Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 2, Pages 135-146
Ergodic cobweb chaos
Department of Economics, Niigata University, 8050 2-No-Cho Ikarashi, Niigata 950-21, Japan
Received 9 October 1996
Copyright © 1997 Akio Matsumoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output
constraints and the dynamics of the modified model. Due to the upper and lower bounds,
a transitional function takes on a tilted -profile having three piecewise segments with
two turning points. It prevents the price (or quantity) dynamics from explosive
oscillations. This study demonstrates, by presenting numerical examples, that the
modified cobweb model can generate various dynamics ranging from stable periodic
cycles to ergodic chaos if a product of the marginal propensity to consume and the
marginal product is greater than unity.