Chapter

Optimization, Dynamics, and Economic Analysis

pp 86-100

The Dynamics of the Cobweb When Producers are Risk Averse Learners

  • Carl ChiarellaAffiliated withSchool of Finance and Economics, University of Technology
  • , Xue-Zhong HeAffiliated withSchool of Finance and Economics, University of Technology

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Abstract

In this paper we investigate the dynamics of the traditional cobweb model where producers 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.