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A cobweb model with alternating demand and supply functions

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  • Fausto, Cavalli

Abstract

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 non-autonomous 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.

Suggested Citation

  • Fausto, Cavalli, 2016. "A cobweb model with alternating demand and supply functions," Working Papers 325, University of Milano-Bicocca, Department of Economics, revised 07 Feb 2016.
  • Handle: RePEc:mib:wpaper:325
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    References listed on IDEAS

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    1. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
    2. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    3. Marc Nerlove, 1958. "Adaptive Expectations and Cobweb Phenomena," The Quarterly Journal of Economics, Oxford University Press, vol. 72(2), pages 227-240.
    4. Nicholas Kaldor, 1934. "A Classificatory Note on the Determinateness of Equilibrium," Review of Economic Studies, Oxford University Press, vol. 1(2), pages 122-136.
    5. Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
    6. Lundberg, Liv & Jonson, Emma & Lindgren, Kristian & Bryngelsson, David & Verendel, Vilhelm, 2015. "A cobweb model of land-use competition between food and bioenergy crops," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 1-14.
    7. Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
    8. Hommes,Cars, 2015. "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems," Cambridge Books, Cambridge University Press, number 9781107564978, March.
    9. J. A. Carlson, 1968. "An Invariably Stable Cobweb Model," Review of Economic Studies, Oxford University Press, vol. 35(3), pages 360-362.
    10. Mordecai Ezekiel, 1938. "The Cobweb Theorem," The Quarterly Journal of Economics, Oxford University Press, vol. 52(2), pages 255-280.
    11. R. Manning, 1971. "A Generalization of a Cobweb Theorem," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 123-125.
    12. 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.
    13. Ahmad Naimzada & Gian Italo Bischi, 2007. "Mann Iterations with Power Means," Working Papers 106, University of Milano-Bicocca, Department of Economics, revised 2007.
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    More about this item

    Keywords

    Cobweb model; cyclic demand and supply; non-autonomous equations; complex dynamics;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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