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    References listed on IDEAS

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    1. Parisio, Lucia & Bosco, Bruno, 2008. "Electricity prices and cross-border trade: Volume and strategy effects," Energy Economics, Elsevier, vol. 30(4), pages 1760-1775, July.
    2. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
    3. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    4. Hommes,Cars, 2015. "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems," Cambridge Books, Cambridge University Press, number 9781107564978.
    5. Gian-Italo Bischi & Michael Kopel & Ferenc Szidarovszky, 2005. "Expectation-Stock Dynamics in Multi-Agent Fisheries," Annals of Operations Research, Springer, vol. 137(1), pages 299-329, July.
    6. Ahmad Naimzada & Gian Italo Bischi, 2007. "Mann Iterations with Power Means," Working Papers 106, University of Milano-Bicocca, Department of Economics, revised 2007.
    7. Karakatsani, Nektaria V. & Bunn, Derek W., 2008. "Forecasting electricity prices: The impact of fundamentals and time-varying coefficients," International Journal of Forecasting, Elsevier, vol. 24(4), pages 764-785.
    8. Marc Nerlove, 1958. "Adaptive Expectations and Cobweb Phenomena," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 72(2), pages 227-240.
    9. J. A. Carlson, 1968. "An Invariably Stable Cobweb Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(3), pages 360-362.
    10. R. Manning, 1971. "A Generalization of a Cobweb Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 123-125.
    11. 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.
    12. Elke Moser & Dieter Grass & Gernot Tragler, 2016. "A non-autonomous optimal control model of renewable energy production under the aspect of fluctuating supply and learning by doing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 545-575, July.
    13. Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
    14. Karakatsani Nektaria V & Bunn Derek W., 2010. "Fundamental and Behavioural Drivers of Electricity Price Volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-42, September.
    15. Mordecai Ezekiel, 1938. "The Cobweb Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 52(2), pages 255-280.
    16. Jason H. Grant & Dayton M. Lambert & Kenneth A. Foster, 2010. "A Seasonal Inverse Almost Ideal Demand System for North American Fresh Tomatoes," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 58(2), pages 215-234, June.
    17. Bruno Bosco & Lucia Parisio & Matteo Pelagatti & Fabio Baldi, 2010. "Long-run relations in european electricity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(5), pages 805-832.
    18. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    19. Clark, Colin W. & Munro, Gordon R., 1975. "The economics of fishing and modern capital theory: A simplified approach," Journal of Environmental Economics and Management, Elsevier, vol. 2(2), pages 92-106, December.
    20. Ferenc Szidarovszky & Gian Italo Bischi (ed.), 2020. "Games and Dynamics in Economics," Springer Books, Springer, number 978-981-15-3623-6, November.
    21. Karakatsani, Nektaria V. & Bunn, Derek W., 2008. "Intra-day and regime-switching dynamics in electricity price formation," Energy Economics, Elsevier, vol. 30(4), pages 1776-1797, July.
    22. Gonca P. Soysal & Lakshman Krishnamurthi, 2012. "Demand Dynamics in the Seasonal Goods Industry: An Empirical Analysis," Marketing Science, INFORMS, vol. 31(2), pages 293-316, March.
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    Cited by:

    1. Dieci, Roberto & Mignot, Sarah & Westerhoff, Frank, 2022. "Production delays, technology choice and cyclical cobweb dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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    More about this item

    Keywords

    Double-phase market; Expectations; Cobweb model; Time-dependent demand/supply functions; Stability; Complex dynamics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices
    • Q02 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Commodity Market

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