The Dynamics of the Cobweb when Producers are Risk Averse Learners
In this paper we investigate the dynamics of the traditional cobweb model where producres are risk averse and seek to learn the distribution of asset prices. We consider the subjective estimates of the statistical distribution of the market prices based on L-step backward time series of market clearing prices. With constant absolute risk aversion, the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of the nonlinear model are derived and, consequently, we show that the local stability region is proportional to the lag length L. When the equilibrium loses its local stability, we show that, for L = 2, the model has a strong 1:3 resonance bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. For general lag lengths, numerical simulations suggest that the model displays a variety of complex dynamics.
|Date of creation:||01 Sep 1999|
|Date of revision:|
|Publication status:||Published as: Chiarella, C. and He, X., 2000, "The Dynamics of the Cobweb When Producers are Risk Averse Learners", In Engelbert J. Dockner, Richard F. Hartl, Mikulas Luptacik and Gerhard Sorger (eds) Optimization, Dynamics, and Economic Analysis: Essays in Honor of Gustav Feichtinger, 86-100.|
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- Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
- Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
- Boussard, Jean-Marc, 1996. "When risk generates chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 29(3), pages 433-446, May.
- Jensen, Roderick V. & Urban, Robin, 1984. "Chaotic price behavior in a non-linear cobweb model," Economics Letters, Elsevier, vol. 15(3-4), pages 235-240.
- 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.
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